**Previous months:**

2010 - 1003(10) - 1004(7) - 1005(4) - 1006(1) - 1007(2) - 1008(4) - 1010(1) - 1011(1)

2011 - 1105(2) - 1107(1) - 1111(1) - 1112(1)

2012 - 1203(1) - 1204(2) - 1205(1) - 1208(1) - 1210(1) - 1211(6) - 1212(1)

2013 - 1301(2) - 1304(3) - 1306(2) - 1307(1) - 1310(2)

2014 - 1402(1) - 1403(3) - 1404(2) - 1405(2) - 1409(4) - 1410(4) - 1411(13) - 1412(4)

2015 - 1503(1) - 1505(2) - 1506(2) - 1507(3) - 1508(3) - 1509(1) - 1511(3) - 1512(6)

2016 - 1601(6) - 1602(3) - 1603(4) - 1604(2) - 1605(1) - 1607(5) - 1608(1)

Any replacements are listed further down

[135] **viXra:1608.0152 [pdf]**
*submitted on 2016-08-15 04:41:51*

**Authors:** Tahsin Olgu Benli, Hatice Sengul

**Comments:** 10 Pages.

It is very vital for suppliers and distributors to predict the deregulated electricity prices for creating their bidding strategies in the competitive market area. Pre requirement of succeeding in this field, accurate and suitable electricity tariff price forecasting tools are needed. In the presence of effective forecasting tools, taking the decisions of production, merchandising, maintenance and investment with the aim of maximizing the profits and benefits can be successively and effectively done. According to the electricity demand, there are four various electricity tariffs pricing in Turkey; monochromic, day, peak and night. The objective is find the best suitable tool for predicting the four pricing periods of electricity and produce short term forecasts (one year ahead-monthly). Our approach based on finding the best model, which ensures the smallest forecasting error measurements of; MAPE, MAD and MSD. We conduct a comparison of various forecasting approaches in total accounts for nine teen, at least all of those have different aspects of methodology. Our beginning step was doing forecasts for the year 2015. We validated and analyzed the performance of our best model and made comparisons to see how well the historical values of 2015 and forecasted data for that specific period matched. Results show that given the time-series data, the recommended models provided good forecasts. Second part of practice, we also include the year 2015, and compute all the models with the time series of January 2011 – December 2015. Again by choosing the best appropriate forecasting model, we conducted the forecast process and also analyze the impact of enhancing of time series periods (January, 2007 to December, 2015) to model that we used for forecasting process.

**Category:** Statistics

[134] **viXra:1607.0526 [pdf]**
*submitted on 2016-07-27 14:23:22*

**Authors:** Sergio Arciniegas-Alarcón, Marisol García-Peña, Wojtek Krzanowski

**Comments:** 9 Pages.

We propose a new methodology for multiple imputation when faced with missing data in multi-environmental trials with genotype-by-environment interaction, based on the imputation system developed by Krzanowski that uses the singular value decomposition (SVD) of a matrix. Several different iterative variants are described; differential weights can also be included in each variant to represent the influence of different components of SVD in the imputation process. The methods are compared through a simulation study based on three
real data matrices that have values deleted randomly at different percentages, using as measure of overall accuracy a combination of the variance between imputations and their mean square deviations relative to the deleted values. The best results are shown by two of the iterative schemes that use weights belonging to the interval [0.75, 1]. These schemes provide imputations that have higher quality when compared with other multiple imputation methods based on the Krzanowski method.

**Category:** Statistics

[133] **viXra:1607.0497 [pdf]**
*submitted on 2016-07-26 16:13:09*

**Authors:** Glenn Healey

**Comments:** 7 Pages.

Given information about batted balls for a set of players, we review techniques for estimating the reliability of a statistic as a function of the sample size. We also review methods for using the estimated reliability to compute the variance of true talent and to generate forecasts.

**Category:** Statistics

[132] **viXra:1607.0471 [pdf]**
*submitted on 2016-07-25 06:41:23*

**Authors:** Baokun Li, Gang Xiang, Vladik Kreinovich, Panagios Moscopoulos

**Comments:** 12 Pages.

One of the main objectives of statistics is to estimate the parameters of a probability distribution based on a sample taken from this distribution.

**Category:** Statistics

[131] **viXra:1607.0393 [pdf]**
*submitted on 2016-07-21 14:54:41*

**Authors:** Marisol García-Peña, Sergio Arciniegas-Alarcón, Kaye Basford, Carlos Tadeu dos Santos Dias

**Comments:** 13 Pages.

In multi-environment trials it is common to measure several response variables or attributes to determine the genotypes with the best characteristics. Thus it is important to have techniques to analyse multivariate multi-environment trial data. The main objective is to complement the literature on two multivariate techniques, the mixture maximum likelihood method of clustering and three-mode principal component analysis, used to analyse genotypes, environments and attributes simultaneously. In this way, both global and detailed statements about the performance of the genotypes can be made, highlighting the benefit of using three-way data in a direct way and providing an alternative analysis for researchers. We illustrate using sunflower data with twenty genotypes, eight environments and three attributes. The procedures provide an analytical procedure which is relatively easy to apply and interpret in order to describe the patterns of performance and associations in multivariate multi-environment trials.

**Category:** Statistics

[130] **viXra:1607.0244 [pdf]**
*submitted on 2016-07-18 06:02:32*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

As in nature nothing is absolute, evidently there will not exist a precise border between the scientific language and “the literary” one (the language used in literature): thus there will be zones where these two languages intersect.

**Category:** Statistics

[129] **viXra:1605.0241 [pdf]**
*submitted on 2016-05-23 09:32:06*

**Authors:** Jianwen Huang

**Comments:** 11 Pages.

In this article, the high-order asymptotic
expansions of cumulative distribution function and probability
density function of extremes for generalized Maxwell distribution
are established under nonlinear normalization. As corollaries, the
convergence rates of the distribution and density of maximum are
obtained under nonlinear normalization.

**Category:** Statistics

[128] **viXra:1604.0302 [pdf]**
*submitted on 2016-04-22 01:25:58*

**Authors:** Bradly Alicea

**Comments:** 13 pages, 7 Figures, 2 Supplemental Figures. Full dataset can be found at doi:10.6084/m9.figshare.944542

What makes a good prediction good? Generally, the answer is thought to be a faithful accounting of both tangible and intangible factors. Among sports teams, it is thought that if you get enough of the tangible factors (e.g. roster, prior performance, schedule) correct, then the predictions will be correspondingly accurate. While there is a role for intangible factors, they are thought to gum up the works, so to speak. Here, I start with the hypothesis that the best and worst teams in a league or tournament are easy to predict relative to teams with average performance. Data from the 2013 MLB and NFL seasons plus data from the 2014 NCAA Tournament were used. Using a model-free approach, data representing various aspects of competition reveal that mainly the teams predicted to perform the worst actually conform to expectation. The reasons for this are then discussed, including the role of shot noise on performance driven by tangible factors.

**Category:** Statistics

[127] **viXra:1604.0009 [pdf]**
*submitted on 2016-04-01 12:11:19*

**Authors:** Ioannis Koukoutsidis

**Comments:** 28 pages, 8 figures

Mobile crowdsensing can facilitate environmental surveys by leveraging sensor equipped mobile devices that carry out measurements covering a wide area in a short time, without bearing the costs of traditional field work. In this paper, we
examine statistical methods to perform an accurate estimate of the mean value of an environmental parameter in a region, based on such measurements. The main focus is on estimates produced by taking a "snapshot" of the mobile device readings at a random instant in time. We compare stratified sampling with different stratification weights to sampling without stratification, as well as an appropriately modified version of systematic sampling. Our main result is that stratification with weights proportional to stratum areas can produce significantly smaller bias, and gets arbitrarily close to the true area average as the number of mobiles and the number of strata increase. The performance of the methods is evaluated for an application scenario where we estimate the mean area temperature in a linear region that exhibits the so-called *Urban Heat Island* effect, with mobile users moving in the region according to the Random Waypoint Model.

**Category:** Statistics

[126] **viXra:1603.0252 [pdf]**
*submitted on 2016-03-17 17:00:15*

**Authors:** Glenn Healey

**Comments:** 4 Pages.

This file contains an intrinsic contact list for batters.

**Category:** Statistics

[125] **viXra:1603.0251 [pdf]**
*submitted on 2016-03-17 17:02:40*

**Authors:** Glenn Healey

**Comments:** 3 Pages.

This file contains an intrinsic contact list for pitchers.

**Category:** Statistics

[124] **viXra:1603.0215 [pdf]**
*submitted on 2016-03-14 21:01:06*

**Authors:** Glenn Healey

**Comments:** 7 Pages.

Given a set of observed batted balls and their outcomes, we develop a method for learning
the dependence of a batted ball’s intrinsic value on its measured parameters.

**Category:** Statistics

[123] **viXra:1603.0180 [pdf]**
*submitted on 2016-03-11 17:50:17*

**Authors:** L. Martino, J. Plata, F. Louzada

**Comments:** 5 Pages.

In this work, we design an efficient Monte Carlo
scheme for diffusion estimation, where global and local parameters are involved in a unique inference problem. This
scenario often appears in distributed inference problems in
wireless sensor networks. The proposed scheme uses parallel local MCMC chains and then an importance sampling (IS) fusion for obtaining an efficient estimation of the global parameters. The resulting algorithm is simple and flexible. It can be easily applied iteratively, or extended in a sequential framework. In order to apply the novel scheme, the only assumption required about the model is that the measurements are conditionally independent given the related parameters.

**Category:** Statistics

[122] **viXra:1602.0333 [pdf]**
*submitted on 2016-02-25 18:17:42*

**Authors:** L. Martino, V. Elvira, F. Louzada

**Comments:** 5 Pages.

The Sequential Importance Resampling (SIR) method is the core of the Sequential Monte Carlo (SMC) algorithms (a.k.a., particle filters). In this work, we point out a suitable choice for weighting properly a resampled particle. This observation entails several theoretical and practical consequences, allowing also the design of novel sampling schemes. Specifically, we describe one theoretical result about the sequential estimation of the marginal likelihood. Moreover, we suggest a novel resampling procedure for SMC algorithms called partial resampling, involving only a subset of the current cloud of particles. Clearly, this scheme attenuates the additional variance in the Monte Carlo estimators generated by the use of the resampling.

**Category:** Statistics

[121] **viXra:1602.0112 [pdf]**
*submitted on 2016-02-09 14:48:10*

**Authors:** L. Martino, V. Elvira, F. Louzada

**Comments:** 31 Pages.

The Effective Sample Size (ESS) is an important measure of efficiency of Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) techniques. In IS context, an approximation of the theoretical ESS definition is widely applied, $\widehat{ESS}$, involving the sum of the squares of the normalized importance weights. This formula $\widehat{ESS}$ has become an essential piece within Sequential Monte Carlo (SMC) methods using adaptive resampling procedures. The expression $\widehat{ESS}$ is related to the Euclidean distance between the probability mass described by the normalized weights and the discrete uniform probability mass function (pmf). In this work, we derive other possible ESS functions based on different discrepancy measures between these pmfs. Several examples are provided involving, for instance, the geometric and harmonic means of the weights, the discrete entropy (including the perplexity measure, already proposed in literature) and the Gini coefficient. We list five requirements which a generic ESS function should satisfy, allowing us to classify different ESS measures. We also compare the most promising ones by means of numerical simulations.

**Category:** Statistics

[120] **viXra:1602.0053 [pdf]**
*submitted on 2016-02-05 03:06:47*

**Authors:** Jason Lind

**Comments:** 2 Pages. Very early stages

Defines a rated set and uses it to calculated a weight directly from the statistics that enabled broad unified interpretation of data.

**Category:** Statistics

[119] **viXra:1601.0179 [pdf]**
*submitted on 2016-01-16 22:40:19*

**Authors:** D. Luengo, L. Martino, V. Elvira, M. Bugallo

**Comments:** 22 Pages.

Many signal processing applications require performing statistical inference on large datasets, where computational and/or memory restrictions become an issue. In this big data setting, computing an exact global centralized estimator is often unfeasible. Furthermore, even when approximate numerical solutions (e.g., based on Monte Carlo methods) working directly on the whole dataset can be computed, they may not provide a satisfactory performance either. Hence, several authors have recently started considering distributed inference approaches, where the data is divided among multiple workers (cores, machines or a combination of both). The computations are then performed in parallel and the resulting distributed or partial estimators are finally combined to approximate the intractable global estimator. In this paper, we focus on the scenario where no communication exists among the workers, deriving efficient linear fusion rules for the combination of the distributed estimators. Both a Bayesian perspective (based on the Bernstein-von Mises theorem and the asymptotic normality of the estimators) and a constrained optimization view are provided for the derivation of the linear fusion rules proposed. We concentrate on minimum mean squared error (MMSE) partial estimators, but the approach is more general and can be used to combine any kind of distributed estimators as long as they are unbiased. Numerical results show the good performance of the algorithms developed, both in simple problems where analytical expressions can be obtained for the distributed MMSE estimators, and in a wireless sensor network localization problem where Monte Carlo methods are used to approximate the partial estimators.

**Category:** Statistics

[118] **viXra:1601.0174 [pdf]**
*submitted on 2016-01-16 07:32:42*

**Authors:** V. Elvira, L. Martino, D. Luengo, M. F. Bugallo

**Comments:** 34 Pages.

Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal distribution and assign them weights according to the importance sampling principle. Critical issues in applying PMC methods are the choice of the generating functions for the samples and the avoidance of the sample degeneracy. In this paper, we propose three new schemes that considerably improve the performance of the original PMC formulation by allowing for better exploration of the space of unknowns and by selecting more adequately the surviving samples.
A theoretical analysis is performed, proving the superiority of the novel schemes in terms of variance of the associated estimators and preservation of the sample diversity.
Furthermore, we show that they outperform other state of the art algorithms (both in terms of mean square error and robustness w.r.t. initialization) through extensive numerical simulations.

**Category:** Statistics

[117] **viXra:1601.0167 [pdf]**
*submitted on 2016-01-16 03:40:15*

**Authors:** Ilija Barukčić

**Comments:** Pages.

Titans like Bertrand Russell or Karl Pearson warned us to keep our mathematical and statistical hands off causality and at the end David Hume too. Hume's scepticism has dominated discussion of causality in both analytic philosophy and statistical analysis for a long time. But more and more researchers are working hard on this field and trying to get rid of this positions. In so far, much of the recent philosophical or mathematical writing on causation (Ellery Eells (1991), Daniel Hausman (1998), Pearl (2000), Peter Spirtes, Clark Glymour and Richard Scheines (2000), ...) either addresses to Bayes networks, to the counterfactual approach to causality developed in detail by David Lewis, to Reichenbach's Principle of the Common Cause or to the Causal Markov Condition. None of this approaches to causation investigated the relationship between causation and the law of independence to a necessary extent. Nonetheless, the relationship between causation and the law of independence, one of the fundamental concepts in probability theory, is very important. May an effect occur in the absence of a cause? May an effect fail to occur in the presence of a cause? In so far, what does constitute the causal relation? On the other hand, if it is unclear what does constitute the causal relation, maybe we can answer the question, what does not constitute the causal relation. So far, a cause as such can not be independent from its effect and vice versa, if there is a deterministic causal relationship. This publication will prove, that the law of independence defines causation to some extent ex negativo.

**Category:** Statistics

[116] **viXra:1601.0070 [pdf]**
*submitted on 2016-01-07 16:41:10*

**Authors:** J.Tiago de Oliveira

**Comments:** 37 Pages.

Statistical Analysis of Extremes
chapter 3

**Category:** Statistics

[115] **viXra:1601.0069 [pdf]**
*submitted on 2016-01-07 16:42:58*

**Authors:** J.Tiago de Oliveira

**Comments:** 11 Pages.

Statistical Analysis of Extremes
chapter 4

**Category:** Statistics

[114] **viXra:1601.0032 [pdf]**
*submitted on 2016-01-05 10:37:48*

**Authors:** M. Srinivas, S. Sambasiva Rao

**Comments:** 7 Pages. This paper has been published in Indian Journal of Physical Education and Allied Sciences, ISSN: 2395-6895, Vol.1, No.5, pp.37-44.

The statistical analysis of angular data is typically encountered in biological and geological studies, among several other areas of research. Circular data is the simplest case of this category of data called directional data, where the single response is not scalar, but angular or directional. A statistical analysis pertaining to two dimensional directional data is generally referred to as “Circular Statistics”. In this paper, an attempt is made to review various fundamental concepts of circular statistics and to discuss its applicability in sports science.

**Category:** Statistics

[113] **viXra:1512.0448 [pdf]**
*submitted on 2015-12-26 16:50:32*

**Authors:** J.Tiago de Oliveira

**Comments:** 36 Pages.

Second chapter
Statistical Analysis of Extremes
Pendor, Lisbon, 1997

**Category:** Statistics

[112] **viXra:1512.0436 [pdf]**
*submitted on 2015-12-26 12:04:44*

**Authors:** J.Tiago de Oliveira

**Comments:** 9 Pages. First chapter

J. Tiago de Oliveira last book followed the research started by Emil Julius Gumbel

**Category:** Statistics

[111] **viXra:1512.0420 [pdf]**
*submitted on 2015-12-25 09:53:50*

**Authors:** L. Martino, J. Read, V. Elvira, F. Louzada

**Comments:** 21 Pages.

We design a sequential Monte Carlo scheme for the joint purpose of Bayesian inference and model selection, with application to urban mobility context where different modalities of movement can be employed. In this case, we have the joint problem of online tracking and detection of the current modality.
For this purpose, we use interacting parallel particle filters each one addressing a different model. They cooperate for providing a global estimator of the variable of interest and, at the same time, an approximation of the posterior density of the models given the data. The interaction occurs by a parsimonious distribution of the computational effort, adapting on-line the number of particles of each filter according to the posterior probability of the corresponding model. The resulting scheme is simple and provides good results in different numerical experiments with artificial and real data.

**Category:** Statistics

[110] **viXra:1512.0319 [pdf]**
*submitted on 2015-12-14 09:37:41*

**Authors:** H. Jabbari1, M. Erfaniyan

**Comments:** 10 Pages.

Let fXn; n 1g be a strictly stationary sequence of negatively associated random
variables, with common continuous and bounded distribution function F. We consider
the estimation of the two-dimensional distribution function of (X1;Xk+1) based on kernel
type estimators as well as the estimation of the covariance function of the limit empirical
process induced by the sequence fXn; n 1g where k 2 IN0. Then, we derive uniform
strong convergence rates for the kernel estimator of two-dimensional distribution function
of (X1;Xk+1) which were not found already and do not need any conditions on the covari-
ance structure of the variables. Furthermore assuming a convenient decrease rate of the
covariances Cov(X1;Xn+1); n 1, we prove uniform strong convergence rate for covari-
ance function of the limit empirical process based on kernel type estimators. Finally, we
use a simulation study to compare the estimators of distribution function of (X1;Xk+1).

**Category:** Statistics

[109] **viXra:1512.0294 [pdf]**
*submitted on 2015-12-12 02:35:48*

**Authors:** Amelia Carolina Sparavigna

**Comments:** 4 Pages. Published in International Journal of Sciences, 2015, 4(10):1-4. DOI:10.18483/ijSci.845

Mutual information of two random variables can be easily obtained from their Shannon entropies. However, when nonadditive entropies are involved, the calculus of the mutual information is more complex. Here we discuss the basic matter about information from Shannon entropy. Then we analyse the case of the generalized nonadditive Tsallis entropy

**Category:** Statistics

[108] **viXra:1512.0293 [pdf]**
*submitted on 2015-12-12 02:40:18*

**Authors:** Amelia Carolina Sparavigna

**Comments:** 4 Pages. Published in International Journal of Sciences, 2015, 4(10):47-50. DOI:10.18483/ijSci.866

Tsallis and Kaniadakis entropies are generalizing the Shannon entropy and have it as their limit when their entropic indices approach specific values. Here we show some relations existing between Tsallis and Kaniadakis entropies. We will also propose a rigorous discussion of the conditional Kaniadakis entropy, deduced from these relations.

**Category:** Statistics

[107] **viXra:1511.0233 [pdf]**
*submitted on 2015-11-24 04:47:27*

**Authors:** M. F. Bugallo, L. Martino, J. Corander

**Comments:** Digital Signal Processing, Volume 47, Pages 36–49, 2015.

In Bayesian signal processing, all the information about the unknowns of interest is contained in their posterior distributions.
The unknowns can be parameters of a model, or a model and its parameters. In many important problems, these distributions
are impossible to obtain in analytical form. An alternative is to generate their approximations by Monte Carlo-based methods
like Markov chain Monte Carlo (MCMC) sampling, adaptive importance sampling (AIS) or particle filtering (PF). While MCMC
sampling and PF have received considerable attention in the literature and are reasonably well understood, the AIS methodology remains relatively unexplored. This article reviews the basics of AIS as well as provides a comprehensive survey of the state-of the-art of the topic. Some of its most relevant implementations are revisited and compared through computer simulation examples.

**Category:** Statistics

[106] **viXra:1511.0232 [pdf]**
*submitted on 2015-11-24 05:31:30*

**Authors:** V. Elvira, L. Martino, D. Luengo, M. F. Bugallo

**Comments:** 38 Pages.

Importance Sampling methods are broadly used to approximate posterior distributions or some of their moments. In its
standard approach, samples are drawn from a single proposal distribution and weighted properly. However, since the performance depends on the mismatch between the targeted and the proposal distributions, several proposal densities are often employed for the generation of samples. Under this Multiple Importance Sampling (MIS) scenario, many works have addressed the selection or adaptation of the proposal distributions, interpreting the sampling and the weighting steps in different ways. In this paper, we establish a general framework for sampling and weighting procedures when more than one proposal is available. The most relevant MIS schemes in the literature are encompassed within the new framework, and, moreover novel valid schemes appear naturally. All the MIS schemes are compared and ranked in terms of the variance of the associated estimators. Finally, we provide illustrative examples which reveal that, even with a good choice of the proposal densities, a careful interpretation of the sampling and weighting procedures can make a significant difference in the performance of the method.

**Category:** Statistics

[105] **viXra:1511.0003 [pdf]**
*submitted on 2015-11-01 06:07:39*

**Authors:** John R. Dixon

**Comments:** 41 Pages.

This is the technical report to accompany:
Dixon, John R., Michael R. Kosorok, and Bee Leng Lee. "Functional inference in semiparametric models using the piggyback bootstrap." Annals of the Institute of Statistical Mathematics 57, no. 2 (2005): 255-277.

**Category:** Statistics

[104] **viXra:1509.0048 [pdf]**
*submitted on 2015-09-04 05:40:14*

**Authors:** L. Martino, F. Louzada

**Comments:** 13 Pages.

The adaptive rejection sampling (ARS) algorithm is a universal random generator for drawing samples efficiently from a univariate log-concave target probability density function (pdf). ARS generates independent samples from the target via rejection sampling with high acceptance rates. Indeed, ARS yields a sequence of proposal functions that converge toward the target pdf, so that the probability of accepting a sample approaches one. However, sampling from the proposal pdf becomes more computational demanding each time it is updated. In this work, we propose a novel ARS scheme, called Cheap Adaptive Rejection Sampling (CARS), where the computational effort for drawing from the proposal remains constant, decided in advance by the user. For generating a large number of desired samples, CARS is faster than ARS.

**Category:** Statistics

[103] **viXra:1508.0265 [pdf]**
*submitted on 2015-08-27 02:35:07*

**Authors:** B. B. Khare, Habib Ur Rehman, U. Srivastava

**Comments:** 10 Pages.

In this paper, a study of improved chain ratio-cum regression type estimator for population
mean in the presence of non-response for fixed cost and specified precision has been made.
Theoretical results are supported by carrying out one numerical illustration.

**Category:** Statistics

[102] **viXra:1508.0256 [pdf]**
*submitted on 2015-08-27 02:50:36*

**Authors:** B. B. Khare

**Comments:** 8 Pages.

The auxiliary information is used in increasing the efficiency of the estimators for the
parameters of the populations such as mean, ratio, and product of two population means. In this context, the estimation procedure for the ratio and product of two population means using auxiliary characters in special reference to the non response problem has been discussed.

**Category:** Statistics

[101] **viXra:1508.0142 [pdf]**
*submitted on 2015-08-18 02:29:47*

**Authors:** L. Martino, F. Louzada

**Comments:** 17 Pages.

The multiple Try Metropolis (MTM) algorithm
is an advanced MCMC technique based on drawing and testing several candidates at each iteration of the algorithm. One of them is selected according to certain weights and then it is tested according to a suitable acceptance probability. Clearly, since the computational cost increases as the employed number of tries grows, one expects that the performance of an MTM scheme improves as the number of tries increases, as well. However, there are scenarios where the increase of number of tries does not produce a corresponding enhancement of the performance. In this work, we describe these scenarios and then we introduce possible solutions for solving these issues.

**Category:** Statistics

[100] **viXra:1507.0125 [pdf]**
*submitted on 2015-07-16 09:20:20*

**Authors:** editors Rajesh Singh, Florentin Smarandache

**Comments:** 54 Pages.

The present book aims to present some improved estimators using auxiliary and attribute information in case of simple random sampling and stratified random sampling and in some cases when non-response is present.
This volume is a collection of five papers, written by seven co-authors (listed in the order of the papers): Sachin Malik, Rajesh Singh, Florentin Smarandache, B. B. Khare, P. S. Jha, Usha Srivastava and Habib Ur. Rehman.
The first and the second papers deal with the problem of estimating the finite population mean when some information on two auxiliary attributes are available. In the third paper, problems related to estimation of ratio and product of two population mean using auxiliary characters with special reference to non-response are discussed.
In the fourth paper, the use of coefficient of variation and shape parameters in each stratum, the problem of estimation of population mean has been considered. In the fifth paper, a study of improved chain ratio-cum-regression type estimator for population mean in the presence of non-response for fixed cost and specified precision has been made.
The authors hope that the book will be helpful for the researchers and students that are working in the field of sampling techniques.

**Category:** Statistics

[99] **viXra:1507.0110 [pdf]**
*submitted on 2015-07-14 15:18:08*

**Authors:** L. Martino, V. Elvira, D. Luengo, J. Corander, F. Louzada

**Comments:** 20 Pages.

Monte Carlo (MC) methods are widely used in signal processing, machine learning and stochastic optimization. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have been recently introduced. In this work, we describe a novel parallel interacting MCMC scheme, called orthogonal MCMC (O-MCMC), where a set of ``vertical'' parallel MCMC chains share information using some ``horizontal" MCMC techniques working on the entire population of current states. More specifically, the vertical chains are led by random-walk proposals, whereas the horizontal MCMC techniques employ independent proposals, thus allowing an efficient combination of global exploration and local approximation. The interaction is contained in these horizontal iterations. Within the analysis of different implementations of O-MCMC, novel schemes for reducing the overall computational cost of parallel multiple try Metropolis (MTM) chains are also presented. Furthermore, a modified version of O-MCMC for optimization is provided by considering parallel simulated annealing (SA) algorithms. We also discuss the application of O-MCMC in a big bata framework.
Numerical results show the advantages of the proposed sampling scheme in terms of efficiency in the estimation, as well as robustness in terms of independence with respect to initial values and parameter choice.

**Category:** Statistics

[98] **viXra:1507.0029 [pdf]**
*submitted on 2015-07-05 07:21:38*

**Authors:** Khaled Ouafi

**Comments:** 9 Pages.

We investigate the issue of approximate Bayesian parameter inference in nonlinear state space models with complex likelihoods. Sequential Monte Carlo with approximate Bayesian computations (SMC-ABC) is an approach to approximate the likelihood in this type of models. However, such approximations can be noisy and computationally expensive which hinders cost-effective implementations using standard methods based on optimisation and statistical simulation. We propose a innovational method based on the combination of Gaussian process optimisation (GPO) and SMC-ABC to create a Laplace approximation of the intractable posterior. The properties of the resulting GPO-ABC method are studied using stochastic volatility (SV) models with both synthetic and real-world data. We conclude that the algorithm enjoys: good accuracy comparable to particle Markov chain Monte Carlo with a significant reduction in computational cost and better robustness to noise in the estimates compared with a gradient-based optimisation algorithm. Finally, we make use of GPO-ABC to estimate the Value-at-Risk for a portfolio using a copula model with SV models for the margins.

**Category:** Statistics

[97] **viXra:1506.0175 [pdf]**
*submitted on 2015-06-24 13:01:14*

**Authors:** Ilija Barukčić

**Comments:** 19 pages. (C) Ilija Barukčić, Jever, Germany, 2015,

The deterministic relationship between cause and effect is deeply connected with our understanding of the physical sciences and their explanatory ambitions. Though progress is being made, the lack of theoretical predictions and experiments in quantum gravity makes it difficult to use empirical evidence to justify a theory of causality at quantum level in normal circumstances, i. e. by predicting the value of a well-confirmed experimental result. For a variety of reasons, the problem of the deterministic relationship between cause and effect is related to basic problems of physics as such. Despite the common belief, it is a remarkable fact that a theory of causality should be consistent with a theory of everything and is because of this linked to problems of a theory of everything. Thus far, solving the problem of causality can help to solve the problems of the theory of everything (at quantum level) too.

**Category:** Statistics

[96] **viXra:1506.0067 [pdf]**
*submitted on 2015-06-08 14:58:47*

**Authors:** Christopher Goddard

**Comments:** 4 Pages.

It is a common problem in statistics to determine the appropriate heuristic to select from a set of hypotheses (or equivalently, models), prior to optimising that model to fit the data. In this short note I sketch a technique based on the construction of an information in order to compute the optimal model within a given model space and given data.

**Category:** Statistics

[95] **viXra:1505.0136 [pdf]**
*submitted on 2015-05-19 00:31:36*

**Authors:** Vorobyev O.Yu., Golovkov L.S.

**Comments:** 10 Pages.

This article brings in two new discrete distributions: multidimensional Binomial
distribution and multidimensional Poisson distribution. Also there are its characteristics and properties.

**Category:** Statistics

[94] **viXra:1505.0135 [pdf]**
*submitted on 2015-05-18 10:45:07*

**Authors:** L. Martino, V. Elvira, D. Luengo, J. Corander

**Comments:** 26 Pages.

Monte Carlo algorithms represent the \textit{de facto} standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use simpler proposal probability densities for drawing candidate samples. Performance of any such method is strictly related to the specification of the proposal distribution, such that unfortunate choices easily wreak havoc on the resulting estimators. In this work, we introduce a \textit{layered}, that is a hierarchical, procedure for generating samples employed within a Monte Carlo scheme. This approach ensures that an appropriate equivalent proposal distribution is always obtained automatically (thus eliminating the risk of a catastrophic performance), although at the expense of a moderate increase in the complexity of the resulting algorithm. A hierarchical interpretation of two well-known methods, such as of the random walk Metropolis-Hastings (MH) and the Population Monte Carlo (PMC) techniques, is provided.
Furthermore, we provide a general unified importance sampling (IS) framework where multiple proposal densities are employed, and several IS schemes are introduced applying the so-called deterministic mixture approach.
Finally, given these schemes, we also propose a novel class of adaptive importance samplers using a population of proposals, where the adaptation is driven by independent parallel or interacting Markov Chain Monte Carlo (MCMC) chains. The resulting algorithms combine efficiently the benefits of both IS and MCMC methods.

**Category:** Statistics

[93] **viXra:1503.0088 [pdf]**
*submitted on 2015-03-12 09:09:50*

**Authors:** Jianwen Huang, Shouquan Chen

**Comments:** 10 Pages.

We introduce logarithmic generalized Maxwell
distribution which is an extension of the generalized Maxwell
distribution. Some interesting properties of this distribution are
studied and the asymptotic distribution of the partial maximum of an
independent and identically distributed sequence from the
logarithmic generalized Maxwell distribution is gained.

**Category:** Statistics

[92] **viXra:1412.0276 [pdf]**
*submitted on 2014-12-31 01:34:35*

**Authors:** Jianwen Huang, Yanmin Liu

**Comments:** 7 Pages.

In this paper, with optimal normalized constants,
the asymptotic expansions of the distribution of the normalized
maxima from generalized Maxwell distribution is derived. It shows
that the convergence rate of the normalized maxima to the Gumbel
extreme value distribution is proportional to $1/\log n.$

**Category:** Statistics

[91] **viXra:1412.0275 [pdf]**
*submitted on 2014-12-31 01:42:41*

**Authors:** Jianwen Huang, Yanmin Liu

**Comments:** 12 Pages.

In this paper, the higher-order asymptotic
expansion of the moment of extreme from generalized Maxwell
distribution is gained, by which one establishes the rate of
convergence of the moment of the normalized partial
maximum to the moment of the associate Gumbel extreme value distribution.

**Category:** Statistics

[90] **viXra:1412.0247 [pdf]**
*submitted on 2014-12-26 15:30:26*

**Authors:** Sergio Arciniegas-Alarcón, Marisol García-Peña, Wojtek Krzanowski, Carlos Tadeu dos Santos Dias

**Comments:** 14 Pages.

A common problem in multi-environment trials arises when some genotype-by-environment combinations are missing. In Arciniegas-Alarcón et al. (2010) we outlined a method of data imputation to estimate the missing values, the computational algorithm for which was a mixture of regression and lower-rank approximation of a matrix based on its singular value decomposition (SVD). In the present paper we provide two extensions to this methodology, by including weights chosen by cross-validation and allowing multiple as well as simple imputation. The three methods are assessed and compared in a simulation study, using a complete set of real data in which values are deleted randomly at different rates. The quality of the imputations is evaluated using three measures: the Procrustes statistic,the squared correlation between matrices and the normalised root mean squared error between these estimates and the true observed values. None of the methods makes any distributional or structural assumptions, and all of them can be used for any pattern or mechanism of the missing values.

**Category:** Statistics

[89] **viXra:1412.0003 [pdf]**
*submitted on 2014-12-01 04:45:04*

**Authors:** Marisol García-Peña, Sergio Arciniegas-Alarcón, Décio Barbin

**Comments:** 10 Pages.

A common problem in climate data is missing information. Recently, four methods have been developed which are based in the singular value decomposition of a matrix (SVD). The aim of this paper is to evaluate these new developments making a comparison by means of a simulation study based on two complete matrices of real data. One corresponds to the historical precipitation of Piracicaba / SP - Brazil and the other matrix corresponds to multivariate meteorological characteristics in the same city from year 1997 to 2012. In the study, values were deleted randomly at different percentages with subsequent imputation, comparing the methodologies by three criteria: the normalized root mean squared error, the similarity statistic of Procrustes and the Spearman correlation coefficient. It was concluded that the SVD should be used only when multivariate matrices are analyzed and when matrices of precipitation are used, the monthly mean overcome the performance of other methods based on the SVD.

**Category:** Statistics

[88] **viXra:1411.0396 [pdf]**
*submitted on 2014-11-20 03:16:54*

**Authors:** A. Borumand Saeid, A. Namdar

**Comments:** 7 Pages.

We introduce the notion of Smarandache BCH-algebra and Smarandache (fresh, clean and fantastic) ideals, some example are given and related properties are investigated. Relationship between
Q-Smarandache (fresh, clean and fantastic) ideals and other types of ideals are given. Extension properties for Q-Smarandache (fresh, clean and fantastic) ideals are established.

**Category:** Statistics

[87] **viXra:1411.0270 [pdf]**
*submitted on 2014-11-19 01:04:21*

**Authors:** Florentin Smarandache

**Comments:** 2 Pages.

In this note the author presents a new proof for the theorem of I. Patrascu.

**Category:** Statistics

[86] **viXra:1411.0267 [pdf]**
*submitted on 2014-11-19 01:14:33*

**Authors:** Florentin Smarandache

**Comments:** 1 Page.

It is possible to cover all (positive) integers with n geometrical progressions of integers?
Find a necessary and sufficient condition for a general class of positive integer sequences
such that, for a fixed n , there are n (distinct) sequences of this class which cover all integers.

**Category:** Statistics

[85] **viXra:1411.0265 [pdf]**
*submitted on 2014-11-19 01:17:32*

**Authors:** Marian Niţu, Florentin Smarandache, Mircea Eugen Şelariu

**Comments:** 22 Pages.

Ideea centrală a lucrarii este prezentarea unor transformări noi, anterior inexistente în Matematica ordinară, denumită centrică (MC), dar, care au devenit posibile graţie apariţiei matematicii excentrice şi, implicit, a supermatematicii.

**Category:** Statistics

[84] **viXra:1411.0264 [pdf]**
*submitted on 2014-11-19 01:18:41*

**Authors:** Mircea E.selariu, Florentin Smarandache, Marian Nitu

**Comments:** 18 Pages.

Lucrarea prezintă corespondentele din matematica excentrică ale funcţiilor cardinale şi integrale din matematica centrică, sau matematica ordinară, funcţii centrice prezentate şi în introducerea lucrării, deoarece sunt prea puţin cunoscute, deşi sunt utilizate pe larg în fizica ondulatorie

**Category:** Statistics

[83] **viXra:1411.0260 [pdf]**
*submitted on 2014-11-19 01:38:40*

**Authors:** Octavian Cira, Florentin Smarandache

**Comments:** 8 Pages.

The first prime number with the special property that its addition with its reversal gives as result a prime number too is 299. The prime numbers with this property will be called Luhn prime numbers. In this article we intend to present a performing
algorithm for determining the Luhn prime numbers.

**Category:** Statistics

[82] **viXra:1411.0258 [pdf]**
*submitted on 2014-11-19 01:40:47*

**Authors:** Said Broumi, Pinaki Majumdar, Florentin Smarandache

**Comments:** 11 Pages.

In this paper , we have defined First Zadeh’s implication , First Zadeh’s intuitionistic fuzzy conjunction and intuitionistic fuzzy disjunction of two intuitionistic fuzzy soft sets and some their basic properties are studied with proofs and examples.

**Category:** Statistics

[81] **viXra:1411.0255 [pdf]**
*submitted on 2014-11-19 02:04:12*

**Authors:** Ion Patrascu, Florentin Smarandache

**Comments:** 3 Pages.

Open problem
Construct, using a ruler and a compass, two non-congruent triangles, which have equal
perimeters and arias.
In preparation for the proof of this problem we recall several notions and we prove a
Lemma.

**Category:** Statistics

[80] **viXra:1411.0253 [pdf]**
*submitted on 2014-11-19 02:07:41*

**Authors:** C.Dumitrescu, N.Varlan, St Zanfir, N.Radescu, F.Smarandache

**Comments:** 23 Pages.

In this paper we extend the Smarandache function.

**Category:** Statistics

[79] **viXra:1411.0252 [pdf]**
*submitted on 2014-11-19 02:09:03*

**Authors:** Ion Patrascu

**Comments:** 6 Pages.

In this article, we review some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles.

**Category:** Statistics

[78] **viXra:1411.0072 [pdf]**
*submitted on 2014-11-08 15:25:10*

**Authors:** Suhoparov Stanislav Yurievich

**Comments:** 5 Pages.

Derivation of the recurrence relation for orthogonal polynomials and usage.
Вывод рекуррентного соотношения ортогональных многочленов из процесса ортогонализации Грама-Шмидта, а также схема применения полученного рекуррентного соотношения

**Category:** Statistics

[77] **viXra:1411.0064 [pdf]**
*submitted on 2014-11-07 17:22:14*

**Authors:** Jean Claude Dutailly

**Comments:** 16 Pages.

The purpose of this paper is to present a general method to estimate the probability of transitions of a system between phases. The system must be represented in a quantitative model, with vectorial variables depending on time, satisfying general conditions which are usually met. The method can be implemented in Physics, Economics or Finances.

**Category:** Statistics

[76] **viXra:1411.0016 [pdf]**
*submitted on 2014-11-03 07:05:31*

**Authors:** Sergio Arciniegas-Alarcón, Marisol García-Peña, Wojtek Krzanowski, Carlos Tadeu dos Santos Dias

**Comments:** 17 Pages.

Missing values for some genotype-environment combinations are commonly encountered in multienvironment trials. The recommended methodology for analyzing such unbalanced data combines the Expectation-Maximization (EM) algorithm with the additive main effects and multiplicative interaction (AMMI) model. Recently, however, four imputation algorithms based on the Singular Value Decomposition of a matrix (SVD) have been reported in the literature (Biplot imputation, EM+SVD, GabrielEigen imputation, and distribution free multiple imputation - DFMI). These algorithms all fill in the missing values, thereby removing the lack of balance in the original data and permitting simpler standard analyses to be performed. The aim of this paper is to compare these four algorithms with the gold standard EM-AMMI. To do this, we report the results of a simulation study based on three complete sets of real data (eucalyptus, sugar cane and beans) for various imputation percentages. The methodologies were compared using the normalised root mean squared error, the Procrustes similarity statistic and the Spearman correlation coefficient. The conclusion is that imputation using the EM algorithm plus SVD provides competitive results to those obtained with the gold standard. It is also an excellent alternative to imputation with an additive model, which in practice ignores the genotype-by-environment interaction and therefore may not be appropriate in some cases.

**Category:** Statistics

[75] **viXra:1410.0191 [pdf]**
*submitted on 2014-10-29 07:37:19*

**Authors:** Carlos Tadeu dos Santos Dias, Kuang Hongyu, Lúcio B. Araújo, Maria Joseane C. Silva, Marisol García-Peña, Mirian F. C. Araújo, Priscila N. Faria, Sergio Arciniegas-Alarcón

**Comments:** 19 Pages. Paper in portuguese.

This work is based on the short course “A Metodologia AMMI: Com Aplicacão ao Melhoramento Genético” taught during the 58a RBRAS and 15o SEAGRO held in Campina Grande - PB and aim to introduce the AMMI method for those that have and no have the mathematical training. We do not intend to submit a detailed work, but the intention is to serve as a light for researchers, graduate and postgraduate students. In other words, is a work to stimulate research and the quest for knowledge in an area of statistical methods. For this propose we make a review about the genotype-by-environment interaction, definition of the AMMI models and some selection criteria and biplot graphic. More details about it can be found in the material produced for the short course.

**Category:** Statistics

[74] **viXra:1410.0121 [pdf]**
*submitted on 2014-10-21 11:16:26*

**Authors:** Sergio Arciniegas-Alarcón, Carlos Tadeu dos Santos Dias, Marisol García-Peña

**Comments:** 9 Pages. Paper in portuguese with abstract in english.

Abstract – The objective of this work was to propose a new distribution‑free multiple imputation algorithm, through modifications of the simple imputation method recently developed by Yan in order to circumvent the problem of unbalanced experiments. The method uses the singular value decomposition of a matrix and was tested using simulations based on two complete matrices of real data, obtained from eucalyptus and sugarcane trials, with values deleted randomly at different percentages. The quality of the imputations was evaluated by a measure of overall accuracy that combines the variance between imputations and their mean square deviations in relation to the deleted values. The best alternative for multiple imputation is a multiplicative model that includes weights near to 1 for the eigenvalues calculated with the decomposition. The proposed methodology does not depend on distributional or structural assumptions and does not have any restriction regarding the pattern or the mechanism of the missing data.

**Category:** Statistics

[73] **viXra:1410.0077 [pdf]**
*submitted on 2014-10-14 13:14:47*

**Authors:** T. Prabhakar Reddy, S. Sambasiva Rao, P. Ramu

**Comments:** 13 Pages. This paper has been published in Journal of Physical Education and Sports Science, pp.226-234,Vol 2, 2014. ISSN 2229-7049.

Unpredictable game of the limited-over cricket brings with it excitement for the audience, expecting mayhem on the field. The huge expectation of audience to watch a good match may be ruined with an interruption due to bad weather or circumstances. Therefore, it is very much necessary to adjust the target score at the time of resumption of an interrupted match in a reasonable manner. Several mathematical models for resetting the target in interrupted one-day international (ODI) cricket matches are available in the literature; none of them is optimal for Twenty20 (T20) format to apply. The purpose of this note is to review the existing Rain Rules to reset the targets in an interrupted ODI cricket matches and to propose a method for resetting the targets in an interrupted T20 cricket match with suitable illustrative examples.

**Category:** Statistics

[72] **viXra:1410.0070 [pdf]**
*submitted on 2014-10-13 10:09:31*

**Authors:** Huang Jianwen, Yang Hongyan

**Comments:** 6 Pages.

Let
$\{X_n,~n\geq1\}$ be independent and identically distributed random
variables with each $X_n$ following skew normal distribution. Let
$M_n=\max\{X_k,~1\leq k\leq n\}$ denote the partial maximum of
$\{X_n,~n\geq1\}$. Liao et al. (2014) considered the convergence
rate of the distribution of the maxima for random variables obeying
the skew normal distribution under linear normalization. In this
paper, we
obtain the asymptotic distribution of the maximum under power
normalization and normalizing constants as well as the associated pointwise convergence rate under power
normalization.

**Category:** Statistics

[71] **viXra:1409.0127 [pdf]**
*submitted on 2014-09-16 10:08:05*

**Authors:** Jianwen Huang, Shouquan Chen

**Comments:** 15 Pages.

Let $\{X_n,~n\geq1\}$ be an independent
and identically distributed random sequence with common
distribution $F$ obeying the lognormal distribution. In
this paper, we obtain the exact uniform convergence rate of the
distribution of the maximum to its extreme value limit under power normalization.

**Category:** Statistics

[70] **viXra:1409.0119 [pdf]**
*submitted on 2014-09-15 10:24:34*

**Authors:** Jianwen Huang, Shouquan Chen

**Comments:** 9 Pages.

Motivated by Finner et al. (2008), the
asymptotic behavior of the probability density function (pdf) and
the cumulative distribution function (cdf) of the generalized
exponential and Maxwell distributions are studied. Specially, we
consider the asymptotic behavior of the ratio of the pdfs (cdfs) of
the generalized exponential and Student's $t$-distributions (likewise
for the Maxwell and Student's $t$-distributions) as the degrees of
freedom parameter approach infinity in an appropriate way. As by
products, Mills' ratios for the generalized exponential and Maxwell
distributions are gained. Moreover, we illustrate some examples to
indicate the application of our results in extreme value theory.

**Category:** Statistics

[69] **viXra:1409.0051 [pdf]**
*submitted on 2014-09-08 03:03:33*

**Authors:** L. Martino, J. Corander

**Comments:** 10 Pages.

Markov Chain Monte Carlo (MCMC) methods are well-known Monte Carlo methodologies, widely used in different fields for statistical inference and stochastic optimization. The Multiple Try Metropolis (MTM) algorithm is an extension of the standard Metropolis-Hastings (MH) algorithm in which the next state of the chain is chosen among a set of candidates, according to certain weights.
The Particle MH (PMH) algorithm is other advanced MCMC technique specifically designed for scenarios where the multidimensional target density can be easily factorized as multiplication of (lower - dimensional) conditional densities. Both are widely studied and applied in literature. In this note, we investigate similarities and differences among the MTM schemes and the PMH method.

**Category:** Statistics

[68] **viXra:1409.0015 [pdf]**
*submitted on 2014-09-02 11:32:22*

**Authors:** Ellida M. Khazen

**Comments:** 25 Pages.

The problem of filtering of unobservable components x(t) of a multidimensional continuous diffusion Markov process z(t)=(x(t),y(t)), given the observations of the (multidimensional) process y(t) taken at discrete consecutive times with small time steps, is analytically investigated. On the base of that investigation the new algorithms for simulation of unobservable components, x(t), and the new algorithms of nonlinear filtering with the use of sequential Monte Carlo methods, or particle filters, are developed and suggested. The analytical investigation of observed quadratic variations is also developed. The new closed form analytical formulae are obtained, which characterize dispersions of deviations of the observed quadratic variations and the accuracy of some estimates for x(t). As an illustrative example, estimation of volatility (for the problems of financial mathematics) is considered. The obtained new algorithms extend the range of applications of sequential Monte Carlo methods, or particle filters, beyond the hidden Markov models and improve their performance.

**Category:** Statistics

[61] **viXra:1603.0215 [pdf]**
*replaced on 2016-03-17 17:28:08*

**Authors:** Glenn Healey

**Comments:** 14 Pages.

Given a set of observed batted balls and their outcomes, we develop a method for learning the dependence of a batted ball’s intrinsic value on its measured parameters.

**Category:** Statistics

[60] **viXra:1603.0180 [pdf]**
*replaced on 2016-03-14 15:52:37*

**Authors:** Luca Martino, Jorge Plata-Chaves, Francisco Louzada

**Comments:** 5 Pages.

In this work, we design an efficient Monte Carlo scheme for a node-specific inference problem where a vector of global parameters and multiple vectors of local parameters are involved. This scenario often appears in inference problems over heterogeneous wireless sensor networks where each node performs observations dependent on a vector of global parameters as well as a vector of local parameters. The proposed scheme uses parallel local MCMC chains and then an importance sampling (IS) fusion step that leverages all the observations of all the nodes when estimating the global parameters. The resulting algorithm is simple and flexible. It can be easily applied iteratively, or extended in a sequential framework.

**Category:** Statistics

[59] **viXra:1603.0180 [pdf]**
*replaced on 2016-03-13 11:19:11*

**Authors:** Luca Martino, Jorge Plata-Chaves, Francisco Louzada

**Comments:** 5 Pages.

In this work, we design an efficient Monte Carlo scheme for a node-specific inference problem where a vector of global parameters and multiple vectors of local parameters are involved. This scenario often appears in inference problems over heterogeneous wireless sensor networks where each node performs observations dependent on a vector of global parameters as well as a vector of local parameters. The proposed scheme uses parallel local MCMC chains and then an importance sampling (IS) fusion step that leverages all the observations of all the nodes when estimating the global parameters. The resulting algorithm is simple and flexible. It can be easily applied iteratively, or extended in a sequential framework.

**Category:** Statistics

[58] **viXra:1603.0180 [pdf]**
*replaced on 2016-03-12 06:01:27*

**Authors:** Luca Martino, Jorge Plata-Chaves, Francisco Louzada

**Comments:** 5 Pages.

In this work, we design an efficient Monte Carlo
scheme for a node-specific inference problem where a vector of
global parameters and multiple vectors of local parameters are
involved. This scenario often appears in inference problems over
heterogeneous wireless sensor networks where each node performs observations dependent on a vector of global parameters as well as a vector of local parameters. The proposed scheme uses parallel local MCMC chains and then an importance sampling (IS) fusion step that leverages all the observations of all the nodes when estimating the global parameters. The resulting algorithm is simple and flexible. It can be easily applied iteratively, or extended in a sequential framework.

**Category:** Statistics

[57] **viXra:1602.0333 [pdf]**
*replaced on 2016-06-15 02:55:00*

**Authors:** L. Martino, V. Elvira, F. Louzada

**Comments:** 9 Pages. This is an extended version of the work: L. Martino,V. Elvira, F. Louzada, "Weighting a Resampled Particle in Sequential Monte Carlo", IEEE Statistical Signal Processing Workshop, (SSP), 2016.

The Sequential Importance Resampling (SIR) method is the core of the Sequential Monte Carlo (SMC) algorithms (a.k.a., particle filters). In this work, we point out a suitable choice for weighting properly a resampled particle. This observation entails several theoretical and practical consequences, allowing also the design of novel sampling schemes. Specifically, we describe one theoretical result about the sequential estimation of the marginal likelihood. Moreover, we suggest a novel resampling procedure for SMC algorithms called partial resampling, involving only a subset of the current cloud of particles. Clearly, this scheme attenuates the additional variance in the Monte Carlo estimators generated by the use of the resampling.

**Category:** Statistics

[56] **viXra:1602.0333 [pdf]**
*replaced on 2016-06-13 04:06:23*

**Authors:** L. Martino, V. Elvira, F. Louzada

**Comments:** 9 Pages. This is an extended version of the work: L. Martino,V. Elvira, F. Louzada, "Weighting a Resampled Particle in Sequential Monte Carlo", IEEE Statistical Signal Processing Workshop, (SSP), 2016.

The Sequential Importance Resampling (SIR) method is the core of the Sequential Monte Carlo (SMC) algorithms (a.k.a.,
particle filters). In this work, we point out a suitable choice for weighting properly a resampled particle. This observation entails
several theoretical and practical consequences, allowing also the design of novel sampling schemes. Specifically, we describe
one theoretical result about the sequential estimation of the marginal likelihood. Moreover, we suggest a novel resampling
procedure for SMC algorithms called partial resampling, involving only a subset of the current cloud of particles. Clearly, this scheme attenuates the additional variance in the Monte Carlo estimators generated by the use of the resampling.

**Category:** Statistics

[55] **viXra:1602.0333 [pdf]**
*replaced on 2016-05-10 08:15:27*

**Authors:** L. Martino, V. Elvira, F. Louzada

**Comments:** 5 Pages.

**Category:** Statistics

[54] **viXra:1602.0112 [pdf]**
*replaced on 2016-03-05 09:11:03*

**Authors:** L. Martino, V. Elvira, F. Louzada

**Comments:** 32 Pages.

The Effective Sample Size (ESS) is an important measure of efficiency of Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) techniques. In the IS context, an approximation $\widehat{ESS}$ of the theoretical ESS definition is widely applied, involving the inverse of the sum of the squares of the normalized importance weights. This formula, $\widehat{ESS}$, has become an essential piece within Sequential Monte Carlo (SMC) methods, to assess the convenience of a resampling step. From another perspective, the expression $\widehat{ESS}$ is related to the Euclidean distance between the probability mass described by the normalized weights and the discrete uniform probability mass function (pmf). In this work, we derive other possible ESS functions based on different discrepancy measures between these two pmfs. Several examples are provided involving, for instance, the geometric and harmonic means of the weights, the discrete entropy (including the perplexity measure, already proposed in literature) and the Gini coefficient among others. We list five requirements which a generic ESS function should satisfy, allowing us to classify different ESS measures. We also compare the most promising ones by means of numerical simulations.

**Category:** Statistics

[53] **viXra:1602.0112 [pdf]**
*replaced on 2016-02-20 06:30:34*

**Authors:** L. Martino, V. Elvira, F. Louzada

**Comments:** 31 Pages.

The Effective Sample Size (ESS) is an important measure of efficiency of Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) techniques. In the IS context, an approximation $\widehat{ESS}$ of the theoretical ESS definition is widely applied, involving the inverse of the sum of the squares of the normalized importance weights. This formula, $\widehat{ESS}$, has become an essential piece within Sequential Monte Carlo (SMC) methods, to assess the convenience of a resampling step. From another perspective, the expression $\widehat{ESS}$ is related to the Euclidean distance between the probability mass described by the normalized weights and the discrete uniform probability mass function (pmf). In this work, we derive other possible ESS functions based on different discrepancy measures between these two pmfs. Several examples are provided involving, for instance, the geometric and harmonic means of the weights, the discrete entropy (including the perplexity measure, already proposed in literature) and the Gini coefficient among others. We list five requirements which a generic ESS function should satisfy, allowing us to classify different ESS measures. We also compare the most promising ones by means of numerical simulations.

**Category:** Statistics

[52] **viXra:1602.0112 [pdf]**
*replaced on 2016-02-19 04:23:27*

**Authors:** L. Martino, V. Elvira, F. Louzada

**Comments:** 31 Pages.

The Effective Sample Size (ESS) is an important measure of efficiency of Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) techniques. In the IS context, an approximation $\widehat{ESS}$ of the theoretical ESS definition is widely applied, involving the sum of the squares of the normalized importance weights. This formula, $\widehat{ESS}$, has become an essential piece within Sequential Monte Carlo (SMC) methods, to assess the convenience of a resampling step. From another perspective, the expression $\widehat{ESS}$ is related to the Euclidean distance between the probability mass described by the normalized weights and the discrete uniform probability mass function (pmf). In this work, we derive other possible ESS functions based on different discrepancy measures between these two pmfs. Several examples are provided involving, for instance, the geometric and harmonic means of the weights, the discrete entropy (including the perplexity measure, already proposed in literature) and the Gini coefficient among others. We list five requirements which a generic ESS function should satisfy, allowing us to classify different ESS measures. We also compare the most promising ones by means of numerical simulations.

**Category:** Statistics

[51] **viXra:1602.0112 [pdf]**
*replaced on 2016-02-14 08:13:03*

**Authors:** L. Martino, V. Elvira, F. Louzada

**Comments:** 31 Pages.

The Effective Sample Size (ESS) is an important measure of efficiency of Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) techniques. In the IS context, an approximation $\widehat{ESS}$ of the theoretical ESS definition is widely applied, involving the sum of the squares of the normalized importance weights. This formula, $\widehat{ESS}$, has become an essential piece within Sequential Monte Carlo (SMC) methods, to assess the convenience of a resampling step. From another perspective, the expression $\widehat{ESS}$ is related to the Euclidean distance between the probability mass described by the normalized weights and the discrete uniform probability mass function (pmf). In this work, we derive other possible ESS functions based on different discrepancy measures between these two pmfs. Several examples are provided involving, for instance, the geometric and harmonic means of the weights, the discrete entropy (including the {\it perplexity} measure, already proposed in literature) and the Gini coefficient among others. We list five requirements which a generic ESS function should satisfy, allowing us to classify different ESS measures. We also compare the most promising ones by means of numerical simulations.

**Category:** Statistics

[50] **viXra:1602.0112 [pdf]**
*replaced on 2016-02-10 07:48:50*

**Authors:** L. Martino, V. Elvira, F. Louzada

**Comments:** 31 Pages.

The Effective Sample Size (ESS) is an important measure of efficiency of Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) techniques. In IS context, an approximation of the theoretical ESS definition is widely applied, $\widehat{ESS}$, involving the sum of the squares of the normalized importance weights. This formula $\widehat{ESS}$ has become an essential piece within Sequential Monte Carlo (SMC) methods using adaptive resampling procedures. The expression $\widehat{ESS}$ is related to the Euclidean distance between the probability mass described by the normalized weights and the discrete uniform probability mass function (pmf). In this work, we derive other possible ESS functions based on different discrepancy measures between these pmfs. Several examples are provided involving, for instance, the geometric and harmonic means of the weights, the discrete entropy (including the perplexity measure, already proposed in literature) and the Gini coefficient. We list five requirements which a generic ESS function should satisfy, allowing us to classify different ESS measures. We also compare the most promising ones by means of numerical simulations.

**Category:** Statistics

[49] **viXra:1602.0053 [pdf]**
*replaced on 2016-02-05 08:42:31*

**Authors:** Jason Lind

**Comments:** 3 Pages. Added preliminary calculations for correcting non-normal distribution

Defines a rated set and uses it to calculated a weight directly from the statistics that enabled broad unified interpretation of data.

**Category:** Statistics

[48] **viXra:1602.0053 [pdf]**
*replaced on 2016-02-05 03:29:44*

**Authors:** Jason Lind

**Comments:** Corrected table on page 2

Defines a rated set and uses it to calculated a weight directly from the statistics that enabled broad unified interpretation of data.

**Category:** Statistics

[47] **viXra:1601.0174 [pdf]**
*replaced on 2016-07-15 02:12:10*

**Authors:** V. Elvira, L. Martino, D. Luengo, M. F. Bugallo

**Comments:** 30 Pages.

Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal distribution and assign them weights according to the importance sampling principle. Critical issues in applying PMC methods are the choice of the generating functions for the samples and the avoidance of the sample degeneracy. In this paper, we propose three new schemes that considerably improve the performance of the original PMC formulation by allowing for better exploration of the space of unknowns and by selecting more adequately the surviving samples. A theoretical analysis is performed, proving the superiority of the novel schemes in terms of variance of the associated estimators and preservation of the sample diversity. Furthermore, we show that they outperform other state of the art algorithms (both in terms of mean square error and robustness w.r.t. initialization) through extensive numerical simulations.

**Category:** Statistics

[46] **viXra:1512.0420 [pdf]**
*replaced on 2015-12-26 13:02:26*

**Authors:** L. Martino, J. Read, V. Elvira, F. Louzada

**Comments:** 21 Pages.

We design a sequential Monte Carlo scheme for the joint purpose of Bayesian inference and model selection, with application to urban mobility context where different modalities of transport and measurement devices can be employed. In this case, we have the joint problem of online tracking and detection of the current modality. For this purpose, we use interacting parallel particle filters each one addressing a different model. They cooperate for providing a global estimator of the variable of interest and, at the same time, an approximation of the posterior density of the models given the data. The interaction occurs by a parsimonious distribution of the computational effort, adapting on-line the number of particles of each filter according to the posterior probability of the corresponding model. The resulting scheme is simple and flexible. We have tested the novel technique in different numerical experiments with artificial and real data, which confirm the robustness of the proposed scheme.

**Category:** Statistics

[45] **viXra:1508.0142 [pdf]**
*replaced on 2016-02-24 08:21:59*

**Authors:** L. Martino, F. Louzada

**Comments:** 15 Pages. To appear in Computational Statistics

The multiple Try Metropolis (MTM) algorithm is an advanced MCMC technique based on drawing and testing several candidates at each iteration of the algorithm. One of them is selected according to certain weights and then it is tested according to a suitable acceptance probability. Clearly, since the computational cost increases as the employed number of tries grows, one expects that the performance of an MTM scheme improves as the number of tries increases, as well. However, there are scenarios where the increase of number of tries does not produce a corresponding enhancement of the performance. In this work, we describe these scenarios and then we introduce possible solutions for solving these issues.

**Category:** Statistics

[44] **viXra:1508.0142 [pdf]**
*replaced on 2015-08-19 03:39:57*

**Authors:** L. Martino, F. Louzada

**Comments:** 17 Pages.

The multiple Try Metropolis (MTM) algorithm is an advanced MCMC technique based on drawing and testing several candidates at each iteration of the algorithm. One of them is selected according to certain weights and then it is tested according to a suitable acceptance probability. Clearly, since the computational cost increases as the employed number of tries grows, one expects that the performance of an MTM scheme improves as the number of tries increases, as well. However, there are scenarios where the increase of number of tries does not produce a corresponding enhancement of the performance. In this work, we describe these scenarios and then we introduce possible solutions for solving these issues.

**Category:** Statistics

[43] **viXra:1507.0110 [pdf]**
*replaced on 2015-07-30 08:34:32*

**Authors:** L. Martino, V. Elvira, D. Luengo, J. Corander, F. Louzada

**Comments:** 25 Pages.

Monte Carlo (MC) methods are widely used in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have been recently introduced. In this work, we describe a novel parallel interacting MCMC scheme, called orthogonal MCMC (O-MCMC), where a set of ``vertical'' parallel MCMC chains share information using some "horizontal" MCMC techniques working on the entire population of current states. More specifically, the vertical chains are led by random-walk proposals, whereas the horizontal MCMC techniques employ independent proposals, thus allowing an efficient combination of global exploration and local approximation. The interaction is contained in these horizontal iterations. Within the analysis of different implementations of O-MCMC, novel schemes for reducing the overall computational cost of parallel multiple try Metropolis (MTM) chains are also presented. Furthermore, a modified version of O-MCMC for optimization is provided by considering parallel simulated annealing (SA) algorithms. We also discuss the application of O-MCMC in a big bata framework. Numerical results show the advantages of the proposed sampling scheme in terms of efficiency in the estimation, as well as robustness in terms of independence with respect to initial values and parameter choice.

**Category:** Statistics

[42] **viXra:1507.0110 [pdf]**
*replaced on 2015-07-28 23:03:29*

**Authors:** L. Martino, V. Elvira, D. Luengo, J. Corander, F. Louzada

**Comments:** 24 Pages.

Monte Carlo (MC) methods are widely used in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have been recently introduced. In this work, we describe a novel parallel interacting MCMC scheme, called orthogonal MCMC (O-MCMC), where a set of ``vertical'' parallel MCMC chains share information using some "horizontal" MCMC techniques working on the entire population of current states. More specifically, the vertical chains are led by random-walk proposals, whereas the horizontal MCMC techniques employ independent proposals, thus allowing an efficient combination of global exploration and local approximation. The interaction is contained in these horizontal iterations. Within the analysis of different implementations of O-MCMC, novel schemes for reducing the overall computational cost of parallel multiple try Metropolis (MTM) chains are also presented. Furthermore, a modified version of O-MCMC for optimization is provided by considering parallel simulated annealing (SA) algorithms. We also discuss the application of O-MCMC in a big bata framework. Numerical results show the advantages of the proposed sampling scheme in terms of efficiency in the estimation, as well as robustness in terms of independence with respect to initial values and parameter choice.

**Category:** Statistics

[41] **viXra:1507.0110 [pdf]**
*replaced on 2015-07-28 08:47:05*

**Authors:** L. Martino, V. Elvira, D. Luengo, J. Corander, F. Louzada

**Comments:** 24 Pages.

Monte Carlo (MC) methods are widely used in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have been recently introduced. In this work, we describe a novel parallel interacting MCMC scheme, called orthogonal MCMC (O-MCMC), where a set of ``vertical'' parallel MCMC chains share information using some "horizontal" MCMC techniques working on the entire population of current states. More specifically, the vertical chains are led by random-walk proposals, whereas the horizontal MCMC techniques employ independent proposals, thus allowing an efficient combination of global exploration and local approximation. The interaction is contained in these horizontal iterations. Within the analysis of different implementations of O-MCMC, novel schemes for reducing the overall computational cost of parallel multiple try Metropolis (MTM) chains are also presented. Furthermore, a modified version of O-MCMC for optimization is provided by considering parallel simulated annealing (SA) algorithms. We also discuss the application of O-MCMC in a big bata framework.
Numerical results show the advantages of the proposed sampling scheme in terms of efficiency in the estimation, as well as robustness in terms of independence with respect to initial values and parameter choice.

**Category:** Statistics

[40] **viXra:1506.0175 [pdf]**
*replaced on 2015-10-04 03:38:05*

**Authors:** Ilija Barukčić

**Comments:** 19 Pages. (C) Ilija Barukčić, Jever, Germany, 2015. Published by: International Journal of Applied Physics and Mathematics vol. 6, no. 2, pp. 45-65, 2016. http://dx.doi.org/10.17706/ijapm.2016.6.2.45-65

The deterministic relationship between cause and effect is deeply connected with our understanding of the physical sciences and their explanatory ambitions. Though progress is being made, the lack of theoretical predictions and experiments in quantum gravity makes it difficult to use empirical evidence to justify a theory of causality at quantum level in normal circumstances, i. e. by predicting the value of a well-confirmed experimental result. For a variety of reasons, the problem of the deterministic relationship between cause and effect is related to basic problems of physics as such. Despite the common belief, it is a remarkable fact that a theory of causality should be consistent with a theory of everything and is because of this linked to problems of a theory of everything. Thus far, solving the problem of causality can help to solve the problems of the theory of everything (at quantum level) too.

**Category:** Statistics

[39] **viXra:1505.0135 [pdf]**
*replaced on 2016-02-25 06:00:34*

**Authors:** L. Martino, V. Elvira, D. Luengo, J. Corander

**Comments:** 24 Pages.

Monte Carlo methods represent the \textit{de facto} standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use simpler proposal probability densities to draw candidate samples. The performance of any such method is strictly related to the specification of the proposal distribution, such that unfortunate choices easily wreak havoc on the resulting estimators. In this work, we introduce a \textit{layered} (i.e., hierarchical) procedure to generate samples employed within a Monte Carlo scheme. This approach ensures that an appropriate equivalent proposal density is always obtained automatically (thus eliminating the risk of a catastrophic performance), although at the expense of a moderate increase in the complexity. Furthermore, we provide a general unified importance sampling (IS) framework, where multiple proposal densities are employed and several IS schemes are introduced by applying the so-called deterministic mixture approach. Finally, given these schemes, we also propose a novel class of adaptive importance samplers using a population of proposals, where the adaptation is driven by independent parallel or interacting Markov Chain Monte Carlo (MCMC) chains. The resulting algorithms efficiently combine the benefits of both IS and MCMC methods.

**Category:** Statistics

[38] **viXra:1505.0135 [pdf]**
*replaced on 2015-05-27 13:09:35*

**Authors:** L. Martino, V. Elvira, D. Luengo, J. Corander

**Comments:** 25 Pages.

Monte Carlo methods represent the de facto standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use simpler proposal probability densities for drawing candidate samples. Performance of any such method is strictly related to the specification of the proposal distribution, such that unfortunate choices easily wreak havoc on the resulting estimators. In this work, we introduce a layered, that is a hierarchical, procedure for generating samples employed within a Monte Carlo scheme. This approach ensures that an appropriate equivalent proposal density is always obtained automatically (thus eliminating the risk of a catastrophic performance), although at the expense of a moderate increase in the complexity. A hierarchical interpretation of two well-known methods, such as of
the random walk Metropolis-Hastings (MH) and the Population Monte Carlo (PMC) techniques, is provided. Furthermore, we provide a general unified importance sampling (IS) framework where multiple proposal densities are employed, and several IS schemes are introduced applying the so-called deterministic mixture approach. Finally, given these schemes, we also propose a novel class of adaptive importance samplers using a population of proposals, where the adaptation is driven by independent parallel or interacting Markov Chain Monte Carlo (MCMC) chains. The resulting algorithms combine efficiently the benefits of both IS and MCMC methods.

**Category:** Statistics

[37] **viXra:1503.0088 [pdf]**
*replaced on 2016-06-13 09:15:01*

**Authors:** Jianwen Huang, Jianjun Wang, Guowang Luo

**Comments:** 15 Pages.

We introduce logarithmic generalized Maxwell
distribution which is an extension of the generalized Maxwell
distribution. Some interesting properties of this distribution are
studied and the asymptotic distribution of the partial maximum of an
independent and identically distributed sequence from the
logarithmic generalized Maxwell distribution is gained. The
expansion of the limit distribution from the normalized maxima is
established under the optimal norming constants, which shows the
rate of convergence of the distribution for normalized
maximum tending to the extreme limit.

**Category:** Statistics

[36] **viXra:1412.0276 [pdf]**
*replaced on 2016-06-13 09:23:33*

**Authors:** Jianwen Huang, Jianjun Wang

**Comments:** 18 Pages.

In this paper, with optimal normalized constants,
the asymptotic expansions of the distribution and density of the
normalized maxima from generalized Maxwell distribution are derived.
For the distributional expansion, it shows that the convergence rate
of the normalized maxima to the Gumbel extreme value distribution is
proportional to $1/\log n.$ For the density expansion, on the one
hand, the main result is applied to establish the convergence rate
of the density of extreme to its limit. On the other hand, the main
result is applied to obtain the asymptotic expansion of the moment
of maximum.

**Category:** Statistics

[35] **viXra:1409.0127 [pdf]**
*replaced on 2015-03-17 07:17:05*

**Authors:** Jianwen Huang, Shouquan Chen

**Comments:** 10 Pages.

Let $\{X_n,n\geq1\}$ be an independent and
identically distributed random sequence with common distribution $F$ obeying the lognormal distribution. In this paper, we obtain the exact uniform convergence rate of the distribution of maxima to its extreme value limit under power normalization.

**Category:** Statistics

[34] **viXra:1409.0051 [pdf]**
*replaced on 2016-05-27 09:29:29*

**Authors:** L. Martino, F. Leisen, J. Corander

**Comments:** 21 Pages.

Markov Chain Monte Carlo (MCMC) algorithms and Sequential Monte Carlo (SMC) methods (a.k.a., particle filters) are well-known Monte Carlo methodologies, widely used in different fields for Bayesian inference and stochastic optimization. The Multiple Try Metropolis (MTM) algorithm is an extension of the standard Metropolis- Hastings (MH) algorithm in which the next state of the chain is chosen among a set of candidates, according to certain weights. The Particle MH (PMH) algorithm is another advanced MCMC technique specifically designed for scenarios where the multidimensional target density can be easily factorized as multiplication of conditional densities. PMH combines jointly SMC and MCMC approaches. Both, MTM and PMH, have been widely studied and applied in literature. PMH variants have been often applied for the joint purpose of tracking dynamic variables and tuning constant parameters in a state space model. Furthermore, PMH can be also considered as an alternative particle smoothing method. In this work, we investigate connections, similarities and differences among MTM schemes and PMH methods. This study allows the design of novel efficient schemes for filtering and smoothing purposes in state space models. More specially, one of them, called Particle Multiple Try Metropolis (P-MTM), obtains very promising results in different numerical simulations.

**Category:** Statistics

[33] **viXra:1409.0051 [pdf]**
*replaced on 2016-05-25 09:33:48*

**Authors:** L. Martino, F. Leisen, J. Corander

**Comments:** 20 Pages.

Markov Chain Monte Carlo (MCMC) algorithms and Sequential Monte Carlo (SMC) methods (a.k.a., particle filters)
are well-known Monte Carlo methodologies, widely used in different fields for Bayesian inference and stochastic
optimization. The Multiple Try Metropolis (MTM) algorithm is an extension of the standard Metropolis-Hastings
(MH) algorithm in which the next state of the chain is chosen among a set of candidates, according to certain weights.
The Particle MH (PMH) algorithm is other advanced MCMC technique specifically designed for scenarios where the
multidimensional target density can be easily factorized as multiplication of conditional densities. PMH combines
SMC and MCMC approaches. Both, MTM and PMH, have been widely studied and applied in literature. PMH
variants have been often applied for the joint purpose of tracking dynamic variables and tuning constant parameters
in a state space model. Furthermore, PMH can be also considered as an alternative particle smoothing method. In
this work, we investigate similarities and differences among the MTM schemes and the PMH method. This study allows the design of novel efficient schemes for filtering and smoothing purposes for state space models. Specially one of them, called particle Multiple Try Metropolis (P-MTM), obtains very promising results in different numerical simulations.

**Category:** Statistics

[32] **viXra:1409.0051 [pdf]**
*replaced on 2016-03-17 14:39:23*

**Authors:** L. Martino, F. Leisen, J. Corander

**Comments:** 16 Pages.

Markov Chain Monte Carlo (MCMC) methods are well-known Monte Carlo methodologies, widely used in different fields for statistical inference and stochastic optimization. The Multiple Try Metropolis (MTM) algorithm is an extension of the standard Metropolis-Hastings (MH) algorithm in which the next state of the chain is chosen among a set of candidates, according to certain weights. The Particle MH (PMH) algorithm is other advanced MCMC technique specifically designed for scenarios where the multidimensional target density can be easily factorized as multiplication of (lower - dimensional) conditional densities. Both have been widely studied and applied in literature. In this note, we investigate similarities and differences among the MTM schemes and the PMH method. Furthermore, novel schemes are also designed.

**Category:** Statistics

[31] **viXra:1409.0051 [pdf]**
*replaced on 2016-02-17 13:27:24*

**Authors:** L. Martino, F. Leisen, J. Corander

**Comments:** 15 Pages.

Markov Chain Monte Carlo (MCMC) methods are well-known Monte Carlo methodologies, widely used in different fields for statistical inference and stochastic optimization. The Multiple Try Metropolis (MTM) algorithm is an extension of the standard Metropolis-Hastings (MH) algorithm in which the next state of the chain is chosen among a set of candidates, according to certain weights. The Particle MH (PMH) algorithm is other advanced MCMC technique specifically designed for scenarios where the multidimensional target density can be easily factorized as multiplication of (lower - dimensional) conditional densities. Both have been widely studied and applied in literature. In this note, we investigate similarities and differences among the MTM schemes and the PMH method. Furthermore, novel schemes are also designed.

**Category:** Statistics

[30] **viXra:1409.0051 [pdf]**
*replaced on 2016-01-14 12:54:49*

**Authors:** L. Martino, F. Leisen, J. Corander

**Comments:** 14 Pages.

Markov Chain Monte Carlo (MCMC) methods are well-known Monte Carlo methodologies, widely used in different fields for statistical inference and stochastic optimization. The Multiple Try Metropolis (MTM) algorithm is an extension of the standard Metropolis-Hastings (MH) algorithm in which the next state of the chain is chosen among a set of candidates, according to certain weights. The Particle MH (PMH) algorithm is other advanced MCMC technique specifically designed for scenarios where the multidimensional target density can be easily factorized as multiplication of (lower - dimensional) conditional densities. Both have been widely studied and applied in literature. In this note, we investigate similarities and differences among the MTM schemes and the PMH method. Furthermore, novel schemes are also designed.

**Category:** Statistics

[29] **viXra:1409.0051 [pdf]**
*replaced on 2016-01-05 08:47:18*

**Authors:** L. Martino, F. Leisen, J. Corander

**Comments:** 11 Pages.

**Category:** Statistics

[28] **viXra:1409.0051 [pdf]**
*replaced on 2016-01-04 12:40:57*

**Authors:** L. Martino, F. Leisen, J. Corander

**Comments:** 11 Pages.

**Category:** Statistics

[27] **viXra:1409.0051 [pdf]**
*replaced on 2014-09-23 02:30:02*

**Authors:** L. Martino, F. Leisen, J. Corander

**Comments:** 10 Pages.

Markov Chain Monte Carlo (MCMC) methods are well-known Monte Carlo methodologies, widely used in different fields for statistical inference and stochastic optimization. The Multiple Try Metropolis (MTM) algorithm is an extension of the standard Metropolis-Hastings (MH) algorithm in which the next state of the chain is chosen among a set of candidates, according to certain weights. The Particle MH (PMH) algorithm is other advanced MCMC technique specifically designed for scenarios where the multidimensional target density can be easily factorized as multiplication of (lower - dimensional) conditional densities. Both are widely studied and applied in literature. In this note, we investigate similarities and differences among the MTM schemes and the PMH method.

**Category:** Statistics

[26] **viXra:1409.0015 [pdf]**
*replaced on 2014-12-15 15:30:35*

**Authors:** Ellida M. Khazen

**Comments:** Pages. The paper is being publuished in Cogent Mathematics (2016), 2:1134031. http://dx.doi.org/10.1080/23311835.2015.1134031

The problem of filtering of unobservable components x(t) of a multidimensional continuous diffusion Markov process z(t)=(x(t),y(t)), given the observations of the (multidimensional) process y(t) taken at discrete consecutive times with small time steps, is analytically investigated. On the base of that investigation the new algorithms for simulation of unobservable components, x(t), and the new algorithms of nonlinear filtering with the use of sequential Monte Carlo methods, or particle filters, are developed and suggested. The analytical investigation of observed quadratic variations is also developed. The new closed form analytical formulae are obtained, which characterize dispersions of deviations of the observed quadratic variations and the accuracy of some estimates for x(t). As an illustrative example, estimation of volatility (for the problems of financial mathematics) is considered. The obtained new algorithms extend the range of applications of sequential Monte Carlo methods, or particle filters, beyond the hidden Markov models and improve their performance.

**Category:** Statistics