[3] **viXra:1712.0244 [pdf]**
*submitted on 2017-12-07 05:24:57*

**Authors:** Luca Martino

**Comments:** 47 Pages.

Many applications in signal processing require the estimation of some parameters of interest given a set of observed data. More specifically, Bayesian inference needs the computation of a-posteriori estimators which are often expressed as complicated multi-dimensional integrals. Unfortunately, analytical expressions for these estimators cannot be found in most real-world applications, and Monte Carlo methods are the only feasible approach. A very powerful class of Monte Carlo techniques is formed by the Markov Chain Monte Carlo (MCMC) algorithms. They generate a Markov chain such that its stationary distribution coincides with the target posterior density. In this work, we perform a thorough review of MCMC methods using multiple candidates in order to select the next state of the chain, at each iteration. With respect to the classical Metropolis-Hastings method, the use
of multiple try techniques foster the exploration of the sample space. We present different Multiple Try Metropolis schemes, Ensemble MCMC methods, Particle Metropolis-Hastings
algorithms and the Delayed Rejection Metropolis technique. We highlight limitations, benefits, connections and dierences among the different methods, and compare them by numerical simulations.

**Category:** Statistics

[2] **viXra:1712.0110 [pdf]**
*submitted on 2017-12-04 22:02:28*

**Authors:** D Williams

**Comments:** 8 Pages.

A possible alternative (and non-standard) model of probability is presented based on non-standard "dx-less" integrals. The possibility of other such models is discussed.

**Category:** Statistics

[1] **viXra:1712.0018 [pdf]**
*submitted on 2017-12-03 02:40:26*

**Authors:** Ilija Barukčić

**Comments:** 50 pages. Copyright © 2017 by Ilija Barukčić, Horandstrasse, Jever, Germany. Published by:

Objective: Many times a positive relationship between Helicobacter pylori infection and gastric cancer has been reported, yet findings are inconsistent.
Methods: A literature search in PubMed was performed to re-evaluate the relationship between Helicobacter pylori (HP) and carcinoma of human stomach. Case control studies with a least 500 participants were consider for a review and meta-analysis. The meta-/re-analysis was conducted using conditio-sine qua non relationship and the causal relationship k. Significance was indicated by a p-value of less than 0.05.
Result: All studies analyzed provide impressive evidence of a cause effect relationship between H. pylori and gastric cancer (GC). Two very great studies were able to make the proof that H. pylori is a necessary condition of human gastric cancer. In other words, without H. pylori infection no human gastric cancer.
Conclusion: Our findings indicate that Helicobacter pylori (H. pylori) is the cause of gastric carcinoma.

**Category:** Statistics