Authors: Ramesh Chandra Bagadi
Comments: 2 Pages.
In this research investigation, the author has presented two Forecasting Models.
Authors: Zhicheng Chen
Comments: 4 Pages.
Distributions play a very important role in many applications. Inspired by the newly developed warping transformation of distributions, an indirect nonparametric distribution to distribution regression method is proposed in this article for predicting correlated one-dimensional continuous probability density functions.
In Structural Health Monitoring, there are usually many strain sensors installed in different places of a single structure. The raw measurement of a strain sensor is generally a mixed response caused by different excitations such as moving vehicle loads, ambient temperature, etc. Monitoring data collected by different strain sensors are usually correlated with each other, correlation structures of responses caused by different excitations for different sensor pairs are quite diverse and complex. In Structural Health Monitoring, quantitatively describing and modeling complicated dependence structures of strain data is very important in many applications. In this article, copulas are exploited to characterize dependence structures and construct joint distributions of monitoring strain data. The constructed joint distribution is also applied in missing data imputation.
It is shown that the formula for the variance of combined series yields surprisingly simple proofs of some well known variance bounds.
Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals involving a posterior distribution by means of weighted samples. In this work, we study the assignation of a single weighted sample which compresses the information contained in a population of weighted samples. Part of the theory that we present as Group Importance Sampling (GIS) has been employed implicitly in different works in the literature. The provided analysis yields several theoretical and practical consequences. For instance, we discuss the application of GIS into the Sequential Importance Resampling framework and show that Independent Multiple Try Metropolis schemes can be interpreted as a standard Metropolis-Hastings algorithm, following the GIS approach. We also introduce two novel Markov Chain Monte Carlo techniques based on GIS. The first one, named Group Metropolis Sampling method, produces a Markov chain of sets of weighted samples. All these sets are then employed for obtaining a unique global estimator. The second one is the Distributed Particle Metropolis-Hastings technique, where different parallel particle filters are jointly used to drive an MCMC algorithm. Different resampled trajectories are compared and then tested with a proper acceptance probability. The novel schemes are tested in different numerical experiments such as learning the hyperparameters of Gaussian Processes, the localization problem in a wireless sensor network and the tracking of vegetation parameters given satellite observations, where they are compared with several benchmark Monte Carlo techniques. Three illustrative Matlab demos are also provided.