Group Importance Sampling for Particle Filtering and MCMC

Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques have become very popular in signal processing over the last years. 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 (MCMC) 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, two localization problems in a wireless sensor network (with synthetic and real data) 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.Comment: To appear in Digital Signal Processing. Related Matlab demos are provided at https://github.com/lukafree/GIS.gi

Effect of Play-Way Method on Academic performance among Nursery school pupils in Gombe Metropolis, Gombe State

This study examined the Effect of Play-Way Method on Academic performance among Nursery school pupils in Gombe Metropolis, Gombe State. The study objectives were: to determine the effect of play way method and conventional teaching method in the pretest mean scores among Nursery school pupils in Gombe Metropolis To determined Performance of pupils taught using Play-way method and those exposed to conventional method in Gombe metropolis and to Determine Performance of male and female pupils taught using Play-way teaching method Nursery school pupils in Gombe Metropolis. Two research questions and one hypothesis guided the study. The study adopted quasi experimental research design. The participants in the study comprised of 45 pupils from two Nursery Schools in Gombe metropolis. Convenience sampling technique was uses in drawing the participants. The data was analyzed using T-test, The findings obtained from the research showed that pupils in the control group had slightly higher initial scores on the pre-test mean scores compared to the experimental group in the pretest, also, experimental group is superior to control group in facilitating achievement among pupils in the post test, finally there is no significant difference in the gender difference of the posttest analysis using the experimental group. The study concluded that given the extensive developmental benefits that play gives during a child's early years, the play-way approach is the most suitable way for children in early childhood programs to develop and learn Recommended that Educators should incorporate more play-based learning activities into their curriculum

A multiple-try Metropolis-Hastings algorithm with tailored proposals

We present a new multiple-try Metropolis-Hastings algorithm designed to be especially beneficial when a tailored proposal distribution is available. The algorithm is based on a given acyclic graph $G$, where one of the nodes in $G$, $k$ say, contains the current state of the Markov chain and the remaining nodes contain proposed states generated by applying the tailored proposal distribution. The Metropolis-Hastings algorithm alternates between two types of updates. The first update type is using the tailored proposal distribution to generate new states in all nodes in $G$ except in node $k$. The second update type is generating a new value for $k$, thereby changing the value of the current state. We evaluate the effectiveness of the proposed scheme in an example with previously defined target and proposal distributions