DeepAI AI Chat
Log In Sign Up

Group Importance Sampling for Particle Filtering and MCMC

by   L. Martino, et al.

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, 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.


Layered Adaptive Importance Sampling

Monte Carlo methods represent the "de facto" standard for approximating ...

Iterative importance sampling with Markov chain Monte Carlo sampling in robust Bayesian analysis

Bayesian inference under a set of priors, called robust Bayesian analysi...

MCMC-driven importance samplers

Monte Carlo methods are the standard procedure for estimating complicate...

Semi-independent resampling for particle filtering

Among Sequential Monte Carlo (SMC) methods,Sampling Importance Resamplin...

Compressed Monte Carlo with application in particle filtering

Bayesian models have become very popular over the last years in several ...

A Sequential Importance Sampling Algorithm for Estimating Linear Extensions

In recent decades, a number of profound theorems concerning approximatio...

Multiple target tracking with interaction using an MCMC MRF Particle Filter

This paper presents and discusses an implementation of a multiple target...