Search results for "Slice sampling"
showing 6 items of 6 documents
Group Metropolis Sampling
2017
Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. Two well-known class of MC methods are the Importance Sampling (IS) techniques and the Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce the Group Importance Sampling (GIS) framework where different sets of weighted samples are properly summarized with one summary particle and one summary weight. GIS facilitates the design of novel efficient MC techniques. For instance, we present the Group Metropolis Sampling (GMS) algorithm which produces a Markov chain of sets of weighted samples. GMS in general outperforms other multiple try schemes…
Recycling Gibbs sampling
2017
Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning and statistics. The key point for the successful application of the Gibbs sampler is the ability to draw samples from the full-conditional probability density functions efficiently. In the general case this is not possible, so in order to speed up the convergence of the chain, it is required to generate auxiliary samples. However, such intermediate information is finally disregarded. In this work, we show that these auxiliary samples can be recycled within the Gibbs estimators, improving their efficiency with no extra cost. Theoretical and exhaustive numerical co…
The Recycling Gibbs sampler for efficient learning
2018
Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from complicated high-dimensional posterior distributions. The key point for the successful application of the Gibbs sampler is the ability to draw efficiently samples from the full-conditional probability density functions. Since in the general case this is not possible, in order to speed up the convergence of the chain, it is required to generate auxiliary samples whose information is eventually disregarded. In this work, we show that these auxiliary sample…
Avoiding Boundary Effects in Wang-Landau Sampling
2003
A simple modification of the ``Wang-Landau sampling'' algorithm removes the systematic error that occurs at the boundary of the range of energy over which the random walk takes place in the original algorithm.
Anti-tempered Layered Adaptive Importance Sampling
2017
Monte Carlo (MC) methods are widely used for Bayesian inference in signal processing, machine learning and statistics. In this work, we introduce an adaptive importance sampler which mixes together the benefits of the Importance Sampling (IS) and Markov Chain Monte Carlo (MCMC) approaches. Different parallel MCMC chains provide the location parameters of the proposal probability density functions (pdfs) used in an IS method. The MCMC algorithms consider a tempered version of the posterior distribution as invariant density. We also provide an exhaustive theoretical support explaining why, in the presented technique, even an anti-tempering strategy (reducing the scaling of the posterior) can …
Monte-Carlo Methods
2003
The article conbtains sections titled: 1 Introduction and Overview 2 Random-Number Generation 2.1 General Introduction 2.2 Properties That a Random-Number Generator (RNG) Should Have 2.3 Comments about a Few Frequently Used Generators 3 Simple Sampling of Probability Distributions Using Random Numbers 3.1 Numerical Estimation of Known Probability Distributions 3.2 “Importance Sampling” versus “Simple Sampling” 3.3 Monte-Carlo as a Method of Integration 3.4 Infinite Integration Space 3.5 Random Selection of Lattice Sites 3.6 The Self-Avoiding Walk Problem 3.7 Simple Sampling versus Biased Sampling: the Example of SAWs Continued 4 Survey of Applications to Simulation of Transport Processes 4.…