An Adaptive Sequential Monte Carlo Sampler
نویسندگان
چکیده
Sequential Monte Carlo (SMC) methods are not only a popular tool in the analysis of state–space models, but offer an alternative to Markov chain Monte Carlo (MCMC) in situations where Bayesian inference must proceed via simulation. This paper introduces a new SMC method that uses adaptive MCMC kernels for particle dynamics. The proposed algorithm features an online stochastic optimization procedure to select the best MCMC kernel and simultaneously learn optimal tuning parameters. Theoretical results are presented that justify the approach and give guidance on how it should be implemented. Empirical results, based on analysing data from mixture models, show that the new adaptive SMC algorithm (ASMC) can both choose the best MCMC kernel, and learn an appropriate scaling for it. ASMC with a choice between kernels outperformed the adaptive MCMC algorithm of Haario et al. (1998) in 5 out of the 6 cases considered.
منابع مشابه
Monte Carlo Techniques for Bayesian Statistical Inference – A comparative review
In this article, we summariseMonte Carlo simulationmethods commonly used in Bayesian statistical computing. We give descriptions for each algorithm and provide R codes for their implementation via a simple 2-dimensional example. We compare the relative merits of these methods qualitatively by considering their general user-friendliness, and numerically in terms of mean squared error and computa...
متن کاملOn sequential Monte Carlo, partial rejection control and approximate Bayesian computation
We present a sequential Monte Carlo sampler variant of the partial rejection control algorithm introduced by Liu (2001), termed SMC sampler PRC, and show that this variant can be considered under the same framework of the sequential Monte Carlo sampler of Del Moral et al. (2006). We make connections with existing algorithms and theoretical results, and extend some theoretical results to the SMC...
متن کاملChannel Tracking for Relay Networks via Adaptive Particle MCMC
This paper presents a new approach for channel tracking and parameter estimation in cooperative wireless relay networks. We consider a system with multiple relay nodes operating under an amplify and forward relay function. We develop a novel algorithm to efficiently solve the challenging problem of joint channel tracking and parameters estimation of the Jakes’ system model within a mobile wirel...
متن کاملGeneralised linear mixed model analysis via sequential Monte Carlo sampling
We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely difficult, even when using the Bayesian approach combined with Markov chain Monte Carlo (MCMC). The Sequential Monte Carlo sampler (SMC) is a new and general...
متن کاملImplementing Random Scan Gibbs Samplers I
The Gibbs sampler, being a popular routine amongst Markov chain Monte Carlo sampling methodologies, has revolutionized the application of Monte Carlo methods in statistical computing practice. The performance of the Gibbs sampler relies heavily on the choice of sweep strategy, that is, the means by which the components or blocks of the random vector X of interest are visited and updated. We dev...
متن کامل