An \(\mathcal{O}(\log_2N)\) SMC\(^2\) Algorithm on Distributed Memory with an Approx. Optimal L-Kernel

Calibrating statistical models using Bayesian inference often requires both accurate and timely estimates of parameters of interest. Particle Markov Chain Monte Carlo (p-MCMC) and Sequential Monte Carlo Squared (SMC\(^2\)) are two methods that use an unbiased estimate of the log-likelihood obtained...

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Bibliographic Details
Published inarXiv.org
Main Authors Rosato, Conor, Varsi, Alessandro, Murphy, Joshua, Maskell, Simon
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.11.2023
Subjects
Algorithms
Bayesian analysis
Biocompatibility
Biomedical materials
Distributed memory
Importance sampling
Kernels
Markov analysis
Markov chains
Recycling programs
Resampling
Statistical inference
Statistical models
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Summary:Calibrating statistical models using Bayesian inference often requires both accurate and timely estimates of parameters of interest. Particle Markov Chain Monte Carlo (p-MCMC) and Sequential Monte Carlo Squared (SMC\(^2\)) are two methods that use an unbiased estimate of the log-likelihood obtained from a particle filter (PF) to evaluate the target distribution. P-MCMC constructs a single Markov chain which is sequential by nature so cannot be readily parallelized using Distributed Memory (DM) architectures. This is in contrast to SMC\(^2\) which includes processes, such as importance sampling, that are described as \textit{embarrassingly parallel}. However, difficulties arise when attempting to parallelize resampling. None-the-less, the choice of backward kernel, recycling scheme and compatibility with DM architectures makes SMC\(^2\) an attractive option when compared with p-MCMC. In this paper, we present an SMC\(^2\) framework that includes the following features: an optimal (in terms of time complexity) \(\mathcal{O}(\log_2N)\) parallelization for DM architectures, an approximately optimal (in terms of accuracy) backward kernel, and an efficient recycling scheme. On a cluster of \(128\) DM processors, the results on a biomedical application show that SMC\(^2\) achieves up to a \(70\times\) speed-up vs its sequential implementation. It is also more accurate and roughly \(54\times\) faster than p-MCMC. A GitHub link is given which provides access to the code.
ISSN:2331-8422