Log In Sign Up

Unbiased approximation of posteriors via coupled particle Markov chain Monte Carlo

by   Willem van den Boom, et al.

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallelisable computation on HPC and cloud environments. Another concern is the identification of the bias and Monte Carlo error of produced averages. The above have prompted the recent development of fully (`embarrassingly') parallelisable unbiased Monte Carlo methodology based on couplings of MCMC algorithms. A caveat is that formulation of effective couplings is typically not trivial and requires model-specific technical effort. We propose couplings of sequential Monte Carlo (SMC) by considering adaptive SMC to approximate complex, high-dimensional posteriors combined with recent advances in unbiased estimation for state-space models. Coupling is then achieved at the SMC level and is, in general, not problem-specific. The resulting methodology enjoys desirable theoretical properties. We illustrate the effectiveness of the algorithm via application to two statistical models in high dimensions: (i) horseshoe regression; (ii) Gaussian graphical models.


page 24

page 33


Sequential Monte Carlo for Graphical Models

We propose a new framework for how to use sequential Monte Carlo (SMC) a...

Variational consensus Monte Carlo

Practitioners of Bayesian statistics have long depended on Markov chain ...

Sketching for Latent Dirichlet-Categorical Models

Recent work has explored transforming data sets into smaller, approximat...

Penalised t-walk MCMC

Handling multimodality that commonly arises from complicated statistical...

Robust graphical modeling of gene networks using classical and alternative T-distributions

Graphical Gaussian models have proven to be useful tools for exploring n...

Regression test of various versions of STRmix

STRmix has been in operational use since 2012 for the interpretation of ...

Code Repositories


Repository with the code used for the paper "Unbiased approximation of posteriors via coupled particle Markov chain Monte Carlo" by Willem van den Boom, Ajay Jasra, Maria De Iorio, Alexandros Beskos and Johan G. Eriksson.

view repo