Global Consensus Monte Carlo

Autor: Anthony Lee, Nick Whiteley, Lewis J. Rendell, Adam M. Johansen
Rok vydání: 2020
Předmět:
Zdroj: Rendell, L J, Johansen, A M, Lee, A & Whiteley, N 2020, ' Global consensus Monte Carlo ', Journal of Computational and Graphical Statistics . https://doi.org/10.1080/10618600.2020.1811105
ISSN: 1537-2715
1061-8600
DOI: 10.1080/10618600.2020.1811105
Popis: To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by global variable consensus optimisation, we introduce an instrumental hierarchical model associating auxiliary statistical parameters with each term, which are conditionally independent given the top-level parameters. One of these top-level parameters controls the unconditional strength of association between the auxiliary parameters. This model leads to a distributed MCMC algorithm on an extended state space yielding approximations of posterior expectations. A trade-off between computational tractability and fidelity to the original model can be controlled by changing the association strength in the instrumental model. We further propose the use of a SMC sampler with a sequence of association strengths, allowing both the automatic determination of appropriate strengths and for a bias correction technique to be applied. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples.\ud \ud
Databáze: OpenAIRE
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