Economics at your fingertips  

Likelihood-free inference in high dimensions with synthetic likelihood

Victor M.-H. Ong, David J. Nott, Minh-Ngoc Tran, Scott A. Sisson and Christopher C. Drovandi

Computational Statistics & Data Analysis, 2018, vol. 128, issue C, 271-291

Abstract: One popular approach to likelihood-free inference is the synthetic likelihood method, which assumes that some data summary statistics which are informative about model parameters are approximately Gaussian for each value of the parameter. Based on this assumption, a Gaussian likelihood can be constructed, where the mean and covariance matrix of the summary statistics are estimated via Monte Carlo. The objective of the current work is to improve on a variational implementation of the Bayesian synthetic likelihood introduced recently in the literature, to enable the application of that approach to high-dimensional problems. Here high-dimensional can mean problems with more than one hundred parameters. The improvements introduced relate to shrinkage estimation of covariance matrices in estimation of the synthetic likelihood, improved implementation of control variate approaches to stochastic gradient variance reduction, and parsimonious but expressive parametrizations of variational normal posterior covariance matrices in terms of factor structures to reduce the dimension of the optimization problem. The shrinkage covariance estimation is particularly important for stability of stochastic gradient optimization with noisy likelihood estimates. However, as the dimension increases, the quality of the posterior approximation deteriorates unless the number of Monte Carlo samples used to estimate the synthetic likelihood also increases. We explore the properties of the method in some real examples in cases where either the number of summary statistics, the number of model parameters, or both, are large.

Keywords: Approximate Bayesian computations; Stochastic gradient ascent; Synthetic likelihood; Variational Bayes (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed

Downloads: (external link)
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Dana Niculescu ().

Page updated 2018-11-10
Handle: RePEc:eee:csdana:v:128:y:2018:i:c:p:271-291