Marginal likelihood estimation via power posteriors

• 成果类型: Article
• 署名作者: Friel, N.; Pettitt, A. N.
• 署名单位: University College Dublin; Queensland University of Technology (QUT); Lancaster University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2007.00650.x
• 发表日期: 2008
• 页码: 589-607
• 关键词: monte-carlo methods; normalizing constants; Bayes Factors; models

摘要

Model choice plays an increasingly important role in statistics. From a Bayesian perspective a crucial goal is to compute the marginal likelihood of the data for a given model. However, this is typically a difficult task since it amounts to integrating over all model parameters. The aim of the paper is to illustrate how this may be achieved by using ideas from thermodynamic integration or path sampling. We show how the marginal likelihood can be computed via Markov chain Monte Carlo methods on modified posterior distributions for each model. This then allows Bayes factors or posterior model probabilities to be calculated. We show that this approach requires very little tuning and is straightforward to implement. The new method is illustrated in a variety of challenging statistical settings.