On the adequacy of variational lower bound functions for likelihood-based inference in Markovian models with missing values

• 成果类型: Article
• 署名作者: Hall, P; Humphreys, K; Titterington, DM
• 署名单位: University of Glasgow; Australian National University; Karolinska Institutet
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/1467-9868.00350
• 发表日期: 2002
• 页码: 549-564
• 关键词: mean-field-theory; em procedures

摘要

Variational methods have been proposed for obtaining deterministic lower bounds for log-likelihoods within missing data problems, but with little formal justification or investigation of the worth of the lower bound surfaces as tools for inference. We provide, within a general Markovian context, sufficient conditions under which estimators from the variational approximations are asymptotically equivalent to maximum likelihood estimators, and we show empirically, for the simple example of a first-order autoregressive model with missing values, that the lower bound surface can be very similar in shape to the true log-likelihood in non-asymptotic situations.