Bayesian Model Comparison with the Hyvarinen Score: Computation and Consistency

• 成果类型: Article
• 署名作者: Shao, Stephane; Jacob, Pierre E.; Ding, Jie; Tarokh, Vahid
• 署名单位: Harvard University; University of Minnesota System; University of Minnesota Twin Cities; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2018.1518237
• 发表日期: 2019
• 页码: 1826-1837
• 关键词: hidden markov-models; selection; estimators; likelihood

摘要

The Bayes factor is a widely used criterion in model comparison and its logarithm is a difference of out-of-sample predictive scores under the logarithmic scoring rule. However, when some of the candidate models involve vague priors on their parameters, the log-Bayes factor features an arbitrary additive constant that hinders its interpretation. As an alternative, we consider model comparison using the Hyvarinen score. We propose a method to consistently estimate this score for parametric models, using sequential Monte Carlo methods. We show that this score can be estimated for models with tractable likelihoods as well as nonlinear non-Gaussian state-space models with intractable likelihoods. We prove the asymptotic consistency of this new model selection criterion under strong regularity assumptions in the case of nonnested models, and we provide qualitative insights for the nested case. We also use existing characterizations of proper scoring rules on discrete spaces to extend the Hyvarinen score to discrete observations. Our numerical illustrations include Levy-driven stochastic volatility models and diffusion models for population dynamics. for this article are available online.