Remarks on consistency of posterior distributions

By Taeryon Choi, Ravi Ramamoorthi. 2008

50 citations recorded by the source corpus.

In recent years, the literature in the area of Bayesian asymptotics has been rapidly growing. It is increasingly important to understand the con- cept of posterior consistency and validate specific Bayesian methods, in terms of consistency of posterior distributions. In this paper, we build up some con- ceptual issues in consistency of posterior distributions, and discuss panoramic views of them by comparing various approaches to posterior consistency that have been investigated in the literature. In addition, we provide interesting results on posterior consistency that deal with non-exponential consistency, improper priors and non i.i.d. (independent but not identically distributed) observations. We describe a few examples for illustrative purposes.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cccc823b5c9b110ec1339bf5359f55c4d4b205bf

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Citations in the corpus

Dynamics of Bayesian Updating with Dependent Data and Misspecified Models (2009, background): “Keywords and phrases: asymptotic equipartition, Bayesian consistency, Bayesian nonparametrics, Egorov’s theorem, large deviations, posterior convergence, replicator dynamics, sofic systems.”
Thompson Sampling for Learning Parameterized Markov Decision Processes (2014, methodology): “…quantities), and (b) control of the posterior probability using properties of the prior in Kullback-Leibler neighborhoods of the true parameter, using techniques analogous to those used to establish frequentist consistency of Bayesian procedures (Ghosal et al., 2000; Choi and Ramamoorthi, 2008).”