Technical Note—Consistency Analysis of Sequential Learning Under Approximate Bayesian Inference

Ye Chen () and Ilya O. Ryzhov ()
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Ye Chen: Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, Virginia 23284
Ilya O. Ryzhov: Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742

Operations Research, 2020, vol. 68, issue 1, 295-307

Abstract: Approximate Bayesian inference is a powerful methodology for constructing computationally efficient statistical mechanisms for sequential learning from incomplete or censored information. Approximate Bayesian learning models have proven successful in a variety of operations research and business problems; however, prior work in this area has been primarily computational, and the consistency of approximate Bayesian estimators has been a largely open problem. We develop a new consistency theory by interpreting approximate Bayesian inference as a form of stochastic approximation (SA) with an additional “bias” term. We prove the convergence of a general SA algorithm of this form and leverage this analysis to derive the first consistency proofs for a suite of approximate Bayesian models from the recent literature.

Keywords: statistical learning; approximate Bayesian inference; censored information; incomplete information; Bayesian logistic regression (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:68:y:2020:i:1:p:295-307

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