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

Author

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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)

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.

Suggested Citation

  • Ye Chen & Ilya O. Ryzhov, 2020. "Technical Note—Consistency Analysis of Sequential Learning Under Approximate Bayesian Inference," Operations Research, INFORMS, vol. 68(1), pages 295-307, January.
    • Handle: RePEc:inm:oropre:v:68:y:2020:i:1:p:295-307
    DOI: 10.1287/opre.2019.1850
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    References listed on IDEAS

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