Parameter Estimation: The Proper Way to Use Bayesian Posterior Processes with Brownian Noise

• 成果类型: Article
• 署名作者: Cohen, Asaf
• 署名单位: Technion Israel Institute of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2014.0674
• 发表日期: 2015
• 页码: 361-389
• 关键词: wiener disorder problem; diffusion-processes; Levy processes; experimentation

摘要

This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior distribution processes is, in general, not equal to the posterior distribution process of the mentioned Brownian motion with the unknown drift. Instead, it is equal to the posterior distribution process associated with a Brownian motion with the same unknown drift and a different standard deviation coefficient. The difference between the two standard deviation coefficients can be arbitrarily large. The characterization of the limit of the posterior distribution processes is then applied to a family of stopping time problems. We show that the proper way to find asymptotically optimal solutions to stopping time problems, with respect to the scaled counting processes, is by looking at the limit of the posterior distribution processes rather than by the naive approach of looking at the limit of the scaled counting processes themselves. The difference between the performances can be arbitrarily large.