Optimal sequential procedures with Bayes decision rules

TL;DR

This paper investigates optimal sequential decision procedures for discrete-time stochastic processes, aiming to minimize sample size while controlling Bayesian risk, and characterizes the structure of these procedures.

Contribution

It provides a characterization of the form of optimal sequential stopping rules and decision procedures under Bayesian risk constraints, including observation costs.

Findings

Optimal stopping rules are characterized mathematically.

Decision procedures balance Bayesian risk and observation costs.

Framework applies to general discrete-time stochastic processes.

Abstract

In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed some given bound. We characterize the form of optimal sequential stopping rules in this problem. In particular, we have a characterization of the form of optimal sequential decision procedures when the Bayesian risk includes both the loss due to incorrect decision and the cost of observations.