Multi-dimensional sequential testing and detection

TL;DR

This paper extends Bayesian sequential testing and detection to higher dimensions for Brownian motion, revealing that the cost function is unilaterally concave, which helps characterize optimal stopping strategies.

Contribution

It introduces a multidimensional extension of classical Bayesian sequential testing and establishes the concavity of the cost function for a broad class of problems.

Findings

Cost function is unilaterally concave in higher dimensions.

Structural properties of continuation and stopping regions are derived.

Concavity aids in understanding optimal detection strategies.

Abstract

We study extensions to higher dimensions of the classical Bayesian sequential testing and detection problems for Brownian motion. In the main result we show that, for a large class of problem formulations, the cost function is unilaterally concave. This concavity result is then used to deduce structural properties for the continuation and stopping regions in specific examples.