Steven Campbell (Columbia University)

A Tractable Triple Problem in Sequential Inference: Filtering, Control, and Stopping

Abstract: We study a Bayesian sequential inference problem for the drift of a Brownian motion in which the observer not only chooses their stopping and decision rules, but also controls the rate at which information is acquired. This extension introduces a cost for information acquisition, transforming the classical formulation of Shiryaev (1967) into a joint problem of filtering, control, and optimal stopping. Problems of this kind arise in adaptive experimental design and real-time inference across domains such as healthcare, finance, and engineering, where information is costly and decision-making must be timely. Our framework accommodates a host of classification losses and general running costs on the control process. Despite the added complexity, the problem admits a remarkably simple and semi-explicit solution that exhibits structural parallels with the classical setting. This work highlights a rare instance in which a triple problem—combining inference, control, and stopping—remains analytically tractable. Based on joint work with Georgy Gaitsgori and Richard Groenewald.