Optimal Sequence of Tests

Abstract

This paper investigates a novel sequential information acquisition problem with correlated information sources, each sampled once. We consider a decision maker choosing between costly information acquisition and implementation, aiming to maximize expected rewards. Our model incorporates multivariate normal signals with source and time correlation. We derive Bayesian update formulas for correlated signals, revealing similarities between sequential and multivariate block update formulas. This simplification enables analytical solutions, though the dynamic programming formulation remains computationally challenging with O(T×2K) complexity. We identify special cases with more efficient O(Klog K+ T2) solutions for problems with small test costs or diagonally dominant covariance matrices. For general cases, we propose the "nCr" approximation method, demonstrating its superiority over a greedy policy through simulations. Our findings contribute to understanding sequential testing problems with correlated information sources, with applications in manufacturing, healthcare, and finance.

Keywords: Sequential Information Acquisition, Correlated Information Sources, Dynamic Programming, Bayesian Updates, Optimal Stopping, Operations Research, Decision making under uncertainty, Multivariate Normal Signals, Simulation