Quantization of Prior Probabilities for Hypothesis Testing

TL;DR

This paper explores how quantizing prior probabilities affects Bayesian hypothesis testing, deriving optimal quantization conditions and analyzing implications for human decision-making in populations.

Contribution

It introduces a framework for quantizing prior probabilities in Bayesian tests, deriving optimality conditions and high-resolution approximations.

Findings

Derived nearest neighbor and centroid conditions for quantization

Established a high-resolution approximation to the distortion-rate function

Applied the theory to human decision-making scenarios

Abstract

Bayesian hypothesis testing is investigated when the prior probabilities of the hypotheses, taken as a random vector, are quantized. Nearest neighbor and centroid conditions are derived using mean Bayes risk error as a distortion measure for quantization. A high-resolution approximation to the distortion-rate function is also obtained. Human decision making in segregated populations is studied assuming Bayesian hypothesis testing with quantized priors.