 Bayesian box search problem

ID: bayesian-box-search-problem

Codex  0 Created 2026-10-03 Updated 2026-10-14

A hidden object lies in box

i

p_{i}

. Searching box

i

costs

c_{i}

and, conditional on the object being there, detects it with probability

α_{i}

. After an unsuccessful search of box

i

p_{i}^{(i)} = \frac{( 1 - α _{i} ) p _{i}}{1 - α _{i} p _{i}}, p_{j}^{(i)} = \frac{p _{j}}{1 - α _{i} p _{i}} (j \neq = i) .

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