Surajit Dutta
Email ralopezm@geologia.unam.mx
https://doi.org/10.61618/LLSH2304
Abstract
Search and rescue (SAR) planning repeatedly confronts the same operational challenge: how to allocate limited search effort across sectors when information is incomplete and detection is imperfect. This paper presents a Bayesian decision-support framework for SAR tasking that maintains a spatial belief map over a discretized search region (interpretable as Probability of Area, POA) and updates it after each unsuccessful search using Bayes’ theorem, explicitly accounting for Probability of Detection (POD) that may vary by terrain, access, and sensing modality. At each step, the framework prioritizes the sector maximizing POA × POD, i.e., the sector with the highest immediate Probability of Success (POS). The title’s “vanishing posterior” refers to a key operational insight: when POD < 1, a negative result does not drive a sector’s POA to zero, formalizing why re-search decisions remain rational in low-detectability terrain. The paper further outlines practical extensions relevant to SAR: (i) terrain-aware POD models, (ii) informed priors derived from geospatial or historical cues, (iii) belief propagation for moving subjects, and (iv) a POMDP framing for longer-horizon planning under explicit costs. Proof-of-concept simulations illustrate how POA concentrates over time and how imperfect detection slows clearance of difficult terrain. Limitations of grid-based simulations are acknowledged, and a worked hypothetical SAR example demonstrates how the framework can support sector prioritization and allocation of effort in planning practice.
KEY WORDS: Bayes’ theorem; Search and rescue (SAR); Probability of Area (POA); Probability of Detection (POD); Probability of Success (POS); Imperfect detection; Terrain-aware search; Belief updating; Dynamic subject modelling