Bayesian Intercept Decision Toy

Inputs

Prior P(Threat)

Sensor P(Evidence | Threat)

Sensor P(Evidence | Decoy)

Interceptor cost C_shot (relative)

Damage cost C_hit (relative)

Scarcity multiplier (magazine depth)

Monte Carlo trials

Interceptor magazine (initial count)

Evidence strength (likelihood ratio noise)

Decision rule: engage if P(Threat|E) × C_hit > C_shot × scarcity

Bayes Update

Posterior P(Threat | Evidence)

Threshold (Cshot×scarcity / Chit)

Decision

Bayes:

P(T|E) = (P(E|T)P(T)) / (P(E|T)P(T) + P(E|D)P(D))

Numerator:

Denominator:

As scarcity rises, effective shot cost rises, so the model demands higher confidence before shooting.

Monte Carlo Outcomes

Shots fired

Wasted shots on decoys

Threats engaged (hits prevented)

Threats NOT engaged (hits)

Magazine depletion

Monte Carlo generates a stream of “tracks.” Each track is threat or decoy (by the prior), then produces noisy evidence consistent with the sensor settings. The model applies the Bayes + threshold rule to decide.