belief_trajectory: Compute a belief trajectory from sequential evidence

In mispitools: Missing Person Identification Tools

Compute a belief trajectory from sequential evidence

Description

Given a prior distribution over hypotheses and a sequence of likelihood ratio vectors (one per evidence step), computes the full Bayesian belief trajectory by sequential multiplicative updating.

Usage

belief_trajectory(prior, lr_list)

Arguments

prior	Numeric vector. Prior distribution over the n hypotheses (must sum to 1, entries in [0, 1]).
lr_list	List of numeric vectors. Each element is the likelihood ratio vector for an evidence step, with one entry per hypothesis (same length as prior).

Details

The update rule is the classical multiplicative Bayesian update:

P_t(H_i) \propto P_{t-1}(H_i) \cdot \mathrm{LR}_t(H_i)

with renormalization after each step. In the two-hypothesis case (n = 2), the ratio of the components of lr_list[[t]] recovers the classical forensic likelihood ratio.

Value

A matrix with (T+1) rows and n columns, where row 1 is the prior and row t+1 is the posterior distribution after the first t evidence steps. Each row is a probability distribution.

References

Marsico, F. L. & Egeland, T. (in preparation). Belief dynamics during the investigative process.

See Also

binary_belief_trajectory for the two-hypothesis special case, trajectory_metrics for summary statistics.

Examples

# Two hypotheses, three evidence steps
prior <- c(0.5, 0.5)
lr_list <- list(c(3, 1), c(1, 2), c(2, 1))
traj <- belief_trajectory(prior, lr_list)
print(traj)

mispitools documentation built on Aug. 26, 2026, 1:08 a.m.