MICH Posterior Credible Sets — mich

The function mich_sets() takes a T x N matrix of posterior change-point location probabilities probs, a coverage level level, and a max set length, and for column i of probs returns the MAP estimator which.max(probs[,i]) and the smallest set of indices s_i such that probs[s_i,i] > level if length(s_i) < max_length.

Usage

mich_sets(probs, max_length = log(nrow(probs))^1.5, level = 0.9)

Arguments

probs: A numeric Matrix. A T x N matrix of posterior probabilities for the location of the change-points.
max_length: A positive scalar. Detection threshold, if a credible set contains more that max_length indices, then no change is detected. Set equal to log(T)^1.5 by default (see Section 2.5 of Berlind, Cappello, and Madrid Padilla (2025)).
level: A scalar. A single number in (0,1) that gives the lower bound for the probability that each credible set contains a change-point.

Value

A list. MAP estimator of each change-point and corresponding credible set.