Simultaneous Credible Regions for Multiple Changepoint Locations

Abstract

Within a Bayesian retrospective framework, we present a way of examining the distribution of \cps through a novel set estimator. For a given level, $\alpha$, we aim at smallest sets that cover all \cps with a probability of at least $1-\alpha$. These so-called smallest simultaneous credible regions, computed for certain values of $\alpha$, provide parsimonious representations of the possible \cp locations. In addition, combining them for a range of different $\alpha$'s enables very informative yet condensed visualisations. Therewith we allow for the evaluation of model choices and the analysis of \cp data to an unprecedented degree. This approach exhibits superior sensitivity, specificity and interpretability in comparison with highest density regions, marginal inclusion probabilities and confidence intervals inferred by \stepR. Whilst their direct construction is usually intractable, asymptotically correct solutions can be derived from posterior samples. This leads to a novel NP-complete problem. Through reformulations into an Integer Linear Program we show empirically that a fast greedy heuristic computes virtually exact solutions.