Simultaneous Credible Regions for Multiple Changepoint Locations

In a Bayesian retrospective approach, we are concerned with smallest sets of timepoints that contain all changepoints simultaneously. Combining such sets for a range of different credibilities enables the measurement of uncertainty in changepoint locations as well as the evaluation of model choices in an unprecedented way. This approach shows strong sensitivity and specificity in comparison with highest density regions, posterior marginal jump probabilities and confidence intervals inferred by stepR. Whilst their direct construction is usually intractable, we show how to compute asymptotically correct solutions utilizing a set of posterior samples. This leads to a novel NP-complete problem, which we examine in the context of hypergraphs. Through reformulations into an Integer Linear Program we show empirically that a greedy heuristic computes virtually exact solutions.