A0656
Title: MCMC inference for latent semi-Markov point processes
Authors: Rosario Barone - Università Cattolica del Sacro Cuore (Italy) [presenting]
Abstract: This contribution develops a Bayesian framework for inference on continuous-time point processes driven by latent semi-Markov dynamics. Unlike standard Markov-modulated models, the latent process is allowed to exhibit non-exponential sojourn times, thus capturing duration dependence and temporal heterogeneity. The framework supports a wide range of conditional intensity functions, including homogeneous Poisson, covariate-modulated, self-exciting, and self-correcting forms. Posterior inference is performed using a Metropolis-within-Gibbs sampler that combines a forward-backward algorithm tailored for semi-Markov models with a uniformization-based path-sampling strategy. This approach enables exact inference under the continuous-time model without requiring discretization or approximation steps. A simulation study confirms the method's ability to recover both latent trajectories and model parameters with high accuracy, while preserving computational efficiency. An empirical application to drug-related arrests in Chicago demonstrates that the semi-Markov specification improves the detection of latent regime shifts compared to Markovian benchmarks, particularly under self-exciting dynamics. The proposed approach offers a flexible and efficient solution for modeling event-driven data with irregular timing and complex latent structure.
