Abstract: Integer-valued autoregressive (INAR) models are widely used for count time series, preserving discreteness and temporal dependence. While early Bayesian developments focused on simple INAR(1) models, inference was primarily based on Gibbs sampling and related MCMC schemes. As models became more flexible, hybrid MCMC algorithms combining Gibbs and Metropolis–Hastings steps were introduced to handle non-conjugacy and richer dynamics.
Particular emphasis has been given to models incorporating structural changes, including threshold and change-point INAR formulations. These approaches allow the underlying process to evolve across regimes, introducing additional uncertainty that can be naturally addressed within a Bayesian framework, often via trans-dimensional MCMC or latent Markov structures.
The talk concludes with a discussion of current challenges and future directions, including scalable inference, improved identification of structural changes, and integration of INAR models within broader probabilistic frameworks.
Isabel Pereira is an Associate Professor in the Department of Mathematics at the University of Aveiro and a researcher at CIDMA. Her research focuses on methodological developments in Bayesian statistics, modeling, and prediction in nonlinear time series and count data, with publications in leading international journals. She has extensive teaching experience in Statistics at undergraduate, master’s, and doctoral levels and has actively contributed to the organization of scientific events, serving on scientific committees and reviewing academic publications. She has also held leadership roles within the Department of Mathematics and the Portuguese Statistical Society, supporting the development of statistical research and education in Portugal.
ORCID: 0000-0002-5152-546X