A latent process approach to change-point detection of mixed-type observations

Mixed-type observations, such as continuous measurements, discrete counts, and binary outcomes, are commonly present in many applications. The change-point detection with mixed-type observations is challenging since it is difficult to quantify the hidden association among mixed-type observations. In this work, we propose a latent process method to model the mixed observations in a joint manner, and effectively detect the changes. Bayesian parameter estimation and inference are developed for the proposed method by combining the discrete particle filter (DPF) and sequential Monte Carlo (SMC) algorithms. Such an algorithm can efficiently update the high dimensional proposal distribution and can exploit the discrete and continuous natures of the latent processes simultaneously. The performance of the proposed method is illustrated by several numerical examples and a case study of civil-unrest data.