Changepoint detection with random partition models

Bayesian nonparametric (BNP) models are a valuable tool for cluster analysis with the advantage of inferring the number of clusters directly from the data. These models rely on a mixture model framework utilizing a discrete random measure, allowing for the induction of distribution over random partitions to cluster the data. This flexibility enables BNP models to handle datasets with varying cluster sizes and shapes, making them suitable for scenarios with unknown data generation processes. To incorporate temporal dependence, BNP models can specify dependent random measures, extending the well-known Dirichlet process (DP). A novel random partition model is introduced that incorporates temporal dependence by connecting the partition of data points at a specific time to the previous time partition. Useful information is leveraged across time while only considering dependence when supported by the data, where a changepoint indicates independence between the partitions at time t and time t-1. The proposed modelling strategy is simpler to implement compared to existing methodologies and utilizes a Gibbs sampling method. Additionally, the construction of the prior distribution for the partition adopts concepts from spike and slab priors, albeit within the space of partitions, introducing added complexity to the framework.