Prior Elicitation in Multiple Change-point Models

This paper discusses Bayesian inference in change-point models. The main existing approaches either attempt to be noninformative by using a Uniform prior over change-points or use an informative hierarchical prior. Both these approaches assume a known number of change-points. We show how they have some potentially undesirable properties and discuss how these properties relate to the imposition of a fixed number of change-points. We develop a new Uniform prior which allows some of the change-points to occur out-of sample. This prior has desirable properties, can reasonably be interpreted as “noninformative” and handles the case where the number of change-points is unknown. We show how the general ideas of our approach can be extended to informative hierarchical priors. With artificial data and two empirical illustrations, we show how these different priors can have a substantial impact on estimation and prediction even with moderately large data sets.