Catalytic Priors: Using Synthetic Data to Specify Prior Distributions in Bayesian Analysis

Catalytic prior distributions provide general, easy-to-use and interpretable specifications of prior distributions for Bayesian analysis. They are particularly beneficial when observed data are inadequate to well-estimate a complex target model. A catalytic prior distribution is constructed by augmenting the observed data with synthetic data that are sampled from the predictive distribution of a simpler model estimated from the observed data. We illustrate the usefulness of the catalytic prior approach in an example from labor economics. In the example, the resulting Bayesian inference reflects many important aspects of the observed data, and the estimation accuracy and predictive performance of the inference based on the catalytic prior are superior to, or comparable to, that of other commonly used prior distributions. We further explore the connection between the catalytic prior approach and a few popular regularization methods. We expect the catalytic prior approach to be useful in many applications.