Bayesian Estimation of Normal and Probit Psychometric Models

This paper synthesizes popular approaches to Bayesian estimation of psychometric models that rely on the multivariate normal distribution, including point estimation of posterior central tendency, Gibbs sampling, and Hamiltonian sampling.We place emphasis on the geometry of the posterior distribution, on building intuition by drawing connections to regression, and on providing background about how relevant matrix results are obtained.We also consider how the results can be extended to handle related psychometric models, including popular item response models.The goal is to provide researchers with ideas and tools for designing their own Bayesian estimation methods, which we hope will lead to continued developments and improvements.