MCMC methods for univariate exponential family models with intractable normalization constants

The exchange algorithm for handling models with intractable partition functions is combined with new methods for adaptive rejection sampling in order to allow Markov chain Monte Carlo methods to sample from the posterior of a new class of exponential family models: exponential of even degree polynomials. It is demonstrated that these models have intuitive properties and can be fit to multimodal univariate datasets. Possible computational benefits of the new approach are contrasted with latent variable methods.