A transdimensional approximate Bayesian computation using the pseudo-marginal approach for model choice

When the likelihood functions are either unavailable analytically or are computationally cumbersome to evaluate, it is impossible to implement conventional Bayesian model choice methods. Instead, approximate Bayesian computation (ABC) or the likelihood-free method can be used in order to avoid direct evaluation of the intractable likelihoods. This paper proposes a new Markov chain Monte Carlo (MCMC) method for model choice. This method is based on the pseudo-marginal approach and is appropriate for situations where the likelihood functions for the competing models are intractable. This method proposes jumps between the models with different dimensionalities without matching the dimensionalities. Therefore, it enables the construction of a flexible proposal distribution. The proposal distribution used in this paper is convenient to implement and works well in the context of ABC. Because the posterior model probabilities can be estimated simultaneously, it is expected that the proposed method will be useful, especially when the number of competing models is large. In the simulation study, a comparison between the proposed and existing methods is presented. The method is then applied to the model choice problem for an exchange return model.