|
Abstract:
|
Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating 2^J terms, with J the number of discrete variables. Currently, data augmentation methods are used to carry out inference for discrete copula and in practice, the computation becomes intractable when J is large. Our article proposes two new fast Bayesian approaches for estimating high dimensional copulas with discrete margins, or a combination of discrete and continuous margins. Both methods are based on recent advances in Bayesian methodology that work with an unbiased estimate of the likelihood rather than the likelihood itself, and our key observation is that we can estimate the likelihood of a discrete copula unbiasedly with much less computation than evaluating the likelihood exactly or with current simulations methods that are based on augmenting the model with latent variables. The first approach builds on the pseudo marginal method. The second approach is based on a Variational Bayes approximation to the posterior.
|
