Abstract
In Bayesian data analysis, it is often important to evaluate quantiles of the posterior distribution of a parameter of interest (e.g., to form posterior intervals). In multi-dimensional problems, when non-conjugate priors are used, this is often difficult generally requiring either an analytic or sampling-based approximation, such as Markov chain Monte-Carlo (MCMC), Approximate Bayesian computation (ABC) or variational inference. We discuss a general approach that reframes this as a multi-task learning problem and uses recurrent deep neural networks (RNNs) to approximately evaluate posterior quantiles. As RNNs carry information along a sequence, this application is particularly useful in time-series. An advantage of this risk-minimization approach is that we do not need to sample from the posterior or calculate the likelihood. We illustrate the proposed approach in several examples.