Visualizing High-Dimensional Posterior Distributions in Bayesian Modeling

In Bayesian modeling inference is based on the posterior distribution of the model parameters. The closed-form solution is seldom known and samples of the posterior have to be computed with Markov Chain Monte Carlo (MCMC) methods. The problem is that for large models the samples are highdimensional, and it is hard to piece together properties of the posterior. Our proposal is to use a non-linear dimensionality reduction method for visualizing sampled posterior distributions; the current method is based on Self-Organizing Maps and Fisher metrics. Sample applications have been included on studies of convergence and mixing of the MCMC simulations, of shape (e.g. multimodality) of the posterior, and of sensitivity of the model.