Tractable nonparametric Bayesian inference in Poisson processes with Gaussian process intensities

The inhomogeneous Poisson process is a point process that has varying intensity across its domain (usually time or space). For nonparametric Bayesian modeling, the Gaussian process is a useful way to place a prior distribution on this intensity. The combination of a Poisson process and GP is known as a Gaussian Cox process, or doubly-stochastic Poisson process. Likelihood-based inference in these models requires an intractable integral over an infinite-dimensional random function. In this paper we present the first approach to Gaussian Cox processes in which it is possible to perform inference without introducing approximations or finite-dimensional proxy distributions. We call our method the Sigmoidal Gaussian Cox Process, which uses a generative model for Poisson data to enable tractable inference via Markov chain Monte Carlo. We compare our methods to competing methods on synthetic data and apply it to several real-world data sets.

Bayesian learning of noisy Markov decision processes

This work addresses the problem of estimating the optimal value function in a Markov Decision Process from observed state-action pairs. We adopt a Bayesian approach to inference, which allows both the model to be estimated and predictions about actions to be made in a unified framework, providing a principled approach to mimicry of a controller on the basis of observed data. A new Markov chain Monte Carlo (MCMC) sampler is devised for simulation from theposterior distribution over the optimal value function. This step includes a parameter expansion step, which is shown to be essential for good convergence properties of the MCMC sampler. As an illustration, the method is applied to learning a human controller.