Conjugate Gamma Markov Random Fields for Modelling Nonstationary Sources

In modelling nonstationary sources, one possible strategy is to define a latent process of strictly positive variables to model variations in second order statistics of the underlying process. This can be achieved, for example, by passing a Gaussian process through a positive nonlinearity or defining a discrete state Markov chain where each state encodes a certain regime. However, models with such constructs turn out to be either not very flexible or non-conjugate, making inference somewhat harder. In this paper, we introduce a conjugate (inverse-) gamma Markov Random field model that allows random fluctuations on variances which are useful as priors for nonstationary time-frequency energy distributions. The main idea is to introduce auxiliary variables such that full conditional distributions and sufficient statistics are readily available as closed form expressions. This allows straightforward implementation of a Gibbs sampler or a variational algorithm. We illustrate our approach on...

• Type: Conference
• Year: 2007
• Where: ICA
• Authors: Ali Taylan Cemgil, Onur Dikmen
• Keywords: Discrete State Markov, ICA 2007, Markov Random Field, Signal Processing, Time-frequency Energy Distributions