Inference and Parameter Estimation in Gamma Chains

We investigate a class of prior models, called Gamma chains, for modelling depedicies in time-frequencyrepresentations of signals. We assume transform coefficients are drawn independently from Gaussians wherethe latent variances are coupled using Markov chains of inverse Gamma random variables. Exact inference isnot feasible but this model class is conditionally conjugate, so standard approximate inference methods likeGibbs sampling, variational Bayes or sequential Monte Carlo can be applied effectively and efficiently. Weshow how hyperparameters, that determine the coupling between prior variances of transform coefficients,can be optimised. We discuss the pros and cons of various inference schemata (variational Bayes, Gibbssampler and Sequential Monte Carlo) in terms of complexity and optimisation performance for this modelclass. We illustrate the effectiveness of our approach in audio denoising and single channel audio sourceseparation applications.