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this paper we review several of these methods, and subsequently compare them in the context of two examples, the first a simple regression example, and the second a much more challenging hierarchical longitudinal model of the kind often encountered in biostatistical practice. We find that the joint model-parameter space search methods perform adequately but can be difficult to program and tune, while the marginal likelihood methods are often less troublesome and require less in the way of additional coding. Our results suggest that the latter methods may be most appropriate for practitioners working in many standard model choice settings, while the former remain important for comparing large numbers of models, or models whose parameters cannot be easily updated in relatively few blocks. We caution however that all of the methods we compare require significant human and computer effort, suggesting that less formal Bayesian model choice methods may offer a more realistic alternative in many cases.

We propose some Bayesian methods to address the problem of fitting a signal modeled by a sequence of piecewise constant linear (in the parameters) regression models, for example, autoregressive or Volterra models. A joint prior distribution is set up over the number of the changepoints/knots, their positions, and over the orders of the linear regression models within each segment if these are unknown. Hierarchical priors are developed and, as the resulting posterior probability distributions and Bayesian estimators do not admit closed-form analytical expressions, reversible jump Markov chain Monte Carlo (MCMC) methods are derived to estimate these quantities. Results are obtained for standard denoising and segmentation of speech data problems that have already been examined in the literature. These results demonstrate the performance of our methods.

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Here we describe novel Bayesian models for time-frequency analysis of non-stationary audio waveforms. These models are based on the idea of a Gabor regression, in which a time series is represented as a superposition of time-frequency shifted versions of a simple window function. Prior distributions over the corresponding time-frequency coefficients are constructed in a manner which favours both smoothness of the estimated function and sparseness of the coefficient representation (either indirectly through scale mixtures of normals, or directly through prior probability mass at zero). In this way prior regularisation may induce a parsimonious, meaningful representation of the underlying audio time series. 1. THE DISCRETE-TIME GABOR EXPANSION The discrete-time Gabor expansion of a periodic sequence f ∈ ℓ 2 (Z) having period L is given by f = M−1 � N−1 � m=0 n=0