weakly informative reparameterisations for location-scale mixtures

January 18, 2017
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(This article was first published on R – Xi'an's Og, and kindly contributed to R-bloggers)

fitted_density_galaxy_data_500itersWe have been working towards a revision of our reparameterisation paper for quite a while now and too advantage of Kate Lee visiting Paris this fortnight to make a final round: we have now arXived (and submitted) the new version. The major change against the earlier version is the extension of the approach to a large class of models that include infinitely divisible distributions, compound Gaussian, Poisson, and exponential distributions, and completely monotonic densities. The concept remains identical: change the parameterisation of a mixture from a component-wise decomposition to a construct made of the first moment(s) of the distribution and of component-wise objects constrained by the moment equation(s). There is of course a bijection between both parameterisations, but the constraints appearing in the latter produce compact parameter spaces for which (different) uniform priors can be proposed. While the resulting posteriors are no longer conjugate, even conditional on the latent variables, standard Metropolis algorithms can be implemented to produce Monte Carlo approximations of these posteriors.

Filed under: Books, pictures, R, Statistics, University life Tagged: compound Gaussian distribution, compound Poisson distribution, MCMC, Metropolis-Hastings algorithm, mixtures of distributions, Monte Carlo Statistical Methods, reparameterisation

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