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(This article was first published on <strong><a href="https://xianblog.wordpress.com/2017/01/19/weakly-informative-reparameterisations-for-location-scale-mixtures/"> R – Xi'an's Og</a></strong>, and kindly contributed to <a rel="nofollow" href="https://www.r-bloggers.com/">R-bloggers)</a> </div>
<p><strong><a target="_blank" rel="nofollow" href="https://i2.wp.com/xianblog.files.wordpress.com/2017/01/fitted_density_galaxy_data_500iters.png?ssl=1"><img sizes="(max-width: 450px) 100vw, 450px" data-image-description="" data-orig-file="https://i2.wp.com/xianblog.files.wordpress.com/2017/01/fitted_density_galaxy_data_500iters.png?resize=450%2C362&amp;ssl=1" data-orig-size="810,652" data-image-title="fitted_density_galaxy_data_500iters" class="wp-image-32555" data-comments-opened="1" data-recalc-dims="1" data-attachment-id="32555" data-permalink="https://xianblog.wordpress.com/2017/01/19/weakly-informative-reparameterisations-for-location-scale-mixtures/fitted_density_galaxy_data_500iters/" alt="fitted_density_galaxy_data_500iters" data-medium-file="https://i2.wp.com/xianblog.files.wordpress.com/2017/01/fitted_density_galaxy_data_500iters.png?resize=450%2C362&amp;ssl=1?w=300" data-large-file="https://i2.wp.com/xianblog.files.wordpress.com/2017/01/fitted_density_galaxy_data_500iters.png?resize=450%2C362&amp;ssl=1?w=450" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}" src="https://i2.wp.com/xianblog.files.wordpress.com/2017/01/fitted_density_galaxy_data_500iters.png?resize=450%2C362&ssl=1"></a>W</strong>e have been working towards a revision of <a target="_blank" rel="nofollow" href="https://xianblog.wordpress.com/2016/01/11/mixtures-are-slices-of-an-orange/">our reparameterisation paper</a> for quite a while now and too advantage of Kate Lee visiting Paris this fortnight to make a final round: we have now <a target="_blank" rel="nofollow" href="https://arxiv.org/pdf/1601.01178">arXived</a> (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.</p>
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