A0977
Title: Nonparametric distributional inference using likelihoods as distributional data
Authors: Karl Gerald van den Boogaart - Helmholtz Zentrum Dresden Rossendorf e.V. (Germany) [presenting]
Abstract: One kind of distributional or density data are likelihoods. This contribution is concerned with a non-parametric Bayes estimation of a (multivariate) distribution from likelihood data through Bayes space methods. For likelihoods generated by complete point observations, the subspace of the Bayes space required for the posterior distribution of the underlying distribution is approximated by a relatively small subspace, only one dimension larger than the Bayes space of the original distribution. The situation, however, gets much more complicated if the data can no longer be represented by likelihoods of point observations, but starts to incorporate partially missing data or measurement errors. Such data can still be represented in terms of likelihoods and their Bayes space representation, but is no longer limited to this subspace. It is, however, possible to project those likelihoods onto the original subspace of the point observation likelihoods and still provide a reasonable Bayes inference that can be stored in a similar number of coefficients as the underlying multivariate distribution and provides relevant knowledge about the most relevant projection of the posterior distribution of the unknown distribution.
