English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Mixtures of product distributions are a powerful device for learning aboutheterogeneity within data populations. In this class of latent structuremodels, de Finetti's mixing measure plays the central role for describing theuncertainty about the latent parameters representing heterogeneity. In thispaper posterior contraction theorems for de Finetti's mixing measure arisingfrom finite mixtures of product distributions will be established, under thesetting the number of exchangeable sequences of observed variables increaseswhile sequence length(s) may be either fixed or varied. The role of both thenumber of sequences and the sequence lengths will be carefully examined. Inorder to obtain concrete rates of convergence, a first-order identifiabilitytheory for finite mixture models and a family of sharp inverse bounds formixtures of product distributions will be developed via a harmonic analysis ofsuch latent structure models. This theory is applicable to broad classes ofprobability kernels composing the mixture model of product distributions forboth continuous and discrete domain $\mathfrak{X}$. Examples of interestinclude the case the probability kernel is only weakly identifiable in thesense of Ho and Nguyen (2016), the case where the kernel is itself a mixturedistribution as in hierarchical models, and the case the kernel may not have adensity with respect to a dominating measure on an abstract domain$\mathfrak{X}$ such as Dirichlet processes.

Convergence of de Finetti's mixing measure in latent structure models for observed exchangeable sequences