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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Pitman-Yor process is a random discrete probability distribution of whichthe atoms can be used to model the relative abundance of species. The processis indexed by a type parameter $\sigma$, which controls the number of differentspecies in a finite sample from a realization of the distribution. A randomsample of size $n$ from the Pitman-Yor process of type $\sigma>0$ will containof the order $n^\sigma$ distinct values (``species''). In this paper weconsider the estimation of the type parameter by both empirical Bayes and fullBayes methods. We derive the asymptotic normality of the empirical Bayesestimator and a Bernstein-von Mises theorem for the full Bayes posterior, inthe frequentist setup that the observations are a random sample from a giventrue distribution. We also consider the estimation of the second parameter ofthe Pitman-Yor process, the prior precision. We apply our results to derive thelimit behaviour of the likelihood ratio in a setting of forensic statistics.

Empirical and Full Bayes estimation of the type of a Pitman-Yor process