A Bayesian Nonparametric Approach to Species Sampling Problems with Ordering

by   Cecilia Balocchi, et al.

Species-sampling problems (SSPs) refer to a vast class of statistical problems that, given an observable sample from an unknown population of individuals belonging to some species, call for estimating (discrete) functionals of the unknown species composition of additional unobservable samples. A common feature of SSPs is the invariance with respect to species labelling, i.e. species' labels are immaterial in defining the functional of interest, which is at the core of the development of the Bayesian nonparametric (BNP) approach to SSPs under the popular Pitman-Yor process (PYP) prior. In this paper, we consider SSPs that are not invariant to species labelling, in the sense that an ordering or ranking is assigned to species' labels, and we develop a BNP approach to such problems. In particular, inspired by the population genetics literature on age-ordered alleles' compositions, with a renowned interest in the frequency of the oldest allele, we study the following SSP with ordering: given an observable sample from unknown population of individuals belonging to some species (alleles), with species' labels being ordered according to weights (ages), estimate the frequencies of the first r order species' labels in an enlarged sample obtained by including additional unobservable samples. Our BNP approach relies on an ordered version of the PYP prior, which leads to an explicit posterior distribution of the first r order frequencies, with corresponding estimates being simple and computationally efficient. We apply our approach to the analysis of genetic variation, showing its effectiveness in the estimation of the frequency of the oldest allele, and then discuss other applications in the contexts of citations to academic articles and online purchases of items.


Bayesian Nonparametric Inference for "Species-sampling" Problems

"Species-sampling" problems (SSPs) refer to a broad class of statistical...

Bayesian nonparametric analysis of Kingman's coalescent

Kingman's coalescent is one of the most popular models in population gen...

Scaled process priors for Bayesian nonparametric estimation of the unseen genetic variation

There is a growing interest in the estimation of the number of unseen fe...

Near-optimal estimation of the unseen under regularly varying tail populations

Given n samples from a population of individuals belonging to different ...

Stick-breaking Pitman-Yor processes given the species sampling size

Random discrete distributions, say F, known as species sampling models, ...

STADS: Software Testing as Species Discovery

A fundamental challenge of software testing is the statistically well-gr...

A Rapidly Deployable Classification System using Visual Data for the Application of Precision Weed Management

In this work we demonstrate a rapidly deployable weed classification sys...

Please sign up or login with your details

Forgot password? Click here to reset