Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ordered and size-biased frequencies in GEM and Gibbs models for species
  sampling   We describe the distribution of frequencies ordered by sample values in a
random sample of size $n$ from the two parameter GEM$(\alpha,\theta)$ random
discrete distribution on the positive integers. These frequencies are a
$($size$-\alpha)$-biased random permutation of the sample frequencies in either
ranked order, or in the order of appearance of values in the sampling process.
This generalizes a well known identity in distribution due to Donnelly and
Tavar\'e (1986) for $\alpha = 0$ to the case $0 \le \alpha < 1$. This
description extends to sampling from Gibbs$(\alpha)$ frequencies obtained by
suitable conditioning of the GEM$(\alpha,\theta)$ model, and yields a
value-ordered version of the Chinese Restaurant construction of
GEM$(\alpha,\theta)$ and Gibbs$(\alpha)$ frequencies in the more usual
size-biased order of their appearance. The proofs are based on a general
construction of a finite sample $(X_1,\dots,X_n)$ from any random frequencies
in size-biased order from the associated exchangeable random partition
$\Pi_\infty$ of $\mathbb{N}$ which they generate.

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The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th