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Bayesian nonparametric estimators derived from conditional Gibbs structures
 J. PHYS. A: MATH. GEN
, 2008
"... We consider discrete nonparametric priors which induce Gibbstype exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian nonparametric estimators, which can be readily exploited for predictin ..."
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Cited by 32 (8 self)
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We consider discrete nonparametric priors which induce Gibbstype exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian nonparametric estimators, which can be readily exploited for predicting various features of additional samples. The results provide useful tools for genomic applications where prediction of future outcomes is required.
Conditional formulae for Gibbstype exchangeable random partitions
 Ann. Appl. Probab
, 2013
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Some issues on nonparametric Bayesian modeling using species sampling models
 Statist. Modllng
, 2008
"... We review some aspects of nonparametric Bayesian data analysis with discrete random probability measures. We focus on the class of species sampling models (SSM). We critically investigate the common use of the Dirichlet process (DP) prior as a default SSM choice. We discuss alternative prior specica ..."
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Cited by 8 (2 self)
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We review some aspects of nonparametric Bayesian data analysis with discrete random probability measures. We focus on the class of species sampling models (SSM). We critically investigate the common use of the Dirichlet process (DP) prior as a default SSM choice. We discuss alternative prior specications from a theoretical, computational and data analysis perspective. We conclude with a recommendation to consider SSM priors beyond the special case of the DP prior and make specic recommendations on how dierent choices can be used to re
ect prior information and how they impact the desired inference. We show the required changes in the posterior simulation schemes, and argue that the additional generality can be achieved without additional computational eort. 1
On the stickbreaking representation of normalized inverse Gaussian priors
, 2012
"... Random probability measures are the main tool for Bayesian nonparametric inference, with their laws acting as prior distributions. Many wellknown priors used in practice admit different, though equivalent, representations. In terms of computational convenience, stickbreaking representations stand ..."
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Cited by 7 (0 self)
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Random probability measures are the main tool for Bayesian nonparametric inference, with their laws acting as prior distributions. Many wellknown priors used in practice admit different, though equivalent, representations. In terms of computational convenience, stickbreaking representations stand out. In this paper we focus on the normalized inverse Gaussian process and provide a completely explicit stickbreaking representation for it. This result is of interest both from a theoretical viewpoint and for statistical practice.
Supplement B to “Bayesian semiparametric inference for multivariate doublyintervalcensored data.” DOI
, 2010
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Generalized Chinese restaurant construction of exchangeable Gibbs partitions and related results. ∗†
, 805
"... By resorting to sequential constructions of exchangeable random partitions (Pitman, 2006), and exploiting some known facts about generalized Stirling numbers, we derive a generalized Chinese restaurant process construction of exchangeable Gibbs partitions of type α (Gnedin and Pitman, 2006). Our con ..."
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Cited by 4 (3 self)
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By resorting to sequential constructions of exchangeable random partitions (Pitman, 2006), and exploiting some known facts about generalized Stirling numbers, we derive a generalized Chinese restaurant process construction of exchangeable Gibbs partitions of type α (Gnedin and Pitman, 2006). Our construction represents the natural theoretical probabilistic framework in which to embed some recent results about a Bayesian nonparametric treatment of estimation problems arising in genetic experiment under Gibbs, species sampling, models priors.
Inconsistency of Pitman–Yor Process Mixtures for the Number of Components
, 2014
"... In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and Pitman–Yor process mixtures (PYMs), more generally. While thes ..."
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Cited by 4 (3 self)
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In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and Pitman–Yor process mixtures (PYMs), more generally. While these models may be wellsuited for Bayesian density estimation, many investigators are using them for inferences about the number of components, by considering the posterior on the number of components represented in the observed data. We show that this posterior is not consistent—that is, on data from a finite mixture, it does not concentrate at the true number of components. This result applies to a large class of nonparametric mixtures, including DPMs and PYMs, over a wide variety of families of component distributions, including essentially all discrete families, as well as continuous exponential families satisfying mild regularity conditions (such as multivariate Gaussians).
2012b) A new estimator of the discovery probability
 Biometrics
"... Summary. Species sampling problems have a long history in ecological and biological studies and a number of issues, including the evaluation of species richness, the design of sampling experiments, and the estimation of rare species variety, are to be addressed. Such inferential problems have recen ..."
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Cited by 4 (1 self)
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Summary. Species sampling problems have a long history in ecological and biological studies and a number of issues, including the evaluation of species richness, the design of sampling experiments, and the estimation of rare species variety, are to be addressed. Such inferential problems have recently emerged also in genomic applications, however, exhibiting some peculiar features that make them more challenging: specifically, one has to deal with very large populations (genomic libraries) containing a huge number of distinct species (genes) and only a small portion of the library has been sampled (sequenced). These aspects motivate the Bayesian nonparametric approach we undertake, since it allows to achieve the degree of flexibility typically needed in this framework. Based on an observed sample of size n, focus will be on prediction of a key aspect of the outcome from an additional sample of size m, namely, the socalled discovery probability. In particular, conditionally on an observed basic sample of size n, we derive a novel estimator of the probability of detecting, at the (n + m + 1)th observation, species that have been observed with any given frequency in the enlarged sample of size n + m. Such an estimator admits a closedform expression that can be exactly evaluated. The result we obtain allows us to quantify both the rate at which rare species are detected and the achieved sample coverage of abundant species, as m increases. Natural applications are represented by the estimation of the probability of discovering rare genes within genomic libraries and the results are illustrated by means of two expressed sequence tags datasets.