A Bayesian Semiparametric Approach for the Differential Analysis of Sequence Counts Data

Guindani, Michele; Sepúlveda, Nuno; Paulino, Carlos Daniel; Müller, Peter

doi:10.1111/rssc.12041

Cited by 33 publications

(44 citation statements)

References 56 publications

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“…/, and the posterior total mass parameter is incremented to MCn. In summary, Result 1 (Ferguson 1973 Example 3 (T-Cell Receptors) Guindani et al (2014) consider data on counts of distinct T-cell receptors. The diversity of T-cell receptor types is an important characteristic of the immune system.…”

Section: Posterior and Marginal Distributionsmentioning

confidence: 98%

Density Estimation: DP Models

Müller

Quintana²,

Jara³

et al. 2015

Springer Series in Statistics

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We discuss the use of nonparametric Bayesian models in density estimation, arguably one of the most basic statistical inference problems. In this chapter we introduce the Dirichlet process prior and variations of it that are the by far most commonly used nonparametric Bayesian models used in this context. Variations include the Dirichlet process mixture and the finite Dirichlet process. One critical reason for the extensive use of these models is the availability of computation efficient methods for posterior simulation. We discuss several such methods.Density estimation is concerned with inference about an unknown distribution G on the basis of an observed i.i.d. sample,If we wish to proceed with Bayesian inference, we need to complete the model with a prior probability model for the unknown parameter G. Assuming a prior model on G requires the specification of a probability model for an infinite-dimensional parameter, that is, a BNP prior. Dirichlet Process DefinitionOne of the most popular BNP models is the Dirichlet process (DP) prior. The DP model was introduced by Ferguson (1973) as a prior on the space of probability measures.Definition 1 (Dirichlet Process-DP) Let M > 0 and G 0 be a probability measure defined on S. A DP with parameters .M; G 0 / is a random probability measure G defined on S which assigns probability G.B/ to every (measurable) set B such that for each (measurable) finite partition fB 1 ; : : : ; B k g of S, the joint distribution of the

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Section: Posterior and Marginal Distributionsmentioning

confidence: 98%

Density Estimation: DP Models

Müller

Quintana²,

Jara³

et al. 2015

Springer Series in Statistics

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“…Gibbs-type priors also stand out for being particularly suited in the context of inferential problems with a large unknown number of species, which typically occur in several genomic applications. See, e.g., Lijoi et al [26], Guindani et al [16] and De Blasi et al [5].…”

Section: I |Pmentioning

confidence: 99%

“…Using the definition of M (n) l,m in (19), 16) where the distribution of (K (n) m , L (n) m ) | A n (j, n) in (A.11) is given by (A.6). We proceed along lines similar to the proof of Theorem 4 in Favaro et al [12].…”

Section: Proof Of Theoremmentioning

confidence: 99%

Posterior analysis of rare variants in Gibbs-type species sampling models

Cesari

Favaro

Nipoti

2014

Journal of Multivariate Analysis

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AMS 2000 subject classifications: 60G57 62G05 62F15 Keywords:Bayesian nonparametric inference Asymptotic credible intervals Exchangeable random partition Gibbs-type random probability measure Index of diversity Sampling formula Species sampling problem Rare variant Two parameter Poisson-Dirichlet process a b s t r a c t Species sampling problems have a long history in ecological and biological studies and a number of statistical issues, including the evaluation of species richness, are still to be addressed. In this paper, motivated by Bayesian nonparametric inference for species sampling problems, we consider the practically important and technically challenging issue of developing a comprehensive posterior analysis of the so-called rare variants, namely those species with frequency less than or equal to a given abundance threshold. In particular, by adopting a Gibbs-type prior, we provide an explicit expression for the posterior joint distribution of the frequency counts of the rare variants, and we investigate some of its statistical properties. The proposed results are illustrated by means of two novel applications to a benchmark genomic dataset.

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“…Of course by integrating the conditional probability (19) with respect to the distribution of T α,F one obtains the probability (14). By combining (18) and (19), a straightforward application of Bayes theorem leads to the following density function Due to the sufficiency of (K n , N 1,n , .…”

Section: Appendixmentioning

confidence: 99%

“…In this paper we consider the Bayesian nonparametric approach introduced in Lijoi et al [24] and further investigated in Favaro et al [13] and Favaro et al [14]. Other recent contributions to species sampling problems in the Bayesian framework are, e.g., Navarrete et al [28], Zhang and Stern [33], Barger and Bunge [6], Bacallado et al [3], Lee et al [23], Airoldi et al [1] and Guindani et al [19].…”

Section: Introductionmentioning

confidence: 99%

A note on nonparametric inference for species variety with Gibbs-type priors

Favaro¹,

James²

2015

Electron. J. Statist.

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A Bayesian nonparametric methodology has been recently introduced for estimating, given an initial observed sample, the species variety featured by an additional unobserved sample of size m. Although this methodology led to explicit posterior distributions under the general framework of Gibbs-type priors, there are situations of practical interest where m is required to be very large and the computational burden for evaluating these posterior distributions makes impossible their concrete implementation. In this paper we present a solution to this problem for a large class of Gibbs-type priors which encompasses the two parameter Poisson-Dirichlet prior and, among others, the normalized generalized Gamma prior. Our solution relies on the study of the large m asymptotic behaviour of the posterior distribution of the number of new species in the additional sample. In particular we introduce a simple characterization of the limiting posterior distribution in terms of a scale mixture with respect to a suitable latent random variable; this characterization, combined with the adaptive rejection sampling, leads to derive a large m approximation of any feature of interest from the exact posterior distribution. We show how to implement our results through a simulation study and the analysis of a dataset in linguistics.MSC 2010 subject classifications: Primary 62F15, 60G57.

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A Bayesian Semiparametric Approach for the Differential Analysis of Sequence Counts Data

Cited by 33 publications

References 56 publications

Density Estimation: DP Models

Density Estimation: DP Models

Posterior analysis of rare variants in Gibbs-type species sampling models

A note on nonparametric inference for species variety with Gibbs-type priors

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