IRIS Uni Torinohttps://iris.unito.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Sun, 15 Dec 2019 01:58:59 GMT2019-12-15T01:58:59Z10591MCMC for normalized random measure mixture modelshttp://hdl.handle.net/2318/142753Titolo: MCMC for normalized random measure mixture models
Abstract: This paper concerns the use of Markov chain Monte Carlo methods for posterior sampling in Bayesian nonparametric mixture models with normalized random measure priors. Making use of some recent posterior characterizations for the class of normalized random measures, we propose novel Markov chain Monte Carlo methods of both marginal type and conditional type. The proposed marginal samplers are generalizations of Neal’s well-regarded Algorithm 8 for Dirichlet process mixture models, whereas the conditional sampler is a variation of those recently introduced in the literature. For both the marginal and conditional methods, we consider as a running example a mixture model with an underlying normalized generalized Gamma process prior, and describe comparative simulation results demonstrating the efficacies of the proposed methods.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/2318/1427532013-01-01T00:00:00ZBayesian nonparametric analysis of reversible Markov chainshttp://hdl.handle.net/2318/142752Titolo: Bayesian nonparametric analysis of reversible Markov chains
Abstract: We introduce a three parameter random walk with reinforcement, called the (t,a,b) scheme, which generalizes the linearly edge reinforced random walk to uncountable spaces. The parameter b smoothly tunes the (t,a,b) scheme between this edge reinforced random walk and the classical exchangeable two-parameter Hoppe urn scheme, while the parameters a and t modulate how many states are typically visited. Resorting to de Finetti’s theorem for Markov chains, we use the (t,a,b) scheme to define a nonparametric prior for Bayesian analysis of reversible Markov chains. The prior is applied in Bayesian nonparametric inference for species sampling problems with data generated from a reversible Markov chain with an unknown transition kernel. As a real example, we analyze data from molecular dynamics simulations of protein folding.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/2318/1427522013-01-01T00:00:00ZA marginal sampler for σ-stable Poisson-Kingman mixture modelshttp://hdl.handle.net/2318/1591190Titolo: A marginal sampler for σ-stable Poisson-Kingman mixture models
Abstract: We investigate the class of σ-stable Poisson-Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs which encompasses most of the popular discrete RPMs used in Bayesian nonparametrics, such as the Dirichlet process, Pitman-Yor process, the normalized inverse Gaussian process and the normalized generalized Gamma process. We show how certain sampling properties and marginal characterisations of σ-stable Poisson-Kingman RPMs can be usefully exploited for devising a Markov chain Monte Carlo (MCMC) algorithm for performing posterior inference with a Bayesian nonparametric mixture model. Specifically, we introduce a novel and efficient MCMC sampling scheme in an augmented space that has a fixed number of auxiliary variables per iteration. We apply our sampling scheme to a density estimation and clustering tasks with unidimensional and multidimensional datasets, and compare it against competing MCMC sampling schemes.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/2318/15911902017-01-01T00:00:00ZOn a class of distributions on the simplexhttp://hdl.handle.net/2318/88037Titolo: On a class of distributions on the simplex
Abstract: In the present paper we define and investigate a novel class of distributions on the simplex, termed normalized infinitely divisible distributions, which includes the Dirichlet distribution. Distributional properties and general moment formulae are derived. Particular attention is devoted
to special cases of normalized infinitely divisible distributions which lead to explicit expressions. As a by--product also new distributions over the unit interval and a generalization of the Bessel function distribution are obtained.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/2318/880372011-01-01T00:00:00ZA class of measure-valued Markov chains and Bayesian nonparametricshttp://hdl.handle.net/2318/83834Titolo: A class of measure-valued Markov chains and Bayesian nonparametrics
Abstract: Measure-valued Markov chains have raised interest in Bayesian nonparametrics since the seminal paper by Feigin and Tweedie where a Markov chain having the law of the Dirichlet process as unique invariant measure has been introduced. In the present paper we propose and investigate a new class of measure-valued Markov chains deﬁned via exchangeable sequences of random variables. Asymptotic properties for this new class are derived and applications related to Bayesian nonparametric mixture modelling, and to a generalization of the Markov chain proposed by [12], are discussed. These results and their applications highlight once again the interplay between Bayesian nonparametrics and the theory of measure-valued
Markov chains.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/2318/838342012-01-01T00:00:00ZAsymptotics for the number of blocks in a conditional Ewens-Pitman sampling modelhttp://hdl.handle.net/2318/155542Titolo: Asymptotics for the number of blocks in a conditional Ewens-Pitman sampling model
Abstract: The study of random partitions has been an active research area in probability over the last twenty years. A quantity that has attracted a lot of attention is the number of blocks in the random partition. Depending on the area of applications this quantity could represent the number of species in a sample from a population of individuals or he number of cycles in a random permutation, etc. In the context of Bayesian nonparametric inference such a quantity is associated with the exchangeable random partition induced by sampling from certain prior models, for instance the Dirichlet process and the two parameter Poisson-Dirichlet process. In this paper we generalize some existing asymptotic results from this prior setting to the so-called posterior, or conditional, setting. Specifically, given an initial sample from a two parameter Poisson-Dirichlet process, we establish conditional fluctuation limits and conditional large deviation principles for the number of blocks generated by a large additional sample.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/2318/1555422014-01-01T00:00:00ZSuperposition of beta processeshttp://hdl.handle.net/2318/91919Titolo: Superposition of beta processes
Abstract: We consider a neutral to the right process that corresponds to the superposition of independent beta processes at the cumulative hazard level. It places a prior distribution on the survival distribution resulting from independent competing failure times. It can be derived as the inﬁnitesimal weak limit of a discrete time process which has the conditional probability of an event at time t given survival up to t deﬁned as the result of a series of m independent Bernoulli experiments. The continuous time version of the process, termed m-fold beta NTR process, is described in terms of completely random measures. We discuss prior speciﬁcation and illustrate posterior inference on a real data example.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/2318/919192009-01-01T00:00:00ZBayesian nonparametric inference on rare species varietyhttp://hdl.handle.net/2318/87072Titolo: Bayesian nonparametric inference on rare species variety
Abstract: A Bayesian nonparametric methodology has been recently proposed for drawing inferences on the overall species variety in species sampling problems. In this paper we consider the practically important and technically challenging issue of estimating the rare species variety, namely the number of species with frequency less than a given threshold: specifically, adopting a two-parameter Poisson-Dirichlet process prior, we provide estimators for this and related quantities and study their properties. The methods are illustrated through an application on genomic data.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/2318/870722010-01-01T00:00:00ZPosterior analysis of rare variants in Gibbs-type species sampling modelshttp://hdl.handle.net/2318/155543Titolo: Posterior analysis of rare variants in Gibbs-type species sampling models
Abstract: 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.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/2318/1555432014-01-01T00:00:00ZOn some issues related to species sampling problemshttp://hdl.handle.net/2318/92613Titolo: On some issues related to species sampling problems
Abstract: Species sampling problems have a long history in ecological and biological studies. Data are recorded from a population which is made of different species and, conditionally on a sample of size n, interest lies in the evaluation of the species variety featured by an additional sample of size m. In this talk we review some recent results obtained by adopting a Bayesian nonparametric approach. In particular, we consider two issues: (i) Measurement of species richness; (ii) Assessment of rare species variety. Natural applications are related to sequencing of genomic libraries such as e.g. Expressed Sequence Tags (EST) and Cap Analysis Gene Expression (CAGE).
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/2318/926132011-01-01T00:00:00Z