Summary A new class of dependent random measures which we call compound is proposed and the use normalized versions these as priors in Bayesian non-parametric mixture models considered. Their tractability allows properties both to be derived. In particular, show how can constructed with gamma, σ-stable generalized gamma process marginals. We also derive several forms Laplace exponent characterize dependence through Lévy copula correlation function. An augmented Pólya urn scheme sampler a...

Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, some applications, exchangeability may not appropriate. We introduce a novel and probabilistically coherent family non-exchangeable sequences by tractable predictive probability function with weights driven sequence independent Beta random variables. compare their theoretical clustering properties those the Dirichlet Process two parameters Poisson-Dirichlet process....

We are living in the big data era, as current technologies and networks allow for easy routine collection of sets different disciplines. Bayesian Statistics offers a flexible modeling approach which is attractive describing complexity these datasets. These models often exhibit likelihood function intractable due to large sample size, high number parameters, or functional complexity. Approximate Computational (ABC) methods provides likelihood-free performing statistical inferences with...

In this paper the theory of species sampling sequences is linked to conditionally identically distributed in order enlarge set which are mathematically tractable. The conditional identity distribution (see Berti, Pratelli and Rigo (2004)) a new type dependence for random variables, generalizes well-known notion exchangeability. class sequences, called generalized , defined condition have given. Moreover, two types sequence that introduced studied: Poisson-Dirichlet Ottawa . Some examples discussed.

We deal with Bayesian model selection for beta autoregressive processes. discuss the choice of parameter and priors possible restrictions suggest a Reversible Jump Markov-Chain Monte Carlo (RJMCMC) procedure based on Metropolis-Hastings within Gibbs algorithm.

Monte Carlo methods have become essential tools to solve complex Bayesian inference problems in different fields, such as computational statistics, machine learning, and statistical signal processing. In this work, we introduce a novel class of adaptive methods, called independent sticky Markov Chain (MCMC) algorithms, sample efficiently from any bounded target probability density function (pdf). The new algorithms employs non-parametric proposal densities, which closer the number iterations...

Summary There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach a set algorithms known as Approximate Computational (ABC) methods. the these that their performance depends appropriate choice summary statistics, distance measure and tolerance level. To circumvent this problem, alternative method based empirical likelihood has been introduced. This can be easily implemented when constraints, related...

Summary Several studies on heritability in twins aim at understanding the different contribution of environmental and genetic factors to specific traits. Considering national merit twin study, our purpose is analyse correctly influence socio-economic status relationship between twins’ cognitive abilities. Our methodology based conditional copulas, which enable us model effect a covariate driving strength dependence main variables. We propose flexible Bayesian non-parametric approach for...

Let X=(X1,X2,…) be a sequence of random variables with values in standard space (S,B). Suppose X1∼νandP(Xn+1∈⋅∣X1,…,Xn)=θν(⋅)+ ∑i=1nK(Xi)(⋅) n+θa.s. where θ>0 is constant, ν probability measure on B, and K B. Then, X exchangeable whenever regular conditional distribution for given any sub-σ-field Under this assumption, enjoys all the main properties classical Dirichlet sequences, including Sethuraman's representation, conjugacy property, convergence total variation predictive distributions....

Random probability vectors are of great interest especially in view their application to statistical inference. Indeed, they can be used for identifying the de Finetti mixing measure representation law a partially exchangeable array random elements taking values separable and complete metric space. In this paper we describe construction vector Dirichlet processes based on normalization an completely measures that jointly infinitely divisible. After deducing form multivariate Laplace exponent...

We build on the derivative pricing calibration literature, and propose a more general model for implied risk neutral densities. Our allows joint of set densities at different maturities dates through Bayesian dynamic Beta Markov Random Field. approach possible time dependence between with same maturity, across point in time. This to density problem encompasses flexibility, parameter parsimony, and, importantly, information pooling proposed methodology can be naturally extended other areas...

AbstractIn the big data era there is a growing need to model main features of large and non-trivial sets. This paper proposes Bayesian nonparametric prior for modelling situations where are divided into different units with densities, allowing information pooling across groups. Leisen Lijoi [(2011), 'Vectors Poisson–Dirichlet processes', J. Multivariate Anal., 102, 482–495] introduced bivariate vector random probability measures marginals dependence induced through Lévy's Copula. In this...

Let (Xn : n ≥ 1) be a sequence of random observations.Let σn(•) = P (Xn+1 ∈ • | X1, . ., Xn) the nth predictive distribution and σ0(•)=P (X1 •) marginal X1.To make predictions on (Xn), Bayesian forecaster needs only collection σ (σn 0).From Ionescu-Tulcea theorem, can assigned directly, without passing through usual prior/posterior scheme.One main advantage is that no prior probability has to selected.This point view adopted in this paper.The choice subject two requirements: (i) resulting...

Abstract In this article, a new Pólya urn model is introduced and studied; in particular, strong law of large numbers two central limit theorems are proved. This generalizes studied Berti et al. (Citation2004), May (Citation2005), Crimaldi (Citation2007), it has natural applications clinical trials. Indeed, the includes both delayed missing (or null) responses. Moreover, connection with conditional identity distribution (Citation2004) given. Keywords: Almost sure coverageClinical...

Normalized compound random measures are flexible nonparametric priors for related distributions. We consider building general regression models using normalized measure mixture models. Posterior inference is made a novel pseudo-marginal Metropolis-Hastings sampler The algorithm makes use of new approach to the unbiased estimation Laplace functionals (which includes completely as special case). illustrated on problems density regression.

The Yule–Simon distribution has been out of the radar Bayesian community, so far. In this note, we propose an explicit Gibbs sampling scheme when a Gamma prior is chosen for shape parameter. performance algorithm illustrated with simulation studies, including count data regression, and real application to text analysis. We compare our proposal frequentist counterparts showing better small sample size considered.

The analysis of categorical response data through the multinomial model is very frequent in many statistical, econometric, and biometric applications. However, one main problems precise estimation parameters when number observations low. We propose a new Bayesian approach where prior distribution constructed transformation multivariate beta Olkin Liu (2003 , I. R. ( 2003 ). A bivariate . Stat. Probab. Lett. 62 : 407 – 412 .[Crossref], [Web Science ®] [Google Scholar]). Moreover, application...

The number of immigrants moving to and settling in Europe has increased over the past decade, making migration one most topical pressing issues European politics. It is without a doubt that immigration multiple impacts, terms economy, society culture, on Union. fundamental policy-makers correctly evaluate people's attitudes towards when designing integration policies. Of critical interest properly discriminate between subjects who are favourable from those against it. Public opinions...