1,721,129 research outputs found
A note on regions of given probability for the extended skew-normal distribution
Full text linkThe construction of regions with assigned probability p and minimum geometric measure has theoretical and practical interests, such as the construction of tolerance regions. Following Azzalini (2001) and exploiting the normal approximation of the extended skew-normal distribution when some of its parameters go to infinity, we discuss an approach for the construction of regions with assigned probability p for the bivariate extended skew-normal distribution
Statistical aspects in the extended skew-normal model
Full text linkThis paper presents some inferential results about the extended skew- normal family in the scalar case. For this family many inferential aspects are still unexplored. The expected information matrix is obtained and some of its properties are discussed. Some simulation experiments and an application to real data are pre- sented pointing out not infrequent estimation problems such as different estimates in function of the starting values of the algorithm which leads to substantially equivalents densities. All these issues underline a problem of near unidentifiability
msBP: An R package to perform Bayesian nonparametric inference using multiscale Bernstein polynomials mixtures
Full text linkmsBP is an R package that implements a new method to perform Bayesian multiscale nonparametric inference introduced by Canale and Dunson (2016). The method, based on mixtures of multiscale beta dictionary densities, overcomes the drawbacks of Pólya trees and inherits many of the advantages of Dirichlet process mixture models. The key idea is that an infinitely-deep binary tree is introduced, with a beta dictionary density assigned to each node of the tree. Using a multiscale stick-breaking characterization, stochastically decreasing weights are assigned to each node. The result is an infinite mixture model. The package msBP implements a series of basic functions to deal with this family of priors such as random densities and numbers generation, creation and manipulation of binary tree objects, and generic functions to plot and print the results. In addition, it implements the Gibbs samplers for posterior computation to perform multiscale density estimation and multiscale testing of group differences described in Canale and Dunson (2016)
Bayesian nonparametric models for count data with applications to customer base management
Full text linkMotivated by the analysis of telecommunications marketing data, which are multidimensional, longitudinal and mostly consisting in counts, this thesis introduces novel Bayesian nonparametric techniques for the estimation of probability mass functions and count stochastic processes. In addition, the theoretical basis of nonparametric mixture models for mixed-scale density estimation are provided. Mixed-scale data consists in joint continuous, count and categorical variables. Although Bayesian nonparametric models for continuous variables are well developed, the literature on related approaches for counts is limited and that for mixed-scale variables is close to none. The leading idea of this work is to induce prior distributions on the spaces of interest via priors on suitable latent spaces and mapping functions. Precisely a class of priors on the space of the probability mass functions and of the mixed-scale densities is induced through priors on the space of continuous densities and another class of priors on count stochastic process is induced through priors on the space of continuous stochastic processes. Asymptotic properties of these procedures are studied and results in terms of large support and posterior consistency are obtained under suitable assumptions.
Efficient Gibbs samplers are developed for posterior computation, and the performance of the proposed methods is assessed in simulation studies and real data applications.Motivati dall'analisi di dati di marketing nelle telecomunicazioni, solitamente multidimensionali, longitudinali e per lo più composti da conteggi,
questo lavoro di tesi introduce nuove tecniche bayesiane nonparametriche per la stima delle funzioni di probabilità e la modellazione dei processi stocastici a valori interi. Sono introdotti inoltre i fondamenti teorici per la stima di densità congiunta con variabili su scale di misura miste (continue, conteggio e categoriali) tramite modelli mistura nonparametrica. Sebbene i modelli bayesiani nonparametrici per variabili continue siano ben sviluppati, la letteratura su approcci simili per dati di conteggio è scarsa, mentre quella per dati su diverse scale di misura è praticamente inesistente. L'idea principale di questo lavoro è quella di indurre distribuzioni a priori sugli spazi astratti di interesse tramite distribuzioni a priori su appropriati spazi latenti e funzioni di mappatura. Nello specifico, attraverso a priori sullo spazio delle densità countinue è introdotta una nuova classe di a priori sullo spazio delle funzioni di probabilità discrete e a scala di misura mista, mentre attravesto a priori sullo spazio dei processi stocastici a valori continui è introdotta una classe di a priori sui processi stocastici di conteggio. Le proprietà asintotiche di queste procedure sono studiate e, sotto opportune ipotesi, vengono dimostrati risultati sull'ampiezza del supporto e sulla consistenza dell'a posteriori. Vengono inoltre sviluppati efficienti algoritmi di campionamento di Gibbs per il calcolo delle a posteriori. Le prestazioni dei metodi proposti sono verificate tramite studi di simulazione e applicazioni a dati reali
Bayesian nonparametric location–scale–shape mixtures
No full textDiscrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location–scale mixture of Gaussian kernels is the golden standard, both having nice theoretical properties and computational tractability. In this paper we explore the use of the skew-normal kernel, which can naturally accommodate several degrees of skewness by the use of a third parameter. The choice of this kernel function allows us to formulate nonparametric location–scale–shape mixture prior with desirable theoretical properties and good performance in different applications. Efficient Gibbs sampling algorithms are also discussed and the performance of the methods are tested through simulations and applications to galaxy velocity and fertility data. Extensions to accommodate discrete data are also discussed
Quantifying prediction uncertainty for functional-and-scalar to functional autoregressive models under shape constraints
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Multiscale Bernstein polynomials for densities
Full text linkOur focus is on constructing a multiscale nonparametric prior for densities. The Bayes density estimation literature is dominated by single scale methods, with the exception of Polya trees, which favor overly-spiky densities even when the truth is smooth. We propose a multiscale Bernstein polynomial family of priors, which produce smooth realizations that do not rely on hard partitioning of the support. At each level in an infinitely-deep binary tree, we place a beta dictionary density; within a scale the densities are equivalent to Bernstein polynomials. Using a stick-breaking characterization, stochastically decreasing weights are allocated to the finer scale dictionary elements. A slice sampler is used for posterior computation, and properties are described. The method characterizes densities with locally-varying smoothness, and can produce a sequence of coarse to fine density estimates. An extension for Bayesian testing of group differences is introduced and applied to DNA methylat..
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