1,720,998 research outputs found
Covariance Ordering for discrete and continuous time Markov Chains
No full textThe covariance ordering, for discrete and continuous time Markov chains, is defined and studied. This partial ordering gives a necessary and sufficient condition for MCMC estimators to have small asymptotic variance. Connections between this ordering, eigenvalues, and suprema of the spectrum of the Markov transition kernel, are provided. A representation of the asymptotic variance of MCMC estimators in terms of eigenvalues and eigenvectors is extended to continuous time. This representation is used to establish convergence of the asymptotic variance of MCMC estimators derived from the discretization of a continuous time Markov chain
Bayesian Model Selection for Beta Autoregressive Processes
No full textWe deal with Bayesian model selection for beta autoregressive processes. We discuss the choice of parameter and model priors with possible parameter restrictions and suggest a Reversible Jump Markov-Chain Monte Carlo (RJMCMC) procedure based on a Metropolis-Hastings within Gibbs algorithm.We deal with Bayesian model selection for beta autoregressive processes. We discuss the choice of parameter and model priors with possible parameter restrictions and suggest a Reversible Jump Markov-Chain Monte Carlo (RJMCMC) procedure based on a Metropolis-Hastings within Gibbs algorithm
Merging Exchangeable Occupancy Distributions: The Family M^(a) and its Connection with the Maximum Entropy Principle
No full textIn this paper a new transformation of occupancy distributions, called merging, is introduced. In particular, it will be studied the effect of merging on a class of occupancy distributions that was recently introduced in Collet et al. (Probab Eng Inf Sci. 27:533-552 2013). These results have an interesting interpretation in the so-called entropy maximization inference. The last part of the paper is devoted to highlight the impact of our findings in this research area
Completely random measures and Lévy bases in free probability
Full text linkThis paper develops a theory for completely random measures in the framework of free probability. A general existence result for free completely random measures is established, and in analogy to the classical work of Kingman it is proved that such random measures can be decomposed into the sum of a purely atomic part and a (freely) infinitely divisible part. The latter part (termed a free Lévy basis) is studied in detail in terms of the free Lévy-Khintchine representation and a theory parallel to the classical work of Rajput and Rosiński is developed. Finally a Lévy-Itô type decomposition for general free Lévy bases is established
Vectors of two-parameter Poisson–Dirichlet processes
Full text linkThe definition of vectors of dependent random probability measures is a topic of interest in applications to Bayesian statistics. They represent dependent nonparametric prior distributions that are useful for modelling observables for which specific covariate values are known. In this paper we propose a vector of two-parameter Poisson–Dirichlet processes. It is well-known that each component can be obtained by resorting to a change of measure of a ?-stable process. Thus dependence is achieved by applying a Lévy copula to the marginal intensities. In a two-sample problem, we determine the corresponding partition probability function which turns out to be partially exchangeable. Moreover, we evaluate predictive and posterior distributions
Beta-Product Dependent Pitman-Yor Processes for Bayesian Inference
No full textMultiple time series data may exhibit clustering over time and the clustering effect may change across different series. This paper is motivated by the Bayesian non–parametric modelling of the dependence between clustering effects in multiple time series analysis. We follow a Dirichlet process mixture approach and define a new class of multivariate dependent Pitman-Yor processes (DPY). The proposed DPY are represented in terms of a vector of stickbreaking processes which determines dependent clustering structures in the time series. We
follow a hierarchical specification of the DPY base measure to accounts for various degrees of information pooling across the series. We discuss some theoretical properties of the DPY and use them to define Bayesian non parametric repeated measurement and vector autoregressive models. We provide efficient Monte Carlo Markov Chain algorithms for posterior computation of the proposed models and illustrate the effectiveness of the method with a simulation study and an application to the United States and the European Union business cycles
Exchangeable occupancy models and discrete processes with the generalized uniform order statistics property
No full textThis work focuses on Exchangeable Occupancy Models (EOMs) and their relations with the Uniform Order Statistics Property (UOSP) for point processes in discrete time. As our main purpose, we show how definitions and results presented in Shaked, Spizzichino, and Suter [8] can be unified and generalized in the frame of occupancy models. We first show some general facts about EOMs. Then we introduce a class of EOMs, called M^(a)-models, and a concept of generalized Uniform Order Statistics Property in discrete time. For processes with this property, we prove a general characterization result in terms of M^(a)-models. Our interest is also focused on properties of closure w.r.t. some natural transformations of EOMs
Adaptive sticky generalized Metropolis
No full textWe introduce a new class of adaptive Metropolis algorithms called adaptive sticky algorithms for efficient general-purpose simulation from a target probability distribution. The transition of the Metropolis chain is based on a multiple-try scheme and the different proposals are generated by adaptive nonparametric distributions. Our adaptation strategy uses the interpolation of support points from the past history of the chain as in the adaptive rejection Metropolis. The algorithm efficiency is strengthened by a step that controls the evolution of the set of support points. This extra stage reduces the computational cost and accelerates the convergence of the proposal distribution to the target. Despite the algorithms are presented for univariate target distributions, we show that they can be easily extended to the multivariate context. We show the ergodicity of the proposed algorithms and illustrate their efficiency and effectiveness through some simulated examples involving target distributions with complex structures
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