1,721,036 research outputs found
Polinomi di Bernstein e processo di Dirichlet
No full textI study the behavior of the Bernstein polynomial approximation of a random distribution having a Dirichlet process probability law
Analisi bayesiana di modelli "annidati" (Bayesian analysis of nested models)
No full textWe describe a Gibbs sampling algorithm for Bayesian analysis of mixtures models with a random number of components, and known components. For this problem (but in the more general case of unknown components), reversible jump MCMC techniques have been recently proposed (Richardson, Green, 1997). The difference between the two approaches is due to the choice of a different parametrization of the problem. This provides an example which shows how the choice of the parametrization also has implications on the computational techniques
On the role of mixtures in Bayesian nonparametrics
No full textMixture models are widely used, in a vaste range of applied fields, to model heterogeneity in the data, or as flexible modeling tools.
In this paper we focus on the role of mixtures in Bayesian nonparametrics. Based on results by Feller, we present a constructive approximation scheme of (random) distribution functions by mixtures. We obtain a general framework to study nonparametric priors based on mixtures. We review some recent results for the univariate case, in particular on consistency
of the posterior distribution. Then, we present novel extensions to the multivariate case
Discussion on "Bayesian nonparametric inference for random distributions and related functions", by Walker, S.G., Damien, P., Laud, P.W., Smith, A.F.M.
No full textDiscussione del lavoro citato e svilupp
Discussion on "Choosing among models when none of them are true", by Key, J.T., Pericchi, L.R. and Smith, A.F.M.
No full textDiscussion, pages 355-358
Bayesian density estimation using Bernstein polynomials
No full textWe propose a Bayesian nonparametric procedure for density estimation, for data in a closed, bounded interval, say [0,1]. To this aim, we use a prior based on Bernstein polynomials. This corresponds to expressing the density of the data as a mixture of given beta densities, with random weights and a random number of components. The density estimate is then obtained as the corresponding predictive density function. Comparison with classical and Bayesian kernel estimates is provided. The proposed procedure is illustrated in an example; an MCMC algorithm for approximating the estimate is also discussed
Random Bernstein Polynomials
No full textRandom Bernstein polynomials which are also probability distribution functions on the closed unit interval are studied. The probability law of a Bernstein polynomial so defined provides a novel prior on the space of distribution functions on [0, 1], which has full support and can easily select absolutely continuous distribution functions with a continuous and smooth derivative. In particular, the Bernstein polynomial which approximates a Dirichlet process is studied. This may be of interest in Bayesian non-parametric inference. In the second part of the paper, we study the posterior from a "Bernstein-Dirichlet" prior and suggest a hybrid Monte Carlo approximation of it. The proposed algorithm has some aspects of novelty since the problem under examination has a "changing dimension" parameter space
Hierarchical reinforced urn processes
No full textWe define a class of reinforced urn processes, based on Hoppe's urn scheme, that are Markov exchangeable, with a
countable and possibly unknown state space. This construction extends the reinforced urn processes widely used in Bayesian nonparametric inference and survival analysis. We also shed light
on the connections with apparently unrelated constructions, recently proposed in the machine learning
literature, such as the infinite hidden Markov model, offering a general framework for a deeper study of their
theoretical properties
A Bayesian predictive approach to sequential searching for an optimal dose: parametric and nonparametric models
No full textThis paper looks at a new approach to the problem of finding the maximal tolerated dose (or optimal dose, Eichhorn and Zacks, 1973) of certain drugs which in addition to their therapeutic effects have secondary harmful effects.
The problem is investigated in a sequential setting from a Bayesian predictive approach. Search procedures are proposed for parametric and nonparametric models
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