Julyan Arbel

Bayesian Optimal Adaptive Estimation Using a Sieve Prior.

We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure, and rate adaptation when the parameter space is, e.g., a Sobolev class. The conditions employed, although standard in the literature, are combined in a different way. The results are applied to density, regression, nonlinear autoregression and Gaussian white noise models. In the latter we have also considered a loss function which is different from the usual l2 norm, namely the pointwise loss. In this case it is possible to prove that the adaptive Bayesian approach for the l2 loss is strongly suboptimal and we provide a lower bound on the rate.

Full Bayesian inference with hazard mixture models

Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical problems, these methods may suffer from some limitations if used to estimate non-linear functionals of the posterior distribution. The main goal is to develop a novel methodology that extends a well-established marginal procedure designed for hazard mixture models, in order to draw approximate inference on survival functions that is not limited to the posterior mean but includes, as remarkable examples, credible intervals and median survival time. The proposed approach relies on a characterization of the posterior moments that, in turn, is used to approximate the posterior distribution by means of a technique based on Jacobi polynomials. The inferential performance of this methodology is analyzed by means of an extensive study of simulated data and real data consisting of leukemia remission times. Although tailored to the survival analysis context, the proposed procedure can be adapted to a range of other models for which moments of the posterior distribution can be estimated.

Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics

Given a sample of size

Bayesian nonparametric dependent model for partially replicated data: The influence of fuel spills on species diversity

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Application of a Bayesian nonparametric model to derive toxicity estimates based on the response of Antarctic microbial communities to fuel-contaminated soil.

from a population of individuals belonging to different species with unknown proportions, a popular problem of practical interest consists in making inference on the probability

Bayesian Survival Model Based on Moment Characterization

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BAYESIAN NONPARAMETRIC DEPENDENT MODEL FOR THE STUDY OF DIVERSITY FOR SPECIES DATA

that the

On diversity under a Bayesian nonparametric dependent model

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Stochastic approximations to the Pitman-Yor process.

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A simple proof of Pitman-Yor's Chinese restaurant process from its stick-breaking representation.

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