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Convergence rates of posterior distributions
We consider the asymptotic behavior of posterior distributions and Bayes estimators for infinite-dimensional statistical models. We give general results on the rate of convergence of the posterior…
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POSTERIOR CONSISTENCY OF DIRICHLET MIXTURES IN DENSITY ESTIMATION
A Dirichlet mixture of normal densities is a useful choice for a prior distribution on densities in the problem of Bayesian density estimation. In the recent years, efficient Markov chain Monte Carlo…
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Convergence rates of posterior distributions for non-i.i.d. observations
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general…
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Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities
We study the rates of convergence of the maximum likelihood estimator (MLE) and posterior distribution in density estimation problems, where the densities are location or location-scale mixtures of…
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Convergence rates for density estimation with Bernstein polynomials
Mixture models for density estimation provide a very useful set up for the Bayesian or the maximum likelihood approach. For a density on the unit interval, mixtures of beta densities form a flexible…
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CONVERGENCE RATES OF POSTERIOR DISTRIBUTIONS FOR NONIID OBSERVATIONS By
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general…
Fundamentals of Nonparametric Bayesian Inference
TLDR
This authoritative text draws on theoretical advances of the past twenty years to synthesize all aspects of Bayesian nonparametrics, from prior construction to computation and large sample behavior of posteriors, making it valuable for both graduate students and researchers in statistics and machine learning.
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Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables
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TESTING MONOTONICITY OF REGRESSION By
We consider the problem of testing monotonicity of the regression function in a nonparametric regression model. We introduce test statistics that are functionals of a certain natural U-process. We…
Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution
We consider the problem of estimating the mean of an infinite-break dimensional normal distribution from the Bayesian perspective. Under the assumption that the unknown true mean satisfies a…
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