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On adaptive posterior concentration rates
Bayesian nonparametrics minimax adaptive estimation poste-rior concentration rates sup-norm rates of convergence
2013/6/14
We investigate the problem of deriving posterior concentration rates under different loss functions in nonparametric Bayes. We first provide a lower bound on posterior coverages of shrinking neighbour...
We review the Bayesian theory of semiparametric inference following Bickel and Kleijn (2012) and Kleijn and Knapik (2013). After an overview of efficiency in parametric and semiparametric estimation p...
Computing the posterior expectation of phylogenetic trees
Bayesian statistics BHV tree space Frechet mean geometric median phylogenetic trees posterior expectation
2013/6/14
Inferring phylogenetic trees from multiple sequence alignments often relies upon Markov chain Monte Carlo (MCMC) methods to generate tree samples from a posterior distribution. To give a rigorous appr...
Dirichlet Posterior Sampling with Truncated Multinomial Likelihoods
Dirichlet Posterior Sampling Multinomial Likelihoods
2012/9/18
This document considers the problem of drawing samples from posterior distributions formed under a Dirichlet prior and a truncated multinomial likelihood, by which we mean a Multi-nomial likelihood fu...
Finite sample posterior concentration in high-dimensional regression
asymptotics Bayesian compressible prior high-dimensional posterior contraction regression shrinkage prior.
2012/9/19
We study the behavior of the posterior distribution in ultra high-dimensional Bayesian Gaussian linear regression models havingp佲n,withpthe number of predictors and nthe sample size. In particular, ou...
A Random Weighting Approach for Posterior Distributions
posterior distribution asymptotic expansion random weighting method
2012/9/19
In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, th...
About the posterior distribution in hidden Markov Models with unknown number of states
Hidden Markov models number of components order selection Bayesian statistics posterior distribution
2012/9/19
In this paper, we investigate the asymptotic behaviour of the posterior distribution in hidden Markov models (HMMs) when using Bayesian methodology. We obtain a general asymptotic result, and give con...
Posterior Consistency of Nonparametric Conditional Moment Restricted Models
identified region limited information likelihood sieve approximation nonparametric instrumental variable ill-posed problem partial identification Bayesian inference
2011/6/20
This paper addresses the estimation of the nonparametric conditional moment
restricted model that involves an infinite dimensional parameter g0. We
estimate it in a quasi-Bayesian way based on the l...
Posterior model probabilities computed from model-specific Gibbs output
Computation (stat.CO) Applications (stat.AP) Methodology (stat.ME)
2010/12/17
We provide a representation of reversible-jump Markov chain Monte Carlo as Gibbs sampling with alternating updates of a model indicator and a "palette" of parameters we denote $\bm \psi$. A key innova...
Free energy methods for efficient exploration of mixture posterior densities
Adaptive Biasing Force Adaptive Biasing Potential Adaptive Markov chainMonte Carlo Importance sampling Mixture models
2010/3/11
Because of their multimodality, mixture posterior densities are difficult to sample with
standard Markov chain Monte Carlo (MCMC) methods. We propose a strategy to enhance
the sampling of MCMC in th...
On the posterior distribution of classes of random means
Bayesian nonparametrics completely random measures means of randomprobability measures normalized random measures Poisson–Dirichlet process
2010/3/10
The study of properties of mean functionals of random probability measures is an important
area of research in the theory of Bayesian nonparametric statistics. Many results are now known
for random ...
Rates of convergence for the posterior distributions of mixtures of Betas and adaptive nonparametric estimation of the density
Bayesian nonparametric rates of convergence mixtures of Betas adaptive estimation kernel
2010/3/9
In this paper, we investigate the asymptotic properties of nonparametric
Bayesian mixtures of Betas for estimating a smooth density
on [0, 1]. We consider a parametrization of Beta distributions in
...
Improved Criteria for Clustering Based on the Posterior Similarity Matrix
adjusted Rand index cluster analysis Dirichlet process mixture model Markov chain Monte Carlo
2009/9/24
In this paper we address the problem of obtaining a single clustering estimate c based on an MCMC sample of clusterings c(1), c(2) . . . , c(M) from the posterior distribution of a Bayesi...
Some Bayesian Credibility Premiums Obtained by Using Posterior Regret Gamma-Minimax Methodology
Classes of distributions Credibility Minimax Premium Robustness
2009/9/24
In this paper,following the robust Bayesian paradigm, a procedure based on
the posterior regret-minimax principle is applied to derive,in a straightforwar
way, new credibility formula,making use of ...
Posterior predictive arguments in favor of the Bayes-Laplace prior as the consensus prior for binomial and multinomial parameters
Bayesian inference binomial distribution invariance noninformative prior
2009/9/24
It is argued that the posterior predictive distribution for the binomial
and multinomial distributions,when viewed via a hypergeometric-like representa-
tion, suggests the uniform prior on the param...