Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression

Consider a probit regression problem in which Y₁, [ellipsis (horizontal)], Yn are independent Bernoulli random variables such that [graphic removed] where xi is a p-dimensional vector of known covariates that are associated with Yi, β is a p-dimensional vector of unknown regression coefficients and...

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Vydáno v:	Journal of the Royal Statistical Society. Series B, Statistical methodology Ročník 69; číslo 4; s. 607 - 623
Hlavní autoři:	Roy, Vivekananda, Hobert, James P
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Oxford, UK Oxford, UK : Blackwell Publishing Ltd 01.09.2007 Blackwell Publishing Ltd Blackwell Publishers Blackwell Royal Statistical Society Oxford University Press
Edice:	Journal of the Royal Statistical Society Series B
Témata:	Acceleration of convergence Algorithms Asymptotic methods Asymptotic variance Bayesian analysis Bernoulli Hypothesis Central limit theorem Consistent estimators Convergence Data augmentation algorithm Density Efficiency Ergodic theory Errors Estimation methods Exact sciences and technology Gaussian distributions General topics Geometric ergodicity Lupus Markov analysis Markov chain Markov chains Markov processes Mathematical models Mathematics Minorization condition Monte Carlo simulation Normal distribution Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Perceptron convergence procedure Probability and statistics Probability theory and stochastic processes Probit models PX-DA algorithm Random variables Regeneration Regression analysis Reversible Markov chain Sciences and techniques of general use Simulation Standard error Statistical methods Statistical models Statistical variance Statistics Studies Variance Variance estimation PX-DA algorithm Gaussian distribution Geometric ergodicity Covariate Stochastic method Distribution function Simulation model Random variable Posterior distribution Monte Carlo method Existence theorem Convergence acceleration Prior distribution Asymptotic behavior Algorithm Computational complexity Statistical method Statistical regression Regression coefficient Numerical analysis Ergodic theorem Density estimation Second moment Statistical distribution Error estimation Error rate Non parametric estimation Asymptotic variance Asymptotic convergence Limit theorem Markov chain Data augmentation algorithm Convergence rate Approximation theory Bayes estimation Minorization condition Reversible Markov chain Covariance analysis Statistical moment Average Ergodicity Statistical estimation Variance analysis Mean estimation Independent variable Regeneration Central limit theorem Simulation
ISSN:	1369-7412, 1467-9868
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