The Polya-Gamma Gibbs Sampler for Bayesian Logistic Regression is Uniformly Ergodic
نویسندگان
چکیده
One of the most widely used data augmentation algorithms is Albert and Chib’s (1993) algorithm for Bayesian probit regression. Polson, Scott and Windle (2013) recently introduced an analogous algorithm for Bayesian logistic regression. The main difference between the two is that Albert and Chib’s (1993) truncated normals are replaced by so-called Polya-Gamma random variables. In this note, we establish that the Markov chain underlying Polson et al.’s (2013) algorithm is uniformly ergodic. This theoretical result has important practical benefits. In particular, it guarantees the existence of central limit theorems that can be used to make an informed decision about how long the simulation should be run.
منابع مشابه
Comparison of Maximum Likelihood Estimation and Bayesian with Generalized Gibbs Sampling for Ordinal Regression Analysis of Ovarian Hyperstimulation Syndrome
Background and Objectives: Analysis of ordinal data outcomes could lead to bias estimates and large variance in sparse one. The objective of this study is to compare parameter estimates of an ordinal regression model under maximum likelihood and Bayesian framework with generalized Gibbs sampling. The models were used to analyze ovarian hyperstimulation syndrome data. Methods: This study use...
متن کاملOn convergence rates of Gibbs samplers for uniform distributionsbyGareth
We consider a Gibbs sampler applied to the uniform distribution on a bounded region R R d. We show that the convergence properties of the Gibbs sampler depend greatly on the smoothness of the boundary of R. Indeed, for suuciently smooth boundaries the sampler is uniformly ergodic, while for jagged boundaries the sampler could fail to even be geometrically ergodic.
متن کاملOn Convergence Rates of Gibbs Samplers for Uniform Distributions
We consider a Gibbs sampler applied to the uniform distribution on a bounded region R ⊆ R. We show that the convergence properties of the Gibbs sampler depend greatly on the smoothness of the boundary of R. Indeed, for sufficiently smooth boundaries the sampler is uniformly ergodic, while for jagged boundaries the sampler could fail to even be geometrically ergodic.
متن کاملPlackett-Luce regression: A new Bayesian model for polychotomous data
Multinomial logistic regression is one of the most popular models for modelling the effect of explanatory variables on a subject choice between a set of specified options. This model has found numerous applications in machine learning, psychology or economy. Bayesian inference in this model is non trivial and requires, either to resort to a MetropolisHastings algorithm, or rejection sampling wi...
متن کاملConvergence of Conditional Metropolis-Hastings Samplers, with an Application to Inference for Discretely-Observed Diffusions
We consider Markov chain Monte Carlo algorithms which combine Gibbs updates with Metropolis-Hastings updates, resulting in a conditional Metropolis-Hastings sampler. We develop conditions under which this sampler will be geometrically or uniformly ergodic. We apply our results to an algorithm for drawing Bayesian inferences about the entire sample path of a diffusion process, based only upon di...
متن کامل