Gibbs Sampling, Conjugate Priors and Coupling

نویسندگان

  • P. Diaconis
  • Kshitij Khare
چکیده

We give a large family of simple examples where a sharp analysis of the Gibbs sampler can be proved by coupling. These examples involve standard statistical models – exponential families with conjugate priors or location families with natural priors. Many of them seem difficult to succesfully analyze using spectral or Harris recurrence techniques.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Gibbs Sampling, Exponential Families and Coupling

We give examples of a quantitative analysis of the bivariate Gibbs sampler using coupling arguments. The examples involve standard statistical models – exponential families with conjugate priors or location families with natural priors. Our main approach uses a single eigenfunction (always explicitly available in the examples in question) and stochastic monotonicity.

متن کامل

Gibbs Sampling for Logistic Normal Topic Models with Graph-Based Priors

Previous work on probabilistic topic models has either focused on models with relatively simple conjugate priors that support Gibbs sampling or models with non-conjugate priors that typically require variational inference. Gibbs sampling is more accurate than variational inference and better supports the construction of composite models. We present a method for Gibbs sampling in non-conjugate l...

متن کامل

Bayesian analysis of covariance matrices and dynamic models for longitudinal data

Parsimonious modelling of the within-subject covariance structure while heeding its positive-definiteness is of great importance in the analysis of longitudinal data. Using the Cholesky decomposition and the ensuing unconstrained and statistically meaningful reparameterisation, we provide a convenient and intuitive framework for developing conditionally conjugate prior distributions for covaria...

متن کامل

Convergence Analysis of the Gibbs Sampler for Bayesian General Linear Mixed Models with Improper Priors by Jorge

Bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density. However, if a conditionally conjugate prior density is adopted, then there is a simple Gibbs sampler that can be employed to explore the posterior density. A popular default among the conditionally conjugate priors is an improper prior that takes a...

متن کامل

Gibbs Sampling, Exponential Families and Orthogonal Polynomials

We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate priors. In each case, the transition operator is explicitly diagonalizable with classical orthogonal polynomials as eigenfunctions.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008