Kshitij Khare

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.

A spectral analytic comparison of trace-class data augmentation algorithms and their sandwich variants

The data augmentation (DA) algorithm is a widely used Markov chain Monte Carlo algorithm that is easy to implement but often suffers from slow convergence. The sandwich algorithm is an alternative that can converge much faster while requiring roughly the same computational effort per iteration. Theoretically, the sandwich algorithm always converges at least as fast as the corresponding DA algorithm in the sense that

RATES OF CONVERGENCE OF SOME MULTIVARIATE MARKOV CHAINS WITH POLYNOMIAL EIGENFUNCTIONS

\Vert {K^*}\Vert \le \Vert {K}\Vert

Geometric ergodicity of the Bayesian lasso

, where

Necessary and Sufficient Conditions for High-Dimensional Posterior Consistency under

K

g

and

-Priors

K^*

Convergence properties of Gibbs samplers for Bayesian probit regression with proper priors

are the Markov operators associated with the DA and sandwich algorithms, respectively, and

Tautomeric equilibria of iso-guanine and related purine analogs

\Vert\cdot\Vert

A Bayesian approach for envelope models

denotes operator norm. In this paper, a substantial refinement of this operator norm inequality is developed. In particular, under regularity conditions implying that