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Block Gibbs Sampling for Bayesian Random Effects Models With Improper Priors: Convergence and Regeneration

Bayesian versions of the classical one-way random effects model are widely used to analyze data. If the standard diffuse prior is adopted, there is a simple block Gibbs sampler that can be employed… Expand

Estimates and Standard Errors for Ratios of Normalizing Constants from Multiple Markov Chains via Regeneration.

- Hani Doss, Aixin Tan
- Mathematics, Medicine
- Journal of the Royal Statistical Society. Series…
- 1 September 2014

In the classical biased sampling problem, we have k densities π1(·), …, πk (·), each known up to a normalizing constant, i.e. for l = 1, …, k, πl (·) = νl (·)/ml , where νl (·) is a known function… Expand

When is Eaton’s Markov chain irreducible?

- J. Hobert, Aixin Tan, Ruitao Liu
- Mathematics
- 1 August 2007

Consider a parametric statistical model P(dx\0) and an improper prior distribution v(d0) that together yield a (proper) formal posterior distribution Q(d6\x). The prior is called strongly admissible… Expand

Bayesian inference for high‐dimensional linear regression under mnet priors

Abstract: For regression problems that involve many potential predictors, the Bayesian variable selection (BVS) method is a powerful tool, which associates each model with its posterior… Expand

Estimating standard errors for importance sampling estimators with multiple Markov chains

- Vivekananda Roy, Aixin Tan, J. Flegal
- Mathematics
- 21 September 2015

The naive importance sampling estimator, based on samples from a single importance density, can be numerically unstable. Instead, we consider generalized importance sampling estimators where samples… Expand

Honest Importance Sampling With Multiple Markov Chains

- Aixin Tan, Hani Doss, J. Hobert
- Mathematics, Medicine
- Journal of computational and graphical statistics…
- 3 July 2015

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π1, is used to estimate an expectation with respect to another, π. The importance… Expand

On the Geometric Ergodicity of Two-Variable Gibbs Samplers

- Aixin Tan, Galin L. Jones, J. Hobert
- Mathematics
- 21 June 2012

A Markov chain is geometrically ergodic if it converges to its in- variant distribution at a geometric rate in total variation norm. We study geo- metric ergodicity of deterministic and random scan… Expand

Convergence rates and regeneration of the block Gibbs sampler for Bayesian random effects models

- Aixin Tan
- Computer Science
- 2009

Supplement to “ Bayesian inference for high-dimensional linear regression under the mnet priors ”

Here, a q-dim binary vector γ = (γ1, . . . , γq) ∈ {0, 1}q =: Γ indicates a selected set of predictors, and βγ denotes the subvector of coefficients for the predictors selected by γ. Prior of the BVS… Expand

Sandwich algorithms for Bayesian variable selection

- Joyee Ghosh, Aixin Tan
- Mathematics, Computer Science
- Comput. Stat. Data Anal.
- 2015

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