# Trace-class Monte Carlo Markov chains for Bayesian multivariate linear regression with non-Gaussian errors

@article{Qin2018TraceclassMC, title={Trace-class Monte Carlo Markov chains for Bayesian multivariate linear regression with non-Gaussian errors}, author={Qian Qin and James P. Hobert}, journal={J. Multivar. Anal.}, year={2018}, volume={166}, pages={335-345} }

## 5 Citations

Convergence Analysis of MCMC Algorithms for Bayesian Multivariate Linear Regression with Non‐Gaussian Errors

- Mathematics
- 2018

When Gaussian errors are inappropriate in a multivariate linear regression setting, it is often assumed that the errors are iid from a distribution that is a scale mixture of multivariate normals.…

Uncertainty Quantification for Modern High-Dimensional Regression via Scalable Bayesian Methods

- Computer ScienceJournal of Computational and Graphical Statistics
- 2018

It is demonstrated that the proposed class of two-step blocked samplers exhibits vastly superior convergence behavior compared to the original three-step sampler in high-dimensional regimes on simulated data as well as data from a variety of applications including gene expression data, infrared spectroscopy data, and socio-economic/law enforcement data.

Consistent estimation of the spectrum of trace class Data Augmentation algorithms

- Mathematics, Computer ScienceBernoulli
- 2019

This paper proposes a novel method to consistently estimate the entire spectrum of a general class of Markov chains arising from a popular and widely used statistical approach known as Data Augmentation.

Estimating the spectral gap of a trace-class Markov operator

- MathematicsElectronic Journal of Statistics
- 2019

The utility of a Markov chain Monte Carlo algorithm is, in large part, determined by the size of the spectral gap of the corresponding Markov operator. However, calculating (and even approximating)…

Estimating accuracy of the MCMC variance estimator: Asymptotic normality for batch means estimators

- MathematicsStatistics & Probability Letters
- 2021

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When Gaussian errors are inappropriate in a multivariate linear regression setting, it is often assumed that the errors are iid from a distribution that is a scale mixture of multivariate normals.…

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A substantial refinement of this operator norm inequality is developed, and under regularity conditions implying that $K$ is a trace-class operator, it is shown that it is also a positive, trace- class operator, and that the spectrum of $K^*$ dominates that of$K$ in the sense that the ordered elements of the former are all less than or equal to the corresponding element of the latter.

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The reversible Markov chains that drive the data augmentation (DA) and sandwich algorithms define self-adjoint operators whose spectra encode the convergence properties of the algorithms. When the…

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It is proved that Rao-Blackwellization causes a one-lag delay for the autocovariances among dependent samples obtained from data augmentation, and consequently, the mixture approximation produces estimates with smaller variances than the empirical approximation.

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