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arXiv · 2606.05672

Trace-Class Results for MCMC Algorithms for Student-$t$ Regression Models

Yasuyuki Hamura
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Abstract

In this paper, we consider MCMC algorithms for Student-$t$ regression models. In three cases, we investigate the efficiency of Markov chains based on the algorithms in terms of whether trace-class results hold or not. First, we consider the case where the parameters follow a matrix-normal-inverse-Wishart distribution and show that the Markov operator associated with a standard data augmentation algorithm is trace-class. Second, we consider the case of an improper prior and univariate outcomes. In this case, the standard Markov operator is not trace-class but the Markov operator associated with a collapsed Gibbs algorithm is trace-class. Third, we consider the case of an improper prior and multivariate outcomes. We obtain a trace-class result for a parameter expanded data augmentation algorithm which is based on a univariate working parameter. Finally, we consider the problem of numerially estimating a convergence rate of the trace-class Markov operator in the second case.

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Yasuyuki Hamura. 2026-09-18. Trace-Class Results for MCMC Algorithms for Student-$t$ Regression Models. https://arxiv.org/abs/2606.05672

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