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

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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BibTeX RIS

BibTeX

@misc{hamura2026traceclass,
  title = {{Trace-Class Results for MCMC Algorithms for Student-$t$ Regression Models}},
  author = {Yasuyuki Hamura},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.05672},
  eprint = {2606.05672},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.05672},
}

RIS

TY  - UNPB
TI  - Trace-Class Results for MCMC Algorithms for Student-t Regression Models
AU  - Yasuyuki Hamura
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2606.05672
UR  - https://arxiv.org/abs/2606.05672
AB  - 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.
ER  -

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