{"ID":3084828,"CreatedAt":"2026-06-05T06:46:15.197025399Z","UpdatedAt":"2026-06-07T03:38:11.424509713Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.05672","arxiv_id":"2606.05672","title":"Trace-Class Results for MCMC Algorithms for Student-t Regression Models","abstract":"In this paper, we consider MCMC algorithms for Student-$t$ regression models. We investigate the efficiency of Markov chains based on the algorithms in terms of whether trace-class results hold or not. We first consider the case where the regression coefficients and error variance follow the invariant improper prior distributions. The Markov operator associated with a standard data augmentation algorithm is not trace-class but that associated with a collpased Gibbs algorithm is trace-class. We next consider the case where the parameters follow a normal-inverse gamma distribution. In this case, the standard Markov operator is trace-class.","short_abstract":"In this paper, we consider MCMC algorithms for Student-$t$ regression models. We investigate the efficiency of Markov chains based on the algorithms in terms of whether trace-class results hold or not. We first consider the case where the regression coefficients and error variance follow the invariant improper prior di...","url_abs":"https://arxiv.org/abs/2606.05672","url_pdf":"https://arxiv.org/pdf/2606.05672v1","authors":"[\"Yasuyuki Hamura\"]","published":"2026-06-04T03:51:21Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}