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

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.