Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trace-class Monte Carlo Markov Chains for Bayesian Multivariate Linear
  Regression with Non-Gaussian Errors   Let $\pi$ denote the intractable posterior density that results when the
likelihood from a multivariate linear regression model with errors from a scale
mixture of normals is combined with the standard non-informative prior. There
is a simple data augmentation algorithm (based on latent data from the mixing
density) that can be used to explore $\pi$. Let $h(\cdot)$ and $d$ denote the
mixing density and the dimension of the regression model, respectively. Hobert
et al. (2016) [arXiv:1506.03113v2] have recently shown that, if $h$ converges
to 0 at the origin at an appropriate rate, and $\int_0^\infty u^{\frac{d}{2}}
\, h(u) \, du < \infty$, then the Markov chains underlying the DA algorithm and
an alternative Haar PX-DA algorithm are both geometrically ergodic. In fact,
something much stronger than geometric ergodicity often holds. Indeed, it is
shown in this paper that, under simple conditions on $h$, the Markov operators
defined by the DA and Haar PX-DA Markov chains are trace-class, i.e., compact
with summable eigenvalues. Many of the mixing densities that satisfy Hobert et
al.'s (2016) conditions also satisfy the new conditions developed in this
paper. Thus, for this set of mixing densities, the new results provide a
substantial strengthening of Hobert et al.'s (2016) conclusion without any
additional assumptions. For example, Hobert et al. (2016) showed that the DA
and Haar PX-DA Markov chains are geometrically ergodic whenever the mixing
density is generalized inverse Gaussian, log-normal, Fr\'{e}chet (with shape
parameter larger than $d/2$), or inverted gamma (with shape parameter larger
than $d/2$). The results in this paper show that, in each of these cases, the
DA and Haar PX-DA Markov operators are, in fact, trace-class.

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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org