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Spectral properties of MCMC algorithms for Bayesian linear regression with generalized hyperbolic errors
Affiliation:1. CIRAD, UMR BGPI, 34398, Montpellier, France;2. BGPI, Univ Montpellier, CIRAD, INRA, Montpellier SupAgro, Montpellier, France;3. CIRAD, UMR AGAP, 34398, Montpellier, France;4. AGAP, Univ Montpellier, CIRAD, INRA, Montpellier SupAgro, Montpellier, France;5. Department of Biochemistry, University of Cape Coast, Ghana;6. Cocoa Research Institute of Ghana, P. O. Box 8, Akim Tafo, Ghana;7. Department of Molecular Biology and Biotechnology, University of Cape Coast, Ghana;8. World Cocoa Foundation, Abidjan, Cote d’Ivoire;9. University of Jaffna, Faculty of Science, Department of Botany, Jaffna, Sri Lanka;10. University of the West of England, Frenchay Campus, Coldharbour Lane, Bristol, BS16 1QY, United Kingdom;11. School of Agriculture, Policy and Development, University of Reading, Whiteknights, Reading, RG6 7BE, United Kingdom;1. Department of Probability and Statistics, Beijing Institute of Technology, Beijing, 100081, China;2. Department of Statistics, North China University of Technology, Beijing, 100144, China;1. Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan;2. The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan;3. Nagoya University Graduate School of Medicine, 65 Tsurumai-cho, Showa-ku, Nagoya 466-8550, Japan;4. National Institute of Advanced Industrial Science and Technology, 2-4-7 Aomi, Koto-ku, Tokyo 135-0064, Japan
Abstract:We study MCMC algorithms for Bayesian analysis of a linear regression model with generalized hyperbolic errors. The Markov operators associated with the standard data augmentation algorithm and a sandwich variant of that algorithm are shown to be trace-class.
Keywords:Bessel function  Data augmentation algorithm  Geometric convergence rate  Markov operator  Sandwich algorithm  Trace-class operator
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