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On rates of convergence for posterior distributions in infinite–dimensional models

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Author Info
Antonio Lijoi ()
Igor Prünster ()
Stephen G. Walker ()
Abstract

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. Crucially, no sieve or entropy measures are required and so rates do not depend on the rate of convergence of the corresponding sieve maximum likelihood estimator. In particular, we improve on current rates for mixture models.

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Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 24-2004.

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Length: 16 pages
Date of creation: Oct 2004
Date of revision:
Handle: RePEc:icr:wpmath:24-2004

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Keywords: Hellinger consistency mixture of Dirichlet process posterior distribution rates of convergence

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  1. Haberman, Steven & Vigna, Elena, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 35-69, August. [Downloadable!] (restricted)
  2. Taizhong Hu & Alfred Müller & Marco Scarsini, 2002. "Some Counterexamples in Positive Dependence," ICER Working Papers - Applied Mathematics Series 28-2003, ICER - International Centre for Economic Research, revised Jul 2003. [Downloadable!]
  3. Erio Castagnoli & Fabio Maccheroni & Massimo Marinacci, 2002. "Choquet insurance pricing: a caveat," ICER Working Papers - Applied Mathematics Series 14-2003, ICER - International Centre for Economic Research, revised May 2003. [Downloadable!]
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  5. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo & Siniscalchi, Marciano, 2001. "A Subjective Spin on Roulette Wheels," Working Papers 1127, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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  6. Massimo Marinacci & Luigi Montrucchio, 2003. "Cores and stable sets of finite dimensional games," ICER Working Papers - Applied Mathematics Series 07-2003, ICER - International Centre for Economic Research. [Downloadable!]
  7. Castagnoli, Erio & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Insurance premia consistent with the market," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 267-284, October. [Downloadable!] (restricted)
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  8. Domenico Menicucci, 2001. "Optimal two-object auctions with synergies," ICER Working Papers - Applied Mathematics Series 18-2001, ICER - International Centre for Economic Research. [Downloadable!]
  9. Guido Cozzi & Fabio Privileggi, 2002. "Wealth Polarization and Pulverization in Fractal Societies," ICER Working Papers - Applied Mathematics Series 39-2002, ICER - International Centre for Economic Research. [Downloadable!]
  10. Montrucchio, Luigi & Privileggi, Fabio, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," Journal of Economic Theory, Elsevier, vol. 101(1), pages 158-188, November. [Downloadable!] (restricted)
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  11. Adriana Castaldo & Massimo Marinacci, 2001. "Random correspndences as bundles of random variables," ICER Working Papers - Applied Mathematics Series 12-2001, ICER - International Centre for Economic Research. [Downloadable!]
  12. Umberto Cherubini & Elisa Luciano, 2002. "Pricing Vulnerable Options with Copulas," ICER Working Papers - Applied Mathematics Series 06-2002, ICER - International Centre for Economic Research. [Downloadable!]
  13. Massimo Marinacci & Fabio Maccheroni & Alain Chateauneuf & Jean-Marc Tallon, 2003. "Monotone Continuous Multiple Priors," ICER Working Papers - Applied Mathematics Series 30-2003, ICER - International Centre for Economic Research. [Downloadable!]
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  15. Marinacci, Massimo & Montrucchio, Luigi, 2004. "A characterization of the core of convex games through Gateaux derivatives," Journal of Economic Theory, Elsevier, vol. 116(2), pages 229-248, June. [Downloadable!] (restricted)
  16. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Ambiguity from the Differential Viewpoint," Working Papers 1130, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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  18. Umberto Cherubini & Elisa Luciano, 2002. "Multivariate Option Pricing with Copulas," ICER Working Papers - Applied Mathematics Series 05-2002, ICER - International Centre for Economic Research. [Downloadable!]
  19. Bruno Bassan & Olivier Gossner & Marco Scarsini & Shmuel Zamir, 2001. "Positive value of information in games," ICER Working Papers - Applied Mathematics Series 26-2003, ICER - International Centre for Economic Research, revised Jul 2003. [Downloadable!]
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  20. Alfred Müller & Marco Scarsini, 2003. "Archimedean Copulae and Positive Dependence," ICER Working Papers - Applied Mathematics Series 25-2003, ICER - International Centre for Economic Research. [Downloadable!]
  21. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2002. "Certainty Independence and the Separation of Utility and Beliefs," ICER Working Papers - Applied Mathematics Series 40-2002, ICER - International Centre for Economic Research. [Downloadable!]
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  22. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004. "Variational representation of preferences under ambiguity," ICER Working Papers - Applied Mathematics Series 05-2004, ICER - International Centre for Economic Research. [Downloadable!]
  23. Thibault Gajdos & Eric Maurin, 2002. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," ICER Working Papers - Applied Mathematics Series 15-2003, ICER - International Centre for Economic Research, revised Mar 2003. [Downloadable!]
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  24. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research. [Downloadable!]
  25. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2002. "A smooth model of decision making under ambiguity," ICER Working Papers - Applied Mathematics Series 11-2003, ICER - International Centre for Economic Research, revised Apr 2003. [Downloadable!]
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  26. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Bibliography 7616, UCLA Department of Economics. [Downloadable!]
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  27. Massimo Marinacci & Luigi Montrucchio, 2003. "Ultramodular functions," ICER Working Papers - Applied Mathematics Series 13-2003, ICER - International Centre for Economic Research. [Downloadable!]
  28. Claudio Mattalia, 2003. "Existence of solutions and asset pricing bubbles in general equilibrium models," ICER Working Papers - Applied Mathematics Series 02-2003, ICER - International Centre for Economic Research. [Downloadable!]
  29. Enrico Diecidue & Fabio Maccheroni, 2002. "Coherence without Additivity," ICER Working Papers - Applied Mathematics Series 10-2002, ICER - International Centre for Economic Research. [Downloadable!]
  30. Marco Dall’Aglio & Marco Scarsini, 2000. "Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex," ICER Working Papers - Applied Mathematics Series 27-2003, ICER - International Centre for Economic Research, revised Jul 2003. [Downloadable!]
  31. Jerome Renault & Sergio Scarlatti & Marco Scarsini, 2003. "A folk theorem for minority games," ICER Working Papers - Applied Mathematics Series 10-2003, ICER - International Centre for Economic Research. [Downloadable!]
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  32. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series 18-2003, ICER - International Centre for Economic Research, revised May 2003. [Downloadable!]
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  33. Maitreesh Ghatak & Massimo Morelli & Tomas Sjoström, 2001. "Credit rationing, wealth inequality, and allocation of talent," ICER Working Papers - Applied Mathematics Series 23-2001, ICER - International Centre for Economic Research. [Downloadable!]
  34. Fabio Maccheroni, 2000. "Yaari dual theory without the completeness axiom," ICER Working Papers - Applied Mathematics Series 30-2001, ICER - International Centre for Economic Research, revised Oct 2001. [Downloadable!]
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