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A Consistency Theorem for Regular Conditional Distributions

Author

Listed:
  • Patrizia Berti

    (Department of Mathematics, University of Modena and Reggio Emilia)

  • Pietro Rigo

    (Department of Economics and Quantitative Methods, University of Pavia)

Abstract

Let (omega, beta) be a measurable space, An in B a sub-sigma-field and µn a random probability measure, n >= 1. In various frameworks, one looks for a probability P on B such that µn is a regular conditional distribution for P given An for all n. Conditions for such a P to exist are given. The conditions are quite simple when (omega, beta) is a compact Hausdorff space equipped with the Borel or the Bairesigma-field (as well as under other similar assumptions). Such conditions are then applied to Bayesian statistics.

Suggested Citation

  • Patrizia Berti & Pietro Rigo, 2010. "A Consistency Theorem for Regular Conditional Distributions," Quaderni di Dipartimento 136, University of Pavia, Department of Economics and Quantitative Methods.
    • Handle: RePEc:pav:wpaper:136
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