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A detailed treatment of Doob's theorem · Around

2018

A detailed treatment of Doob's theorem

Miller, Jeffrey W.

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Understand

Doob's theorem provides guarantees of consistent estimation and posterior consistency under very general conditions.

Despite the limitation that it only guarantees consistency on a set with prior probability 1, for many models arising in practice, Doob's theorem is an easy way of showing that consistency will hold almost everywhere.
In this article, we give a detailed proof of Doob's theorem.

Built on

Application of the theory of martingales
J. L. Doob · 1949
Earlier work this paper cites.
On the asymptotic behavior of Bayes’ estimates in the discrete case
D. A. Freedman · 1963
Earlier work this paper cites.
On Bayes procedures
L. Schwartz · 1965
Earlier work this paper cites.
Bayesian Analysis of Finite Mixture Distributions
A. Nobile · 1994
Earlier work this paper cites.

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Then

Bayesian Nonparametrics
J. K. Ghosh and R. V. Ramamoorthi · 2003
Later among the works it cites.
Extending Doob’s consistency theorem to nonparametric densities
A. Lijoi, I. Prünster, and S. G. Walker · 2004
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Probability Measures on Metric Spaces
K. R. Parthasarathy · 2005
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Fundamentals of Nonparametric Bayesian Inference
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