Kitagawa, T;
Montiel-Olea, J;
Payne, J;
(2016)
Posterior Distribution of Nondifferentiable Functions.
(cemmap working paper
20/16).
Institute for Fiscal Studies: London, UK.
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Abstract
This paper examines the asymptotic behavior of the posterior distribution of a possibly nondifferentiable function g(theta), where theta is a finite dimensional parameter. The main assumption is that the distribution of the maximum likelihood estimator theta_n, its bootstrap approximation, and the Bayesian posterior for theta all agree asymptotically. It is shown that whenever g is Lipschitz, though not necessarily differentiable, the posterior distribution of g(theta) and the bootstrap distribution of g(theta_n) coincide asymptotically. One implication is that Bayesians can interpret bootstrap inference for g(theta) as approximately valid posterior inference in a large sample. Another implication—built on known results about bootstrap inconsistency—is that the posterior distribution of g(theta) does not coincide with the asymptotic distribution of g(theta_n) at points of nondifferentiability. Consequently, frequentists cannot presume that credible sets for a nondifferentiable parameter g(theta) can be interpreted as approximately valid confidence sets (even when this relation holds true for theta).
Type: | Working / discussion paper |
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Title: | Posterior Distribution of Nondifferentiable Functions |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1920/wp.cem.2016.2016 |
Publisher version: | http://dx.medra.org/10.1920/wp.cem.2016.2016 |
Language: | English |
Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
Keywords: | Bootstrap, Bernstein-von Mises Theorem, Directional Differentiability, Posterior Inference |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL SLASH UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics |
URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1522146 |
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