The practical implementation of Bayesian inference requires numerical
approximation when closed-form expressions are not available. What types of
accuracy (convergence) of the numerical approximations guarantee robustness and
what types do not? In particular, is the recursive application of Bayes' rule
robust when subsequent data or posteriors are approximated? When the prior is
the push forward of a distribution by the map induced by the solution of a PDE,
in which norm should that solution be approximated? Motivated by such
questions, we investigate the sensitivity of the distribution of posterior
distributions (i.e. posterior distribution-valued random variables, randomized
through the data) with respect to perturbations of the prior and data
generating distributions in the limit when the number of data points grows
towards infinity.
Description
[1411.3984] Qualitative Robustness in Bayesian Inference
%0 Journal Article
%1 owhadi2014qualitative
%A Owhadi, Houman
%A Scovel, Clint
%D 2014
%K bayesian probability robustness stats
%T Qualitative Robustness in Bayesian Inference
%U http://arxiv.org/abs/1411.3984
%X The practical implementation of Bayesian inference requires numerical
approximation when closed-form expressions are not available. What types of
accuracy (convergence) of the numerical approximations guarantee robustness and
what types do not? In particular, is the recursive application of Bayes' rule
robust when subsequent data or posteriors are approximated? When the prior is
the push forward of a distribution by the map induced by the solution of a PDE,
in which norm should that solution be approximated? Motivated by such
questions, we investigate the sensitivity of the distribution of posterior
distributions (i.e. posterior distribution-valued random variables, randomized
through the data) with respect to perturbations of the prior and data
generating distributions in the limit when the number of data points grows
towards infinity.
@article{owhadi2014qualitative,
abstract = {The practical implementation of Bayesian inference requires numerical
approximation when closed-form expressions are not available. What types of
accuracy (convergence) of the numerical approximations guarantee robustness and
what types do not? In particular, is the recursive application of Bayes' rule
robust when subsequent data or posteriors are approximated? When the prior is
the push forward of a distribution by the map induced by the solution of a PDE,
in which norm should that solution be approximated? Motivated by such
questions, we investigate the sensitivity of the distribution of posterior
distributions (i.e. posterior distribution-valued random variables, randomized
through the data) with respect to perturbations of the prior and data
generating distributions in the limit when the number of data points grows
towards infinity.},
added-at = {2019-06-06T15:57:30.000+0200},
author = {Owhadi, Houman and Scovel, Clint},
biburl = {https://www.bibsonomy.org/bibtex/24d43973cfbd1b59f314045c83ce1b69d/kirk86},
description = {[1411.3984] Qualitative Robustness in Bayesian Inference},
interhash = {be4bbee67a59e9674e4ddc8ad9eb6a8a},
intrahash = {4d43973cfbd1b59f314045c83ce1b69d},
keywords = {bayesian probability robustness stats},
note = {cite arxiv:1411.3984},
timestamp = {2019-06-06T15:57:30.000+0200},
title = {Qualitative Robustness in Bayesian Inference},
url = {http://arxiv.org/abs/1411.3984},
year = 2014
}