Simple variance bounds with applications to Bayesian posteriors and intractable distributions
Probability
2019-11-11 v1
Abstract
Using coupling techniques based on Stein's method for probability approximation, we revisit classical variance bounding inequalities of Chernoff, Cacoullos, Chen and Klaassen. Taking advantage of modern coupling techniques allows us to establish novel variance bounds in settings where the underlying density function is unknown or intractable. Applications include bounds for asymptotically Gaussian random variables using zero-biased couplings, bounds for random variables which are New Better (Worse) than Used in Expectation, and analysis of the posterior in Bayesian statistics.
Keywords
Cite
@article{arxiv.1911.03396,
title = {Simple variance bounds with applications to Bayesian posteriors and intractable distributions},
author = {Fraser Daly and Fatemeh Ghaderinezhad and Christophe Ley and Yvik Swan},
journal= {arXiv preprint arXiv:1911.03396},
year = {2019}
}