Simple variance bounds with applications to Bayesian posteriors and intractable distributions

Fraser Daly; Fatemeh Ghaderinezhad; Christophe Ley; Yvik Swan

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arXiv · 1911.03396

Simple variance bounds with applications to Bayesian posteriors and intractable distributions

Fraser Daly·Fatemeh Ghaderinezhad·Christophe Ley·Yvik Swan

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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.

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BibTeX RIS

Fraser Daly, Fatemeh Ghaderinezhad, Christophe Ley, Yvik Swan. 2019-11-08. Simple variance bounds with applications to Bayesian posteriors and intractable distributions. https://arxiv.org/abs/1911.03396

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