Semiparametric Inference for the Means of Heavy-Tailed Distributions

• Activity Number: 14 - Data Science with Semiparametric Bayes
• Type: Invited
• Date/Time: Sunday, July 30, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Hedibert Lopes* and Matt Taddy and Matt Gardner
• Companies: Insper and University of Chicago Booth School of Business and eBay
• Keywords: generalized pareto distribution ; MCMC ; Dirichlet process ; A/B experiments ; Average Treatment Effect ; Big Data

Abstract

We have a tough inference problem involving heavy tailed data. The goal is to provide a gold-standard Bayesian analysis for this problem, with nonparametric inference for the bulk of the distribution combined with parametric models - motivated from extreme value theory - in the tail. This gold standard analysis is then used to evaluate common decision rules and strategies for variance reduction (such as winsorization). The work is motivated and illustrated by a set of 72 A/B experiments on ebay.com. Our contributions include this practical semi-parametric Bayesian modelling scheme, as well as a new independence Metropolis Hastings algorithm that samples from the distribution for tail parameters through small adjustments to a parametric bootstrap distribution. Finally, we extend our analysis in a hierarchical model that shrinks tails across treatment groups to an overall background tail; this takes advantage of prior beliefs that the treatments we apply have little effect in the tail.