Bayesian Inference for Truncated and Interval-Valued Regression Models

• Activity Number: 354
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Alicia Lloro* and Phillip Li
• Companies: FDIC and Office of the Comptroller of the Currency
• Keywords: Interval Data ; Bayesian ; MCMC ; Markov Chain Monte Carlo ; Truncated Data ; Symbolic Data

Abstract

This paper develops Bayesian methods to analyze the truncated regression model, which is a relatively understudied subclass of limited dependent variable (LDV) models. Although there has been much work on Bayesian analysis of LDV models, little to no discussion on truncated regression models from a Bayesian point of view is available. We believe the lack of a Bayesian perspective is mainly due to computational difficulties in the posterior distribution. Although MCMC methods are straightforward for censored regression models, the data augmentation methods from censored regression literatures cannot be applied to truncated regressions. We develop a novel MCMC-based approach, which utilizes an auxiliary, untruncated normal distribution to facilitate posterior sampling. We show through a simulation study that our proposed MCMC sampler performs well for both the univariate and multivariate settings. We also demonstrate that interval-valued data, where each observation takes the form of an interval (e.g. a min and a max), can be modeled with a bivariate truncated normal distribution. We apply our MCMC algorithm to sample the resulting posterior distribution and show it performs well.