Electronic Journal of Statistics

Bayesian inference in partially identified models: Is the shape of the posterior distribution useful?

Paul Gustafson

Full-text: Open access

Abstract

Partially identified models are characterized by the distribution of observables being compatible with a set of values for the target parameter, rather than a single value. This set is often referred to as an identification region. From a non-Bayesian point of view, the identification region is the object revealed to the investigator in the limit of increasing sample size. Conversely, a Bayesian analysis provides the identification region plus the limiting posterior distribution over this region. This purports to convey varying plausibility of values across the region. Taking a decision-theoretic view, we investigate the extent to which having a distribution across the identification region is indeed helpful.

Article information

Source
Electron. J. Statist., Volume 8, Number 1 (2014), 476-496.

Dates
First available in Project Euclid: 9 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1399646048

Digital Object Identifier
doi:10.1214/14-EJS891

Mathematical Reviews number (MathSciNet)
MR3205730

Zentralblatt MATH identifier
1348.62081

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 62F15: Bayesian inference
Secondary: 62F12: Asymptotic properties of estimators

Keywords
Bayesian inference partial identification posterior distribution

Citation

Gustafson, Paul. Bayesian inference in partially identified models: Is the shape of the posterior distribution useful?. Electron. J. Statist. 8 (2014), no. 1, 476--496. doi:10.1214/14-EJS891. https://projecteuclid.org/euclid.ejs/1399646048


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