## Electronic Journal of Statistics

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

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

#### 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