## Electronic Journal of Statistics

- Electron. J. Statist.
- Volume 12, Number 2 (2018), 2515-2536.

### A noninformative Bayesian approach for selecting a good post-stratification

Patrick Zimmerman and Glen Meeden

#### Abstract

In the standard design approach to survey sampling prior information is often used to stratify the population of interest. A good choice of the strata can yield significant improvement in the resulting estimator. However, if there are several possible ways to stratify the population, it might not be clear which is best. Here we assume that before the sample is taken a limited number of possible stratifications have been defined. We will propose an objective Bayesian approach that allows one to consider these several different possible stratifications simultaneously. Given the sample the posterior distribution will assign more weight to the good stratifications and less to the others. Empirical results suggest that the resulting estimator will typically be almost as good as the estimator based on the best stratification and better than the estimator which does not use stratification. It will also have a sensible estimate of precision.

#### Article information

**Source**

Electron. J. Statist., Volume 12, Number 2 (2018), 2515-2536.

**Dates**

Received: March 2018

First available in Project Euclid: 27 July 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.ejs/1532678418

**Digital Object Identifier**

doi:10.1214/18-EJS1461

**Mathematical Reviews number (MathSciNet)**

MR3833471

**Zentralblatt MATH identifier**

06917484

**Subjects**

Primary: 62D05: Sampling theory, sample surveys

Secondary: 62F15: Bayesian inference

**Keywords**

Finite population sampling stratification prior information stepwise Bayes

**Rights**

Creative Commons Attribution 4.0 International License.

#### Citation

Zimmerman, Patrick; Meeden, Glen. A noninformative Bayesian approach for selecting a good post-stratification. Electron. J. Statist. 12 (2018), no. 2, 2515--2536. doi:10.1214/18-EJS1461. https://projecteuclid.org/euclid.ejs/1532678418