A Bayesian approach to custer sampling

Loading...

View/Download File

Soma_umn_0130E_13324.pdf (1.48 MB)

Persistent link to this item

https://hdl.handle.net/11299/144325

Statistics

View Statistics

Journal Title

Journal ISSN

Volume Title

Title

A Bayesian approach to custer sampling

Authors

Soma, Michael Blohm

Published Date

2012-12

Publisher

Type

Thesis or Dissertation

Abstract

Cluster sampling is a survey design that is commonly used when a simple random sample may be too costly or inefficient to implement for a population. The idea of a cluster sample is that a population can be divided into groups called clusters. The usual cluster sample consists of sampling n of the N clusters within a population. Within these clusters, a further sample may be taken of secondary sampling units. When a further sample is taken within the primary sample, this is called a two-stage cluster sampling design. Design-based estimates of mean and total are well-established for two-stage cluster samples. For certain populations, however, a Bayesian approach may be preferred for ease of interpretation or to estimate a parameter not well-developed in the design-based literature. When a Bayesian approach is used, a commonly desired property of the model is that the sampled and unsampled units are exchangeable. In this way, the data and not the model is influencing population estimates. A Bayesian approach in which the sampled and unsampled units are exchangeable is the Bayes Urn model. In this dissertation, we will show how the Bayes Urn model can provide admissible estimators under any finite parameter space. Using simulation studies for a variety of two-stage cluster samples, we will show how the Bayes Urn estimates are similar to the standard design-based estimates. As an extension, we will use the Bayes Urn model to incorporate auxiliary information for two-stage cluster samples. For both of these cases we will compare the Bayes Urn estimate of the population total to the standard design-based estimates as well as two standard Bayesian estimates. In the case when auxiliary information is available for a two-stage cluster sample, there is no well-developed Bayesian approach in the literature. In addition to population total, we will also consider estimates of cluster median, in which no design-based approach is well-developed in the literature. Through these simulation studies, the admissibility proof, and the flexible properties inherent of the Bayes Urn model, we will see that this approach can provide useful estimations in complex designs beyond the two-stage cluster sample design.

Keywords

Bayesian

Bayes Urn

Cluster sample

Complex design

Polya posterior

Two-stage

Description

University of Minnesota Ph.D. dissertation. December 2012. Major: Statistics. Advisor:Glen Meeden. 1 computer file (PDF); x, 130 pages.

Related to

Replaces

License

Collections

Dissertations

Series/Report Number

Funding information

Isbn identifier

Doi identifier

Previously Published Citation

Suggested citation

Soma, Michael Blohm. (2012). A Bayesian approach to custer sampling. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/144325.

Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.