Title

Sample size determination under Bayesian modeling

Date of Completion

January 1999

Keywords

Statistics

Degree

Ph.D.

Abstract

Sample size determination (SSD) is an important aspect of experimental design. In most comparative experiments, a decision about sample size must be made prior to data acquisition. This involves power analysis within a classical statistical framework. We are going to formulate required sample size determination within a Bayesian framework. Required sample size is chosen to achieve a pre-specified model performance criterion. We also take sample size determination into a model selection environment. Here a sample size is calculated to separate two different models. We also provide analytical results on the behavior of our sample size determination criteria when possible. ^ Determination of sample size is an issue frequently faced by practitioners. Bayesian methods are ideally suited to this design aspect. First, information is usually available prior to experiment. It is better to incorporate this prior information into the study at design stage. In fact, the prior can play the role of a “what if” specification, allowing the designer to assess Bayesian learning as a function of sample size over a range of specifications. Second, it is sensible to average over the sample space since the sample has not yet been observed and the general principle of averaging over what is unknown applies. ^ Historically, sample size determination has been confined primarily to one and two sample problems. We are aiming to address the sample size problem for more complicated modeling frameworks, e.g., the attractive hierarchical models which are the standard Bayesian environment. Simulation-based model fitting is customarily employed for inference under hierarchical models. For sample size determination we require replications of such simulation adequate to assess performance averaged over the sample space. As a result, our approach is computationally intensive and does not provide explicit formulas for required sample size. We present illustrative examples to show our sample size determination approaches. In summary, this dissertation involves addressing the sample size problem under Bayesian modeling for rather general classes of models. ^