M.S. (Master of Science)
Department of Statistics
Statistics; Statistics--Study and teaching
Sample Size Determination is an important tool in the design of experiments. Researchers often need to choose an appropriate sample size to arrive at a precise and accurate conclusion. Researchers prefer the Bayesian approach over the frequentist approach for sample size determination because it allows for uncertainty about model parameters. In Bayesian Sample Size Determination, given an appropriate model and various sample sizes, data are simulated from the model to learn how the resultant posteriors will behave for various sample sizes. Then, the minimal sample size needed to achieve the results with pre-fixed accuracy is chosen. In this thesis, two Bayesian Sample Size Determination (BSSD) methods are discussed. They are the posterior predictive probability approach and the Bayes Factor approach. In the posterior predictive probability approach, the goal is to find the minimum sample size needed to achieve a pre-determined large predictive probability that a hypothesis or model of interest is found to be true, given that the hypothesis or the model is true, for a pre-fixed large proportion of simulated data sets. In the Bayes Factor Approach, Bayes Factor is computed to discriminate between two hypotheses or models of interest, for assumed simulated data sets from the models in question. The minimum sample size needed for achieving a pre-fixed strength of model separation and a pre-fixed confidence in such model separation is then recommended. In this thesis, several R packages such as "Bayes Factor" and "MCMCpack" are used to find the sample size.
Lakshmanan, Devi Chitra, "Bayesian sample size determination for some ANOVA designs and regressions" (2015). Graduate Research Theses & Dissertations. 1611.
Northern Illinois University
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