Senior Honors Projects, 2010-current

Date of Award

Spring 2014

Document Type

Thesis

Degree Name

Bachelor of Science (BS)

Department

Department of Mathematics and Statistics

Advisor(s)

Samantha Prins

Ling Xu

Lihua Chen

Abstract

We discuss a comparison of the Bayesian approaches to uncertainty assessment in deterministic models developed in Sohn and Small (2000) and Bates et al. (2003). The methods were compared within the context of the environmental risk assessment model discussed in Bates et al. (2003). Each approach was run with the same data and priors, their specific likelihood forms, and a sample from the posterior distributions obtained using the same algorithm, namely, sampling importance resampling. To determine similarities and differences between the two approaches we compared the general shape, location and spread of the posterior distributions as well as the analytic form of the likelihoods each used. The comparison showed that there was a difference in the likelihoods of each model and that this resulted in differences in some of the posterior distributions. Bates et al. (2003) used the mean and standard deviation of the observed data in their likelihood while Sohn and Small (2000) used each individual data point in their likelihood. For this reason, we believe that Sohn and Small (2000) seemed to represent the data better.

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