Using Bayesian statistics to analyze environmental toxicology data from native freshwater mussels
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Scientists at the US Geological Survey are looking at the effects of the chemical combination 3-trifluoromethyl-4-nitrophenol (TFM) with 1% niclosamide on native freshwater mussels’ behavior and reproduction. Mussels were exposed to the chemicals for 24 hours and reproductive and behavioral outcomes were measured throughout the exposure and 10-day recovery period. The objective of the study is to compare the treatments with respect to these outcome variables. This is usually done using traditional statistical methods like the analysis of variance (ANOVA) or the Kruskal-Wallis test. In this thesis, alternative methods are proposed, using Bayesian methodology. To compare the six treatments, a Bayesian linear regression procedure, a Bayesian logistic mixed effects procedure, and a Bayesian ordinal model were used. This thesis will illustrate how these Bayesian procedures can be implemented using two new R packages. These two R packages use MCMC methods to simulate from the posterior distributions. These simulated values allowed the construction of credible intervals, which can be used in comparing the treatments. Results obtained using the Bayesian methods applied to the native freshwater mussel toxicology data were similar to the results from traditional statistical methods. Some additional benefits of using Bayesian statistics are also discussed in this thesis.
Bayesian statistical decision theory