FIGURE 7.3 Species sensitivity distribution for atrazine

1 Case Study Example of Bayesian Hierarchical Modeling 

Two very different approaches to inferential statistics exist the classical or fre-quentist approach and the Bayesian approach. Each approach is used to draw conclusions (or inferences) regarding the magnitude of some unknown quantity, such as the intercept and slope of a dose-response model. The key difference between classical 

In this section, the sample information was the raw toxicity test data for each species and test. Prior information was not available outside the data set, so vague prior information was used as a basis for implementing the procedures. 

2 Development of Dose-Response Functions for Individual Species 

A number of issues influenced the selection of the dose-response model form and the treatment of the data prior to fitting the model. First, shoot weight and shoot length are continuous response measurements therefore, use of a standardized logistic model form is not appropriate. Second, the natural variation in plant growth often resulted in apparent increased shoot weight and shoot length measurements relative to the control at low herbicide application rates. A dose-response model needs to perform well even when some measurements in treatment levels exceed the controls. 

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