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# Lecture13 - Lecture 13 More Practice With Bayesian Data...

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Lecture 13 More Practice With Bayesian Data Analysis Example 1 : A Bioassay Experiment In the development of drugs and other chemical compounds, acute toxicity tests or bioas- say experiments are commonly performed on animals. Such experiments proceed by administering various dose levels of the compound to batches of animals. The animals’ responses are typically characterized by a dichotomous outcome: for example, alive or dead, tumor or no tumor. An experiment of this kind gives rise to the data shown below where x i represents the i th of N = 4 dose levels (measured on the log scale) given to n i animals, of which y i subsequently respond with positive outcome. Two hundred animals were tested, 50 at each of the four dose levels. Dose, x i Number of Number of (log g/ml) animals, n i deaths, y i -0.863 50 0 -0.296 50 8 -0.053 50 32 0.727 50 50 The Standard Logistic Regression Model The standard logistic regression model for these data is y i | p i Binomial( n i , p i ) y i | p i independent i = 1 , 2 , 3 , 4 logit( p i ) = α + β x i We can check if there is a linear trend between x and the sample logits. Since a linear trend seems appropriate, we fit the model.

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Lecture13 - Lecture 13 More Practice With Bayesian Data...

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