2.10 Exercises

1. Using PyMC, change the parameters of the prior Beta distribution in our_first_model to match those of the previous chapter. Compare the results to the previous chapter.

2. Compare the model our_first_model with prior θ ∼ Beta(1,1) with a model with prior θ ∼(0,1). Are the posteriors similar or different? Is the sampling slower, faster, or the same? What about using a Uniform over a different interval such as [-1, 2]? Does the model run? What errors do you get?

3. PyMC has a function pm.model_to_graphviz that can be used to visualize the model. Use it to visualize the model our_first_model. Compare the result with the Kruschke diagram. Use pm.model_to_graphviz to visualize model comparing_groups.

4. Read about the coal mining disaster model that is part of the PyMC documentation ( https://shorturl.at/hyCX2). Try to implement and run this model by yourself.

5. Modify model_g, change the prior for the mean to a Gaussian distribution centered at the...