5.10 Exercises

1. This exercise is about regularization priors. In the code that generates the x_c, y_c data (see https://github.com/aloctavodia/BAP3), change order=2 to another value, such as order=5. Then, fit model_q and plot the resulting curve. Repeat this, but now using a prior for β with sd=100 instead of sd=1 and plot the resulting curve. How do the curves differ? Try this out with sd=np.array([10, 0.1, 0.1, 0.1, 0.1]), too.

2. Repeat the previous exercise but increase the amount of data to 500 data points.

3. Fit a cubic model (order 3), compute WAIC and LOO, plot the results, and compare them with the linear and quadratic models.

4. Use pm.sample_posterior_predictive() to rerun the PPC example, but this time, plot the values of y instead of the values of the mean.

5. Read and run the posterior predictive example from PyMC’s documentation at https://www.pymc.io/projects/docs/en/stable/learn/core_notebooks/posterior_predictive.html. Pay special attention to the use of...