Exercises

1. Check the following definition of a probabilistic model. Identify the likelihood, the prior, and the posterior:

2. For the model in exercise 1, how many parameters have the posterior? In other words, how many dimensions does it have?
3. Write down Bayes' theorem for the model in exercise 1.

4. Check the following model. Identify the linear model and identify the likelihood. How many parameters does the posterior have?

5. For the model in exercise 1, assume that you have a dataset with 57 data points coming from a Gaussian with a mean of 4 and a standard deviation of 0.5. Using PyMC3, compute:
   
   • The posterior distribution
   • The prior distribution
   • The posterior predictive distribution
   • The prior predictive distribution

Tip: Besides pm.sample(), PyMC3 has other functions to compute samples.

6. Execute model_g using NUTS (the default sampler) and then...