fix BDA exercises

[hawkrobe]

• problem 1 should use forward sampling for looking at the prior
  • While grading the BDA exercises, it seems like a lot of the time the priors come out looking wonky. This is undesirable because this exercise is supposed to introduce the student to the beta family of priors. I suggest refactoring this exercise to have 2 Infers, one with method:"forward" to show the prior, and the other with MCMC or rejection for the posterior.
  • Ask a more specific question about what a and b intuitively correspond to? Currently students mostly waxing poetic about the exact shapes of the 3 things we asked them to plot rather than abstracting away to a view of the whole family.
  • Also, maybe increasing strength {a: 10, b: 10} vs. {a: 30, b:30} and asking how predictive differs?
• problem 2 wording confused several students
  • what is the "metaphor of model or theory evaluation."
  • what is the "paradigm" (intended to mean the psychophysics task paradigm mentioned in the example, but easy to misinterpret as statistical paradigm)
  • can we act more targeted, specific questions here?
• problem 3
  • C is outdated (all straightforward variables to lift have already been lifted). either need to remove this part, or 'unlift' one of these variables in the chapter. also students often thought 'lifting' just meant putting more variables in the model (i.e. the same as part B). need to say more clearly what we mean by this.
  • need to rewrite to be more explicit about what we're getting at in other parts... (e.g. in part A, ask which condition was explained better by one or the other, and why?)
• decide whether data in problem 4 should be generated with guessing? (so that there's actually a real answer to part F?) could change the data so that model predictions are too extreme relative to the data...?