Test 1 Info Sheet

Logistics

• In-class test: Monday, March 8
  • Little or no coding required for this part; closed book.
• Take-home test: Due Wednesday, March 10
  • You may consult your notes and text book (but not the internet or other people).
• Both portions cover through chapter 5 of Statistical Rethinking

Topics

This list isn’t meant to be exhaustive, but I hope it is useful in preparing for the test.

Techniques

1. Creating Numerical and Graphical Summaries

2. Grid Method

3. Quadratic approximation using quap()

4. Prior and posterior sampling

   1. “manually” (for example, when using the grid method)

   2. using extract.samples(), extract.prior(), link(), and sim()

   3. Creating counterfactual data (for example, for use with link() and sim()

   4. creating HDIs for various quantities

   5. creating plots with prior or posterior distributions

5. Centering (and uncentering) variables

6. A non-exhaustive list of R commands you should know

   • Plotting commands for the types of plots we have been making.

   • Working with data frames: tibble(), expand_grid(), mutate(), filter(), bind_rows(), bind_cols()

   • Working with functions: function(), apply(), map2_dbl() (and cousins)

   • From rethinking: quap(), alist(), precis(), extract.samples(), extract.prior(), link(), sim()

   • Distributions: dnorm(), pnorm(), qnorm(),rnorm()` (and similar for other distributions)

   • Miscellaneous: apply(), str(), head(), slice_sample()

Concepts

1. Conditional probability and connections to Bayesian inference

   • definition of conditional probability

   • problems like the pandas, Alice’s hats, etc.

2. \(\mathrm{posterior} \propto \mathrm{prior} \cdot \mathrm{likelihood}\)

3. What grid approximation is, how it works, and why it is limited to models with only a few parameters.

4. Why quadratic approximation is called that and roughly how it works.

   • potential problems with quadratic approximation (and why we will need a third method eventually)

   • advantages of quadratic approximation over the grid method

5. Conjugate priors

   • advantages and disadvantages of working with conjugate priors
   • conjugate priors for estimating a proportion (Beta distributions)

6. What prior sampling is and what can be done with prior samples.

7. What posterior sampling is and what can be done with posterior samples.

8. Creating models

   • selecting priors that are reasonable
   • creating a model relationship (equation with variables and parameters)
   • polynomial and spline regression
   • (additive) linear models
   • handling categorical variables

9. Interpreting models

   • interpreting model coefficients (and their uncertainty).
   • interpreting model predictions (and their uncertainty).
   • interpreting \(\sigma\) in models where the response is modeled with a normal distribution
   • plots for models (especially those with multiple predictors)
   • residuals
   • masking, spurious relationships and other issues that can be revealed by fitting models with multiple predictors.

10. Why and how to center variables used in models

11. Families of distributions we have used: Uniform, Bernouli/Binomial, Beta, Normal, Log-normal, Exponential