Exercise 3

Question 1

Language restrictions: None

Consider the problem of 'pessimistic' prediction: you would like to estimate a success probability $p$ . However, let us say it is absolutely imperative that you do not over-estimate the true success probability, even by a slight amount.

How would you approach this problem?
Implement your idea on your hierarchical model from last time, or on some other problem that involves estimation of a success probability.

Question 2

Language restrictions: Use Stan

Note: there will be a tutorial on Blang and Stan on the Monday office hour. However you must make sure you have a working version of Stan and Blang before the tutorial (see below). You can get help by Piazza to do so.

Implement our Bayesian GLM model in Stan. Run it on the Challenger data from the lectures.
Optional: pick a classification dataset of your choice, e.g. on Kaggle or UCI repository. Modify your Stan code to perform a Bayesian GLM analysis on that dataset. Compare the results to (penalized) MLE.
Optional: compare the efficiency of Stan and JAGS on a Bayesian GLM problem.

Question 3

Language restriction: Use Blang

Have a look at the file titanic.csv from the Titanic dataset.
In this question we will perform Bayesian feature selection on that dataset.
We will use a Bayesian GLM, but we will modify the model so that the posterior distribution puts positive probability to having some of the logistic regression parameters at zero.
More background will be provided during lecture and Monday tutorial.

Setting up

You can use any of the following two methods

Locally

Clone the assignment template repo
Follow the instructions in the README.md file
Test that things run properly (see README.md)

Silico

The problem from last time should be fixed now. You can:

Sign up
Go to the assignment page
Jump to Question 4 to make sure things run properly