Assignment 4: Roundup

Students

Name	Id
Ploni Almoni	123489589
John Smith	923352302

The purpose of this assignment is to let you experiment with models and probabilistic programming frameworks we introduced in class.

This assignment contains two questions. For each question, you are given a data set and asked to perform an analysis on the data. The analysis should include all usual steps, as we learned during the course:

1. Initial data exploration
2. Specification of the initial model
3. Inference of the posterior
4. Predictive posterior checks and sensitivity analysis
5. Expansion of the model and evaluation of the expanded model

You are not allowed to use Turing in this assignment. Rather, you may use any probabilistic programming framework demonstrated or mentioned in class (Infergo, Stan, Pyro, Anglican, Turing,jl, Gen.jl, ...).

Problem 1: Unsupervised exploration of Iris dataset

Iris flower data set contains measurements of features of three related specifes of Iris flowers. How well do the features separate species? Your model should use only the features, not the species labels, for inference. However, you may use species labels to assess the informativeness of the features to identify a species. For your convenience, the data set is provided.

Problem 2. Reedfrog survival

In class, we explored the data set for reedfrog survival experiment. We developed a simple hierarchical model based on the number of aquarium only, as well as a cross-classified model taking predation into account.

1. Implement a linear regression model for the problem. Use population size, aquarium size, and predation as the explanatory variables, and the number of surviving reedfrogs as predicted variable.
2. Check, compare, and evaluate the 3 models:
   • hierarchical model from lecture 5, based on aquarium only.
   • cross-classified hierarchical model from lecture 6, based on aquarium and predation.
   • regression model you have developed.