Tutorial 7: exercise

(c) 2018 Justin Bois. With the exception of pasted graphics, where the source is noted, this work is licensed under a Creative Commons Attribution License CC-BY 4.0. All code contained herein is licensed under an MIT license.

This document was prepared at Caltech with financial support from the Donna and Benjamin M. Rosen Bioengineering Center.

This tutorial exercise was generated from an Jupyter notebook. You can download the notebook here. Use this downloaded Jupyter notebook to fill out your responses.

Exercise 1

a) Explain in words why being able to sample out of a probability distribution is useful.

b) Explain in words the basic idea behind Markov chain Monte Carlo.

Exercise 2

Why is it important to warm up a sampler?

Exercise 3

Say we used MCMC to sample a posterior distribution that had 6 parameters, $g(a_1,a_2,a_3,a_4,a_5,a_6\mid y)$ . From the MCMC samples, how can we get samples for the marginalized distribution $g(a_3 \mid y)$?

Exercise 4

What does it mean for a model to be nonidentifiable?