Tutorial 8: 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

Why is the number of effective independent samples made by a MCMC chain less than the total number of MCMC samples? How can you boost the number of effective independent samples?

Exercise 2

How can locations of divergences be used to diagnose potential problems with the sampler?

Exercise 3

Why do posterior distributions in hierarchical models often have a funnel shape?

Exercise 4

Are you ever guaranteed to properly sample a distribution with a finite number of MCMC steps? If you answered yes, you can stop. If you answered no, explain how this underscores the need for extensive diagnostics.