Tutorial 5: 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

What is the plug-in principle and how is it used in non-parametric statistics?

Exercise 2

What is a bootstrap sample and what is a bootstrap replicate?

Exercise 3

Consider the following data set for waiting times in minutes for nuclear localization events of the gene MSN-2 in yeast (these are real measurements done by Yihan Lin in Michael Elowitz's lab).

In [1]:
t = [3, 6, 11, 5, 5, 4, 73, 31, 7, 6, 
     30, 4, 32, 30, 5, 53, 2, 15, 18, 
     14, 3, 49, 7, 4, 4, 2, 9, 11, 8, 
     5, 14, 6, 32, 40, 3, 5, 24]

You suspect that MSN-2 localization may be a Poisson process and therefore that these waiting times are Exponentially distributed with a characteristic wait time of 20 minutes. Do a quick graphical analysis to check out this idea.