elvis_soln.ipynb

Kernel: Python 3

Think Bayes

This notebook presents example code and exercise solutions for Think Bayes.

Copyright 2018 Allen B. Downey

MIT License: https://opensource.org/licenses/MIT

# Configure Jupyter so figures appear in the notebook
%matplotlib inline

# Configure Jupyter to display the assigned value after an assignment
%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'

# import classes from thinkbayes2
from thinkbayes2 import Hist, Pmf, Suite

Exercise: This exercise is from one of my favorite books, David MacKay's "Information Theory, Inference, and Learning Algorithms":

Elvis Presley had a twin brother who died at birth. What is the probability that Elvis was an identical twin?"

To answer this one, you need some background information: According to the Wikipedia article on twins: "Twins are estimated to be approximately 1.9% of the world population, with monozygotic twins making up 0.2% of the total---and 8% of all twins.''

# Solution

# Here's a Pmf with the prior probability that Elvis 
# was an identical twin (taking the fact that he was a 
# twin as background information)

pmf = Pmf(dict(fraternal=0.92, identical=0.08))

Pmf({'fraternal': 0.92, 'identical': 0.08})

# Solution

# And here's the update.  The data is that the other twin
# was also male, which has likelihood 1 if they were identical
# and only 0.5 if they were fraternal.

pmf['fraternal'] *= 0.5
pmf['identical'] *= 1
pmf.Normalize()
pmf.Print()

fraternal 0.8518518518518517
identical 0.14814814814814814