The Elvis problem revisited

Here’s a problem from Bayesian Data Analysis:

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

I will answer this question in three steps:

First, we need some background information about the relative frequencies of identical and fraternal twins.Then we will use Bayes’s Theorem to take into account one piece of data, which is that Elvis’s twin was male.Finally, living up to the name of this blog, I will overthink the problem by taking into account a second piece of data, which is that Elvis’s twin died at birth.

For background information, I’ll use data from 1935, the year Elvis was born, from the U.S. Census Bureau, Birth, Stillbirth, and Infant Mortality Statistics for the Continental United States, the Territory of Hawaii, the Virgin Islands 1935.

It includes this table:

With a few reasonable assumptions, we can use this data to compute the probability that Elvis was an identical twin, given that his twin brother died at birth.

You can see my solution in this Jupyter notebook.