Think Bayes, 2nd Edition

Chapter 6. Odds and Addends

This chapter presents a new way to represent a degree of certainty, odds, and a new form of Bayes’s theorem, called Bayes’s rule. Bayes’s rule is convenient if you want to do a Bayesian update on paper or in your head. It also sheds light on the important idea of evidence and how we can quantify the strength of evidence.

The second part of the chapter is about “addends”, that is, quantities being added, and how we can compute their distributions. We’ll define functions that compute the distribution of sums, differences, products, and other operations. Then we’ll use those distributions as part of a Bayesian update.

Odds

One way to represent a probability is with a number between 0 and 1, but that’s not the only way. If you have ever bet on a football game or a horse race, you have probably encountered another representation of probability, called odds.

You might have heard expressions like “the odds are three to one”, but you might not know what that means. The odds in favor of an event are the ratio of the probability it will occur to the probability that it will not.

The following function does this calculation:

def odds(p):
    return p / (1-p)

For example, if my team has a 75% chance of winning, the odds in their favor are three to one, because the chance of winning is three times the chance of losing:

odds(0.75)

3.0

You can write odds in decimal form, but it is also common to write them as a ratio of integers. So “three to one” is sometimes written ...