Have you heard of Bayes’ Rule? Let’s use an intuitive example to understand an application of this rule. What’s the probability American Hustle wins the Golden Globes given it wins the Oscars?
What is Bayes’ Rule? With the Bayes Rule, we use a known outcome to predict a sequence of events leading up to that outcome. To understand this rule, we rely on conditional probabilities and probability trees. For a quick refresher, see our tutorial post and video here: Conditional Probabilities and the Academy Awards
Here’s our question: What’s the probability American Hustle wins the Golden Globes given it wins the Oscars? Let’s make the assumption American Hustle wins the Oscars (of course, as of the time this tutorial was released, we have no idea what the results of the 2014 Oscars are!) So, in our hypothetical example, American Hustle’s winning of the Oscars is a known outcome. Given this, can we predict what would have been the probability of winning the Golden Globes a few weeks ago? Yes! Bayes’ Rule allows us to solve this problem.
Bayes’ Rule states the following:
P (Wg | Wo) = P (Wo | Wg) P (Wg) = P (Wo and Wg) P (Wo) P (Wo)
This is a ratio that states the probability American Hustle wins both the Oscars and Golden Globes out of a specific subset: the total probability it wins the Oscars. To solve this calculation, here is the link to our sample spreadsheet: Conditional Probabilities & Bayes’ Rule