The Election and Bayes

Jim Albert, a statistics professor at Bowling Green State University, has posted a short article on his statistics blog showing how a simple Bayesian approach can be used to predict the electoral vote outcome in today's election. You should be able to understand his idea quite clearly, as it's not significantly different from what we have been doing. The main difference is that he takes into account people who will vote for a third party candidate, so there is a third term in the likelihood that is equal to the probability of a third party candidate raised to the power equal to the number of people in the poll who said they would vote for a third party candidate. The other thing we've already discussed briefly, but here's the idea: After computing the posterior probability (as a formula, not as a table as we have been doing it), he uses a computer to draw a sample of 5000 values of each of the three possibilities (McCain, Obama, Other) representing the proportion of people that the sample says voted for each. He then counts the number of samples that favored Obama over McCain, and calls the state for that candidate for each sample. He then gets a win probability for each state, and he's listed them in the blog.

The second part is even simpler. He uses the computer to flip a biased coin with the appropriate probability (from his table) for each state, assigns the electoral votes from that state to the winner, and adds them up over all states. This gives him a prediction for the electoral vote for Obama and McCain. He does this 5000 times to get 5000 predictions of the electoral vote, and plots them in the graph at the bottom of the page. His prediction is that Obama will get at least 300 electoral votes, and my eye indicates that the actual outcome is likely to be between 340 and 380, give or take.

This is pretty close to the method being used at fivethirtyeight.com.

This is a method called posterior simulation. What he's doing is drawing a large sample from the posterior distribution, and using that as a proxy for the actual posterior distribution. It is a method that is widely used by professional Bayesian statisticians. We can discuss it in more detail after the test, if you like.

Jim Albert, by the way, is the author of the textbook we will be using next semester in our statistics course on Bayesian statistics.