Nate Silver has a book on this – The Signal and the Noise. He uses presidential election polls in the US as an example.
Is the most accurate indicator the quinnipiac poll , or the Washington Post, or a different source?
Bayesian theory says the most accurate guess will be an aggregate all of them, and to weigh each one proportionally to to how accurate those polls are. (It provides specific math).
Using this method, Silver was famously able to accurately predict not just the 2008 election, but he was actually able to predict the outcome of 49 of the 50 states correctly.
Most importantly – when Bayes says the prediction is 80% certain – it really does predict the correct outcome 80% of the time. This is useful for all sorts of predictions – elections, weather, sports, stocks, etc…
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