Since we're on the subject, can anyone point me in the direction of how to account for correlated inputs? Without adjusting them, it can possibly give nonsensical probabilities (>1) but my math isn't good enough to decipher the few academic texts I've seen regarding this situation.
A (very simple) example: I trade stocks. My starting point is that I think a stock has a 50% chance of rising next year. Then I want to do a Bayesian iteration with the stock's P/E ratio based on historical data for stocks with similar P/E ratios. Then I want to also incorporate the P/E ratio of the industry the stock is in. Obviously these two inputs are correlated and if you have enough correlated variables, the whole thing breaks down because the simple theorem only works if all the inputs are independent of each other.
A (very simple) example: I trade stocks. My starting point is that I think a stock has a 50% chance of rising next year. Then I want to do a Bayesian iteration with the stock's P/E ratio based on historical data for stocks with similar P/E ratios. Then I want to also incorporate the P/E ratio of the industry the stock is in. Obviously these two inputs are correlated and if you have enough correlated variables, the whole thing breaks down because the simple theorem only works if all the inputs are independent of each other.