Monday, November 7, 2011

A quick note on log odds

Probabilties are usually numbers that range from 0 to 1. However, the standard way of representing probabilities is not always optimal. However, there is another mapping of probability that goes from negative infinity to infinity. This system called "log odds" has a number of advantages. In the standard log odds approach, one maps the probability of an event x to the quantity log(x/(1-x)). Brian Lee and Jacob Sanders wrote a good summary (pdf) of this system which discusses its advantage and disadvantages. As they observe, use of log odds allows one to immediately see how something like the change in probability from 51% to 52% isn't that big whereas the change from 98% to 99% is a much larger change in the sense that the chance of the event not happening has now halved. Log odds helps makes this sort of intuition immediatelty obvious from the numbers. Brian and Jacob discuss the advantages and disadvantages of log odds in detail, and show how it is particularly useful for doing Bayesian updates. I strongly recommend reading their piece.