Logistic Regression from Bayes’ Theorem

We started wanting to know \(P(H|D)\), the probability take our cup of coffee would be great given our brewing setup, which is out data \(D\). This means that rather than looking at just the probability of \(P(H|D)\) we needed to look at the odds, \(O(H|D)\) which compares the probability that the coffee is great with the probability that it’s not, \(\bar{H}\). When we transformed our odds to the \(log_{10} O(H|D) \) odds we fix this asymmetry:

So aside from giving us a nice linear way to look at our problem, framing our problem in log odds actually makes a lot of sense when we try to interpret the results!

Source: www.countbayesie.com