It’s a bit like a weighted average, and helps us compare against the overall chance of a positive result.
In our case, Pr(X) gets really large because of the potential for false positives.
Without it, we might think that a positive test result gives us an 80% chance of having cancer.
The article mentions an intuitive understanding about shining a light through your real population and getting a test population.
The analogy makes sense, but it takes a few thousand words to get there :). You do some tests which “shines light” through that real population and creates some test results.
We have Plugged into a more readable formula (from Wikipedia): Bayesian filtering allows us to predict the chance a message is really spam given the “test results” (the presence of certain words).
Clearly, words like “viagra” have a higher chance of appearing in spam messages than in normal ones.
Thank you, normalizing constant, for setting us straight!
This is the part many of us may neglect, which makes the result of 7.8% counter-intuitive.
They became the method of choice for uncertain reasoning in artificial intelligence and expert systems, replacing earlier, ad hoc rule-based schemes.
Bayesian networks are models that consist of two parts, a qualitative one based on a DAG for indicating the dependencies, and a quantitative one based on local probability distributions for specifying the probabilistic relationships.
Spam filtering based on a blacklist is flawed — it’s too restrictive and false positives are too great.