I’ve been thinking about writing an introductory book on linear classifiers. All the math bits are easy, but how do I introduce naive Bayes with a simple example? (Suggestions appreciated!)
While at home over the holidays, my parents (mom‘s a huge British mystery fan) rented Dr. Bell and Mr. Doyle: The Dark Beginnings of Sherlock Holmes (it’s pretty good if you like that sort of thing). That got me thinking about my favorite fictional detective, Encyclopedia Brown. Combined with my love of Martin Gardner‘s mathematical games column in Scientific American, I thought a little puzzle might be in order.
Here’s my first attempt — it could use some help in the story part. Or is this just too undigified for a textbook?
The Case of Who’s Laughing Now?
Mr. and Mrs. Green had very different senses of humor and somewhat distinctive laughs. Only one of them ever laughs at a time. But they both laugh by saying “hee” or “haw”, sometimes using a mix of the two sounds in succession, such as “hee hee haw hee haw”. Over time, Sherlock has observed that when Mr. Green laughs, 20% of the utterances are “hee” and 80% are “haw”; Mrs. Green is more ladylike, with 60% “hee” and only 40% “haw”.
One day, Sherlock was walking by the Green house, and heard the laugh “hee haw haw” from a window. He had no knowledge of whether Mr. or Mrs. Green was more likely to be laughing, but knew it had to be one of them.
What odds should Sherlock post to create a fair bet that the laugh was Mr. Green’s?
I did mention naive Bayes, didn’t I?