(This article was originally published at Statistical Modeling, Causal Inference, and Social Science, and syndicated at StatsBlogs.)
I’m already on record as saying that Ronald Reagan was a statistician so I think this is ok too . . .
Here’s what Columbo does. He hears the killer’s story and he takes it very seriously (it’s murder, and Columbo never jokes about murder), examines all its implications, and finds where it doesn’t fit the data. Then Columbo carefully examines the discrepancies, tries some model expansion, and eventually concludes that he’s proved there’s a problem.
OK, now you’re saying: Yeah, yeah, sure, but how does that differ from any other fictional detective? The difference, I think, is that the tradition is for the detective to find clues and use these to come up with hypotheses, or to trap the killer via internal contradictions in his or her statement. I see Columbo is different—and more in keeping with chapter 6 of Bayesian Data Analysis—in that he is taking the killer’s story seriously and exploring all its implications. That’s the essence of predictive model checking: you take advantage of the fact that you’re working with a generative model, and you generate anything and everything you can.
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