I love it and I hate it. Why I love it: It's precise. It's elegant. It's rigorous. It's based upon solid, proven science & theory. It's a perfect application for a computer. And most of all, it does what's intended: it works. Why I hate it: What human can understand it? I used to implement the first manufacturing and distribution systems that used thinking like this. They figured, "We finally have the horsepower to a…
I talk about this with some of my med school friends that are interested in/want to create/hate/fear automated diagnosis. At one level, having appropriate statistics to make use of a wealth of prior experience, worldwide prevalence, epidemiological data, &c is basically a requirement for the future of proper healthcare.
It's also an obvious terrible mistake to ever convince people that these statistics are anything besides a decision making tool.
I think the right usage of statistics is to enlighten and confuse simultaneously, not to "answer". They should provide analytical depth to a decision, never an escape route.
For this reason, I think proper statistical application is an intersection between mathematics, computer science, and UI design.