[agentofoblivion]

This might be overstating it a bit. Just this week I've been studying the AdaNet paper and grappling with Noise Contrastive Estimation. I agree that with a B.S. in physics you'll at least get the calculus you need, but I think a graduate level degree really deepens your understanding since it's not the first time through and you're already familiar with the basic concepts.

Regarding doctors and stats, I share your concern. But I disagree with the statement that stats should be second nature to anyone that's gone through the courses. If I've learned one thing while going deeper and deeper into stats, it's that there's a lot more nuance than I originally understood, and I'm still not there. Just when I think I have a thorough understanding of p-values and the like, I'll read some "I can't believe everyone doesn't understand THIS" blog and see that there was more to the story still again. It's hard to know what you don't know.