Question

Come up with an example from another course (or real life) in which you can apply Bayes' theorem.

Criteria:

There's some sort of P(A). That is, you have (or had) a probability belief that something was true.

Then there's some sort of B - new evidence, or some new development.

I want you to calculate your new belief that A is true, given B. That is, you could find P(A|B).

2 points for coming up with an example, 2 points for describing your probabilities and solving for P(A|B) properly using Bayes' theorem.

See, the example in http://econlog.econlib.org/archives/2009/11/why_arent_acade.html . (If you're not familiar with the Card and Krueger study, it's basically showing that an increase in the minimum wage didn't raise unemployment in a very specific setting. Economic theory would predict that the minimum wage does cause unemployment (on average in the long run), and there's generally strong evidence to believe that. So Bryan Caplan (the post's author) suggests that it's not that unlikely to get the Card and Krueger result, even in a world where economic theory is right on this, and shows how a Bayesian calculation might affect his beliefs - just not by very much, given the relative probabilities.)

Other examples:

A = Our new marketing plan is good for increasing sales, and B = Our sales went up by 4% the quarter after we put in the new plan

A = Flat management hierarchies improve team morale, and B = I read a case study about a company that flattened its hierarchy and improved team morale

Answer 1

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