“Area of app” depends on granularity: “analysis of running time” (e.g. “how long will this take, I haven’t got all day”) is an area of app, but if we are willing to drill in we can talk about distributions on input vs worst case as separate areas of app. I don’t really see a qualitative difference here: sometimes F is more appropriate, sometimes not. It really depends on how much we know about the problem and how paranoid we are being. Just as with algorithms—sometimes input distributions are reasonable, sometimes not.
Or if we are being theoretical statisticians, our intended target for techniques we are developing. I am not sympathetic to “but the unwashed masses don’t really understand, therefore” kind of arguments. Math techniques don’t care, it’s best to use what’s appropriate.
edit: in fact, let the utility function u(.) be the running time of an algorithm A, and the prior over theta the input distribution for algorithm A inputs. Now consider what the expectation for F vs the expectation for B is computing. This is a degenerate statistical problem, of course, but this isn’t even an analogy, it’s an isomorphism.
“Area of app” depends on granularity: “analysis of running time” (e.g. “how long will this take, I haven’t got all day”) is an area of app, but if we are willing to drill in we can talk about distributions on input vs worst case as separate areas of app. I don’t really see a qualitative difference here: sometimes F is more appropriate, sometimes not. It really depends on how much we know about the problem and how paranoid we are being. Just as with algorithms—sometimes input distributions are reasonable, sometimes not.
Or if we are being theoretical statisticians, our intended target for techniques we are developing. I am not sympathetic to “but the unwashed masses don’t really understand, therefore” kind of arguments. Math techniques don’t care, it’s best to use what’s appropriate.
edit: in fact, let the utility function u(.) be the running time of an algorithm A, and the prior over theta the input distribution for algorithm A inputs. Now consider what the expectation for F vs the expectation for B is computing. This is a degenerate statistical problem, of course, but this isn’t even an analogy, it’s an isomorphism.