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wnoise comments on Open Thread: March 2010 - Less Wrong
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I'm considering doing a post about "the lighthouse problem" from Data Analysis: a Bayesian Tutorial, by D. S. Sivia. This is example 3 in chapter 2, pp. 31-36. It boils down to finding the center and width of a Cauchy distribution (physicists may call it Lorentzian), given a set of samples.
I can present a reasonable Bayesian handling of it -- this is nearly mechanical, but I'd really like to see a competent Frequentist attack on it first, to get a good comparison going, untainted by seeing the Bayesian approach. Does anyone have suggestions for ways to structure the post?
I don't have the book you're referring to. Are you essentially going to walk through a solution for this [pdf], or at least to talk about point #10?
This is a Bayesian problem; the Frequentist answer is the same, just more convoluted because they have to say things like "in 95% of similar situations, the estimate of a and b are within d of the real position of the lighthouse". Alternately, a Frequentist, while always ignorant when starting a problem, never begins wrong. In this case, if the chose prior was very unsuitable, the Frequentist more quickly converges to a correct answer.
Yes, that was the plan.
I thought Frequentists would not be willing to cede such, but insist that any problem has a perfectly good Frequentist solution.
I want to see not just the Frequentist solution, but the derivation of the solution.