Anodyne
Wednesday, September 08, 2021
 

"How do we estimate how many times [the] rock has been painted? The problem is like this: suppose you've got things numbered 1 to N, like the paintings, and you pick k of them (uniformly) at random. You don't know how big N is, but you want to estimate it from the sample. Where do we go from here?

One way, which requires a little knowledge of statistics, is to calculate the 'maximum likelihood estimator.' This turns out to just give the maximum number of the sample. So perhaps Jake did some frequentist analysis in his head, who knows. But this is clearly not the answer - our search continues. How about taking the average distance between numbers in your sample, then adding them to the maximum number? Assuming the data is uniformly distributed, this works like a charm. This gives our first estimate of:

N ≈ m(1+1/k)–1, where m is the maximum of the sample, and k is the size of the sample. In the case of Captain Holt's rocks: m=367, k=2, which gives us approximately 550 paintings of rocks."
- posted by cjb @ 9:16 AM


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