A jeweler reaches into his desk drawer and pulls out 3 photographs of diamonds on velvet backgrounds, he is very proud of the workmanship in cutting these expensive diamonds. "What do you think of that?" He says to his two friends, both of whom are statisticians.

Bayesian: Well, I know something about photography and light and diamonds, so I know that if I were to take the digital photos and apply a Gaussian blur to them then in each of the photographs the center of the diamond would be one of the pixel values that had at least brightness B. (Plausibility of the location is measured by brightness)

Frequentist: I see that the diamonds are at x1,y1 and x2,y2 and x3,y3 so if I assume all of the photographs in your desk drawer are of diamonds on velvet backgrounds, I can reject the hypothesis that the diamonds are on average in the center of those other photographs. (Repeated sampling would almost never produce 3 photos in a row with the diamond this far off center)

Jeweler: Yes, yes, but which one should I give to my wife for our anniversary?

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1. May 6, 2016

"Jeweler: Yes, yes, but which one should I give to my wife for our anniversary?"

That must surely depend on his prior, no?