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redding comments on Justifying (Improper) Priors - Less Wrong
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I had typed up an eloquent reply to address these issues, but instead wrote a program that scored uniform priors vs 1/x^2 priors for this problem. (Un)fortunately, my idea does consistently (slightly) worse using the p*log(p) metric. So, you are correct in your skepticism. Thank you for the feeback!