A Proper Scoring Rule for Confidence Intervals


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Scott Garrabrant

You probably already know that you can incentivise honest reporting of probabilities using a proper scoring rule like log score, but did you know that you can also incentivize honest reporting of confidence intervals?

To incentize reporting of a confidence interval, take the score , where is the size of your confidence interval, and is the distance between the true value and the interval. is whenever the true value is in the interval.

This incentivizes not only giving an interval that has the true value