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A Proper Scoring Rule for Confidence Intervals

Is there a way to adjust this to support better scores for tighter confidence intervals?

For instance, using natural log, with a range of 8-10 and a true value of 10, I get -0.2231 whether I pick a 90% confidence interval, or a 95% confidence interval (coefficient of 40). It'd be nice if the latter scored better.

Lotteries: A Waste of Hope

For powerball to have an Expected Value of 1, the individual take-home jackpot would have to be about $313,124,412 for the lump sum, after taxes. (Which, assuming average state income tax rates, corresponds to an advertised jackpot of roughly $805,000,000 AND assumes the jackpot doesn't have multiple winners, which at that level is pretty unlikely.) Of course, since it's a risky bet, you don't want to blow your whole bankroll on lottery tickets even if the EV is above 1. That's where the Kelly Criterion comes in. According to the easy version of the Kelly Criterion (the hard version gets messy) the calculation is that in order to justify even one $2 ticket, you have to have around $621-Million in the bank. But that assumes you can play the game enough times (multiple rounds) with the same payoff/probability each round to have a good chance of reaching your EV (which would mean that the powerball would have quite the endowment saved up, but whatever). Since powerball jackpot odds are 1/175,223,510, even waiting 175,223,510 /2 weeks (since powerball is drawn twice a week) is 1,684,842 years. And if I did my probability right, if you want to be 99% certain of getting the jackpot, you have to play for 7,758,977 years.

Although, I guess if you're going to live that long, you probably don't need to save your $621-Million ahead of time. Just budget as you go.

Belief in Belief

I asked... he apparently doesn't say much. She's theorizing Münchausen syndrome, which means he's not necessarily conscious that he's feigning illness.

Belief in Belief

Just as a completely non-religious example, my girlfriend is a medical social worker and has been working recently with a patient that is absolutely convinced he has cancer.

There has apparently been some cases of tests that came back clean, and his excuses after the fact, but it's also turned in to him anticipating future tests not finding the cancer, yet with him still certain he has cancer. I had originally suggested that she ask him ahead of time something like, "well if we do this test and it comes back clean, will you let it go?" but he wasn't even open to the question.