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Friday, August 20, 2010
Bayes is Regression Toward The Mean
This comment from another thread sparked the exchange that follows between me and Jared:
You’ve got a weighted die. You know it’s weighted because you built it. It lands on “1” 25% of the time. You also have nine unweighted dice. You built those too.
You put all 10 in a pouch. You roll each die 36 times. You get these counts for the number of times you roll “1” for the 10 dice:
11-9-8-7-6-6-6-5-5-4
Which one is the weighted die? YOU DON’T KNOW!!!
What is the CHANCE that it’s the one that rolled 11 ones? MORE than the chance that it’s the one that rolled 4 ones. But EACH of the 10 has a chance to be the weighted die.
It’s all based on probability, a number that is GREATER than zero and LESS than one.
If anyone says “all luck” or “all skill”, leave this blog, and never come back. WE DON’T KNOW. All we can do is make a best estimate as to the mean, and a best estimate as to the uncertainty of that mean. And, if you like, a best estimate of the uncertainty of the uncertainty of that mean. And so on.