Tonight, a tweet from @CompSciFact led me to a webpage, *“Efficiently Generating a Number in a Range.”* In a subsection titled *“Classic Modulo (Biased),” *the author mentions how the not generating the entire base of the binary tree when seeking a particular range makes the random number biased. I came across this but didn’t have a word for it when I was trying to see how many data points I would need to separate a single binary decision. I wrote about this in *Trapezoids*, *Yes or No in the Core and Tails III*, and the earlier posts *… II*, and *… I*.

When I wrote Yes or No in the Core and Tails III, the variance in the was obvious in the diagram on minimization in machine learning, but the bias was not. I had thought all along that not filling the entire tree should have made the distribution skewed and kurtotic. But the threshold to having a normal distribution is so big, 2^{11}, that we are effectively dividing the skew and kurtosis numbers by 11, or more generally by the number of tiers in the binary tree. That makes the skew and kurtosis negligible. So we are talking about 248/2048=0.1211.

Enjoy.

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September 13, 2018 at 5:04 am |

[…] Beyond the orthodoxy. « Bias […]