John D. Cook

In mathematics, log means natural logarithm by default; the burden of explanation is on anyone taking logarithms to a different base. I elaborate on this a little here. Looking through Andrew Gelman and Jennifer Hill’s regression book, I noticed a justification for natural logarithms I hadn’t thought about before. We prefer natural logs (that is, logarithms […]

Every Wednesday I’ve been pointing out various resources on my web site. So far they’ve all been web pages, but the following are all PDF files. Probability and statistics: How to test a random number generator Predictive probabilities for normal outcomes One-arm binary predictive probability Relating two definitions of expectation Illustrating the error in the […]

A bigram is a pair of letters. For various reasons—word games, cryptography, user interface development, etc.—people are interested in knowing which bigrams occur most often, and so such information is easy to find. But sometimes you might want to know which bigrams occur least often, and that’s harder to find. My interest is finding safe […]

Suppose you have data in an N-dimensional space where N is large and consider the cube [-1, 1]N. The coordinate basis vectors start in the center of the cube and poke out through the middle of the faces. The diagonals of the cube run from the center to one of the corners. If your points cluster along one […]