Daily tweets on probability from @JohnDCook.
Joined November 2009
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A Short Introduction to Optimal Transport and Wasserstein Distance alexhwilliams.info/itsneuron…
A random number generator may have excellent statistical properties and yet be unsuited for cryptography.
'All probabilities are conditional on something, and to be useful they must condition on the right thing.' -- Frank Harrell
The moment generating function of a random variable X is the two-sided Laplace transform of its density function f_X, with the sign of the argument flipped.
The Mellin transform of the product of two independent random variables is the product of their Mellin transforms.
'There are only five probabilities the average human can handle: 99 percent, one percent, 100 percent, zero, and 50-50. That’s it.” — Richard Thaler
If A and B are independent causal factors leading to L, then L is called a collider. After conditioning on L, A and B are /not/ independent.
Counting selections with replacement johndcook.com/blog/select_wi…
For a multivariate normal, the probability of being within two standard deviations of the mean goes to zero as the dimension increases.
Tweedie distributions en.wikipedia.org/wiki/Tweedi…
Pairwise independence does not imply independence johndcook.com/blog/2008/01/1…
The Laplace (double exponential) distribution is commonly used for noise generation in differential privacy applications.
'... the theory of probabilities is at bottom only common sense reduced to calculus.' -- Pierre-Simon Laplace