Statistical Factoids



Frequentists and Bayesians
	There is a continuing debate among statisticians over the proper definition of "probability."
"Probabilistics"
	There is more to Monte Carlo simulation than replacing constants with probability densities.
Bivariate Normal
	Here is a simple algorithm for sampling from a bivariate normal distribution.
Goodness-of-Fit
	Goodness-of-Fit tests, like Anderson-Darling, tell you when you *don't* have a normal distribution.
R-squared ...
	... is an often misused goodness-of-fit metric, where bigger isn't always better.
Other Measures
	R-squared isn't the only way to judge how well the model works.
Curse of Dimensionality
	Direct-sampling Monte Carlo requires the number of samples per variable to increase exponentially with the number of variables to maintain a given level of accuracy.
convergence in distribution
	We engineers are familiar with convergence to a point, but what of convergence to a distribution?
extreme value distributions
	The largest, or smallest, observation in a sample has one of three possible distributions. This is another example of "convergence in distribution."
Joint, Marginal, and Conditional Probability
	We engineers often ignore the distinctions between joint, marginal, and conditional probabilities - to our detriment.
Correlation
	When the correlation between two variables is zero, they're not related. Right? Wrong!
Outliers ...
	Often infuriating, these can be very informative too.
Wrong Grid?
	Choosing the wrong grid can undermine your analysis, mislead your audience, and make you look foolish.
Bayesian Thinking
	... including an example from NDE
InterOcular Trauma Test
	Sometimes the best Goodness-of-Fit test is the easiest.
Central Limit Theorem
	Why is the Average of nearly anything always Normal ?
Bayesian Updating
	We use Bayesian Statistics every day without knowing it.
Sums of Random Variables
	Sometimes you need to know the distribution of some combination of things. Here's an example.
Distributional Inter-relationships
	There are myriad probability distributions. But did you know that most are related to one another, and ultimately related to the Normal?
Bootstrapping
	Bootstrap and Jackknife algorithms don't really give you something for nothing. They give you something you previously ignored.
Bartlett correction (external link)
	A Bartlett correction is a scalar transformation applied to the likelihood ratio statistic that yields an improved test statistic with chi-squared null distribution of order O(1/n), as compared with order O(1) for the LR.