While the best-known statistics come from large numbers of data points, “normal” distributions (See my post of Oct. 24, 2005 on bell curves.), standard deviations and other tools related to frequency, the branch of statistics known as Bayesian reasoning has application to law departments (Economist, Jan. 7, 2006 at 70). Bayesian statisticians, named after the research of an 18th century clergyman, draw strong inferences from sparse data. Sound like lawyers, right?
The key to successful Bayesian reasoning is having an appropriate “prior,” an “assumption about the way the world works … that can be expressed as a mathematical probability distribution of the frequency with which events of a particular magnitude happen.” The bell-curve, aka Gaussian distribution, most of us recognize, but there are also the Poisson distribution, the Erlanger distribution, the power-law distribution (See my post of July 25, 2005 on power-law frequencies.), and many others.
With the correct prior, even a single piece of data can be used to make meaningful Bayesian predictions. For example, if an experienced in-house litigator has sense of the seasonal flow of lawsuits (a good “prior”), a few cases arriving at one time allows an accurate Bayesian prediction of annual volume.