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great probability thinkers

UPDATED: February 18, 2012

"There are three kinds of lies: lies, damned lies and statistics." - Attributed to Mark Twain, but possibly from Sir Charles Wentworth Dilke, 2nd Baronet

Mark Twain, while a great writer and humorist, was not much of a statistician. Like any other information, statistical information can be distorted and misused but made correctly and presented honestly and impartially, statistical analysis gives us information that helps us make sense of complex situations. Everyone should cultivate a statistical mode of thinking, if only to protect themselves from liars who abuse statistics to mislead us. There are thinkers among the statisticians whose work provides non-statisticians with rules of thumb that can be used in self-defense. Here are some of the people I consider this sort of seminal thinker in practical probability. My criteria are that their ideas are easily understood without using highly mathematical methods and can be practically applied to dealing with questions we face daily.

E-mail russell.martin@wdn.com with your nominations for additions to my list.


William Edwards Deming

While Deming’s career covered a wide range of themes and subjects, the particular concept for which I include him here is his "red bead experiment" and its implications for management. In this exercise, a model factory is established in which samples of beads are taken, using a strictly defined method, out of a container which has a mixture of 20% red beads and 80% white beads. The goal is to take a sample out of the container with less than 20% red beads, since those are not usable for the purposes of the customer. Participants are given jobs in the factory including production (taking the sample of beads from the container), accounting (recording the percentage of red beads), management (encouraging or punishing the workers depending on how well they "produce" an acceptably low fraction of read beads), etc. To spoil the surprise for anyone not familiar with the game, the point is that certain aspects of a worker’s performance are outside of his/her control, especially those aspects that are due to random processes, and it is more than pointless, it is actually counterproductive, to reward or punish workers on the basis of good or poor results over which the workers have no control.

The red bead experiment should be kept in mind when considering public policy issues like education reform. Before closing schools or firing teachers for poor performance, we need to remember that student bodies fall on a statistical distribution and as such there will be some schools with student bodies at the less scholarly end of the distribution. This fact is largely beyond the control of the teachers in those schools. A multivariate analysis that separates the contribution of teachers from that of other relevant influences needs to be done before we can fairly determine the extent to which teachers are at fault for the shortcomings of our educational system.


Nassim Nicholas Taleb

In his two popular books, Fooled by Randomness: The Hidden Role of Chance in Life and the Markets and The Black Swan: The Impact of the Highly Improbable, Taleb introduces us to two easily understood principles of probability and how to apply them in our lives.

In the first book he explains how humans are good at seeing patterns in data, but what we see as patterns may not be the result of predictable processes but instead are just the results of whatever random processes are present. We are fooled, sometimes disastrously so, when we use the past behavior of these random processes as forecasts for planning, explicitly or implicitly. We fool ourselves particularly if we believe our decisions have been largely responsible for our success when in fact our biases have led us to a series of decisions which have been coincidently harmonious with a random trend.

In the second book Taleb considers the effects of rare, virtually unexpected, events on financial markets and beyond. These events are members of the collection of "unknown unknowns", events that are impossible to predict or even conceive of. Such events can be severely disruptive since our systems are not designed to deal with them. Worse, many of our systems are not designed to be robust so that the disruptive influence of the Black Swan doesn’t just cause problems but can threaten to destroy the system. The implication is that unless one desires to take foolishly large risks, systems should be designed to be robust and fail gracefully if they fail.


George Edward Pelham Box

His work includes Box-Jenkins time series analysis and the Box-Cox transform, but the main reason he is included here is his quote, "All models are wrong, some are useful."


John W. Tukey

Some of his best known and most used work includes co-development of the Cooley-Tukey algorithm fast Fourier transform algorithm and exploratory data analysis. In The Measurement of Power Spectra from the Point of View of Communications Engineering by Blackman and Tukey there is the statement "All too often the study of spectra requires care". I have generalized this to my data analysis mantra "All too often the study of data requires care".


Dr. John Snow

Arguably the founder of the field of epidemiology, Snow’s mapping of cholera cases near Broad Street in the Soho district of London in 1854 is an inspiring example of dogged data collection, thoughtful, if by today’s standards statistically unsophisticated, analysis and insightful deduction. Modern urban life owes an incalculable debt to his work.


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©2012 Russell Martin