History of Statistics and Probability

The Lady Tasting Tea：How Statistics Revolutionized Science in the Twentieth Century

Motivation

To understand God’s thoughts, we must study statistics, for these are the measure of his purpose. —Florence Nightingale

She used statistical methods to improve healthcare during the Crimean War, demonstrating the power of data visualization.

Error function

Laplace did not need God in his formulation, he did need something he called the “error function”.

–Predictions do not fit observations exactly (eg. planets and comets predicted by formulas due to perturbations in the earth’s atmosphere/ human error)

–use error function to account for slight discrepancies between the observed and the predicted

–early 19th-century science was in the grip of philosophical determinism–the belief that everything that happens is determined in advance by the initial conditions of the universe and the mathematical formulas that describe its motions

–more precise measurement not exactly leads to less error—-instead inversely. Newton and Laplace had used were proving to be only rough approximations.

—new paradigm: statistical model of reality

–by the end of the 20th century almost all of science had shifted to using statistical models.

ideas and expression have drifted into the popular vocabulary

–profound shift in philosophical view: what are these statistical models? How did they come about? What do they mean in real life?

3 mathematical ideas

randomness

past: unpredictablity: one cannot go searching for something which is found at random
morden scientists: probability distribution: allows us to put constraints on this randomness and gives us a limited ability to predict future but random events.—-randomness have a structure that can be described mathematically.

Probability

From Aristotle:”it is the nature of probability that improbable things will happen”

19th century: consisted primarily of sophisticated tricks but lacked a sold theoretical foundation

Early 20th Century: Ronald A. Fisher (rejected by Pearson in the Biometrika and then went to agricultral station) revolutionized statistics with his work on experimental design, MLE, multiple comparison, analysis of variance (ANOVA). Jerzy Neyman and Egon Pearson developed hypothesis testing and confidence intervals.

Mid-20th Century: the development of computers in the 1950s and 1960s enabled more complex data analysis

Bernoullis –Fermat De Moivre(insert Calculus) discern some deep fundabemtal theorems–“laws of large numbers”

Pascal

games of chance, counting equally probable events