Probability and Statistics

Probability is a way of expressing knowledge or belief that an event will occur or has occurred. The concept has been given an exact mathematical meaning in probability theory, which is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.

Statistics is the science of the collection, organization, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments.

A statistician is someone who is particularly well versed in the ways of thinking necessary for the successful application of statistical analysis. Such people have often gained this experience through working in any of a wide number of fields. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject.

The word statistics can either be singular or plural. When it refers to the discipline, "statistics" is singular, as in "Statistics is an art." When it refers to quantities (such as mean and median) calculated from a set of data, statistics is plural, as in "These statistics are misleading."

TUTORIALS:

Elementary Statistics and Probability Tutorials and Problems

TIMELINE

Before 1600

1560s (published 1663) - Cardano's Liber de ludo aleae attempts to calculate probabilities of dice throws
1577 - Bartolomé de Medina defends probabilism, the view that in ethics one may follow a probable opinion even if the opposite is more probable

17th century

1654 - Pascal and Fermat create the mathematical theory of probability,
1657 - Huygens's De ratiociniis in ludo aleae is the first book on mathematical probability,
1662 - Graunt's Natural and Political Observations Made upon the Bills of Mortality makes inferences from statistical data on deaths in London,

18th century

1710 - Arbuthnot argues that the constancy of the ratio of male to female births is a sign of divine providence,
1713 - Posthumous publication of Jacob Bernoulli's Ars Conjectandi, containing the first derivation of a law of large numbers,
1724 - Abraham de Moivre studies mortality statistics and the foundation of the theory of annuities in Annuities on Lives,
1733 - Abraham de Moivre introduces the normal distribution to approximate the binomial distribution in probability,
1739 - Hume's Treatise of Human Nature argues that inductive reasoning is unjustified,
1761 - Thomas Bayes proves Bayes' theorem,
1786 - Playfair's Commercial and Political Atlas introduces graphs and bar charts of data,

19th century

1801 - Gauss predicts the orbit of Ceres using a line of best fit
1805 - Adrien-Marie Legendre introduces the method of least squares for fitting a curve to a given set of observations,
1814 - Laplace's Essai philosophique sur les probabilités defends a definition of probabilities in terms of equally possible cases, introduces generating functions and Laplace transforms, uses conjugate priors for exponential families, proves an early version of the Bernstein von-Mises theorem on the asymptotic irrelevance of prior distributions on the limiting posterior distribution and the role of the Fisher information on asymptotically normal posterior modes.
1835 - Quetelet's Treatise on Man introduces social science statistics and the concept of the "average man",
1866 - Venn's Logic of Chance defends the frequency interpretation of probability.
1877-1883 - Charles Sanders Peirce outlines frequentist statistics, emphasizing the use of objective randomization in experiments and in sampling. Peirce also invented an optimally designed experiment for regression.
1880 - Thiele gives a mathematical analysis of Brownian motion, introduces the likelihood function, and invents cumulants.
1888 - Galton introduces the concept of correlation,

20th century

1900 - Bachelier analyzes stock price movements as a stochastic process,
1908 - Student's t-distribution for the mean of small samples published in English (following earlier derivations in German).
1921 - Keynes' Treatise on Probability defends a logical interpretation of probability,
1928 - Tippett and Fisher's introduce extreme value theory,
1933 - Andrey Nikolaevich Kolmogorov publishes his book Basic notions of the calculus of probability (Grundbegriffe der Wahrscheinlichkeitsrechnung) which contains an axiomatization of probability based on measure theory,
1935 - R. A. Fisher's Design of Experiments (1st ed),
1937 - Neyman introduces the concept of confidence interval in statistical testing,
1946 - Cox's theorem derives the axioms of probability from simple logical assumptions,
1948 - Shannon's Mathematical Theory of Communication defines capacity of communication channels in terms of probabilities,
1953 - Nicholas Metropolis introduces the idea of thermodynamic simulated annealing methods

Twenty-first century

2003 - E.T. Jaynes's Probability Theory: The Logic of Science defends probability theory as a comprehensive method of evaluation of evidence

2009 - David X. Li's Gaussian copula formula blamed as one cause of the Late 2000s recession