Probability Theory

18 Jul 2022 21:03

One of my advisers in graduate school was a probability theorist, as was his adviser before him; I've not bothered to check, but I wouldn't be astonished if the chain went back to someone like Bernoulli. The fact that the chain could go back that far shows that mathematical probability is an old concept, almost as old as any other part of modern science; on the other hand, my adviser's adviser came just after the generation, between the wars, which made probability a respectable and rigorous branch of mathematics and removed countless obscurities from its applications. The first serious use of statistical methods in the sciences came only about a hundred years before that. Now of course error analysis is the first thing my students learn when they enter the lab. (Well, almost the first thing, after "if you don't write it down, it never happened" and "Cosma can be bribed with chocolate.") I am conditioned to attack every problem as some kind of stochastic process; but a few generations back nobody had any but the vaguest idea what a stochastic process was.

Pet peeves: Physicists who do not distinguish between a random variable ("X = the roll of a die") and the value it takes ("x=5"). People who report estimated numbers without error-bars or confidence-intervals. Bayesians.

Cf. math in general, stochastic processes, statistics, information theory, algorithmic information theory, statistical mechanics, ergodic theory, machine learning, statistical inference and induction, dynamics; large deviations; empirical process theory; concentration of measure; deviation inequalities; graph limits and exchangeable random graphs; Hilbert Space Methods for Statistics and Probability; projectivity in statistical models;