This entry is (or will be, one fine day) mainly about general statistics and mathematical statistics. For more about physical applications in statistical mechanics and quantum probability, see there. There is also particle statistics and statistic (singular).
Statistics studies the analysis of collections of random or sample data, and the probabilistic likelihood of various inferences on the basis of these data, as well as the mathematical regularities in large ensembles of occurrences of such data.
In physics, statistics also pertains to the behaviour of large ensembles of [}particles]]. For identical particles, this is the subject of particle statistics and for general systems the subject of statistical mechanics.
Mathematical statistics is based on probability theory. Most of the standard formalism uses measure theory as used in probability. Statistical mechanics in addition heavily uses ergodic theory.
A statistical model is a measurable function , where and are measurable spaces and is the simplex of probability measures over .
Michael Schmitt, Statistics for theorists, quick 3-lecture intro for theoretical physicists at TASI 2020 (each around 1 and half hours) lec1 mp4 slides pdf, lec2 mp4 pdf, lec3 mp4 pdf
Wikipedia: statistics, statistic (singular!), list of statistical packages, descriptive statistics, inferential statistics, data mining, statistical theory, estimation theory, statistical significance, regression analysis, time series analysis, misuse of statistics, applied statistics, Bayesian inference, multivariate statistics, maximal likelihood estimation, Fisher information
Peter McCullagh, What is a statistical model?, Ann. Statist. 30:5 (2002), 1225-1310 euclid MR1936320 doi – on applying category theory to describe statistical models.
Lior Pachter, Bernd Sturmfels, Tropical geometry of statistical models, PNAS 101 no. 46, 16132–16137, doi
Last revised on January 26, 2025 at 16:38:51. See the history of this page for a list of all contributions to it.