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The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. [1] [2] The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches.
Mathematical statistics is the application of probability theory and other mathematical concepts to statistics, as opposed to techniques for collecting statistical data. [1] Specific mathematical techniques that are commonly used in statistics include mathematical analysis , linear algebra , stochastic analysis , differential equations , and ...
Although probability and statistics was once paired together as a single subject, they are conceptually distinct from one another. The former is based on deducing answers to specific situations from a general theory of probability, meanwhile statistics induces statements about a population based on a data set.
Statistics subsequently branched out into various directions, including decision theory, Bayesian statistics, exploratory data analysis, robust statistics, and non-parametric statistics. Neyman-Pearson hypothesis testing made significant contributions to decision theory, which is widely employed, particularly in statistical quality control.
Introduction to Modern Statistical Mechanics. Oxford University Press. ISBN 0-19-504277-8. [77] [78] [79] W.A. Wassam, Jr. (2002). Statistical Mechanics : Encyclopedia of Physical Science and Technology, Third Edition, Volume 15. Academic Press. ISBN 978-0-12-227410-7. Bowley, Roger and Sanchez, Mariana (2000). Introductory Statistical ...
Bayesian statistics (/ ˈ b eɪ z i ə n / BAY-zee-ən or / ˈ b eɪ ʒ ən / BAY-zhən) [1] is a theory in the field of statistics based on the Bayesian interpretation of probability, where probability expresses a degree of belief in an event. The degree of belief may be based on prior knowledge about the event, such as the results of previous ...
Neyman–Pearson decision theory 1 Set up a statistical null hypothesis. The null need not be a nil hypothesis (i.e., zero difference). Set up two statistical hypotheses, H1 and H2, and decide about α, β, and sample size before the experiment, based on subjective cost-benefit considerations. These define a rejection region for each hypothesis. 2
Statistical learning theory is a framework for machine learning drawing from the fields of statistics and functional analysis. [ 1 ] [ 2 ] [ 3 ] Statistical learning theory deals with the statistical inference problem of finding a predictive function based on data.