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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 ...
Romberg's method (numerical analysis) Runge–Kutta method (numerical analysis) Sainte-Laguë method (voting systems) Schulze method (voting systems) Sequential Monte Carlo method; Simplex method; Spectral method (numerical analysis) Variational methods (mathematical analysis, differential equations) Welch's method
The Foundations of Statistics are the mathematical and philosophical bases for statistical methods. These bases are the theoretical frameworks that ground and justify methods of statistical inference , estimation , hypothesis testing , uncertainty quantification , and the interpretation of statistical conclusions.
Meta-analysis: Though independent p-values can be combined using Fisher's method, techniques are still being developed to handle the case of dependent p-values. Behrens–Fisher problem: Yuri Linnik showed in 1966 that there is no uniformly most powerful test for the difference of two means when the variances are unknown and possibly unequal.
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.
The development of statistical reasoning was closely associated with the development of inductive logic and the scientific method, which are concerns that move statisticians away from the narrower area of mathematical statistics. Much of the theoretical work was readily available by the time computers were available to exploit them.
Statistical Methods for Research Workers is a classic book on statistics, written by the statistician R. A. Fisher. It is considered by some [ who? ] to be one of the 20th century's most influential books on statistical methods , together with his The Design of Experiments (1935).
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear operators acting upon these spaces and respecting these structures in a suitable sense.