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The foundations of statistics are the mathematical and philosophical bases for statistical methods. These bases are theoretical frameworks that ground and justify methods of statistical inference, estimation, hypothesis testing, uncertainty quantification, and the interpretation of statistical conclusions. Further, a foundation can be used to ...
Stein's method is a general method in probability theory to obtain bounds on the distance between two probability distributions with respect to a probability metric.It was introduced by Charles Stein, who first published it in 1972, [1] to obtain a bound between the distribution of a sum of -dependent sequence of random variables and a standard normal distribution in the Kolmogorov (uniform ...
Algebraic statistics is the use of algebra to advance statistics. Algebra has been useful for experimental design, parameter estimation, and hypothesis testing. Traditionally, algebraic statistics has been associated with the design of experiments and multivariate analysis (especially time series). In recent years, the term "algebraic ...
Information geometry. The set of all normal distributions forms a statistical manifold with hyperbolic geometry. Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. [1] It studies statistical manifolds, which are Riemannian manifolds whose points ...
Statistics education is the practice of teaching and learning of statistics, along with the associated scholarly research. Statistics is both a formal science and a practical theory of scientific inquiry, and both aspects are considered in statistics education. Education in statistics has similar concerns as does education in other mathematical ...
Reissued as Statistical Methods Applied to Experiments in Agriculture and Biology in 1940 and then again as Statistical Methods with Cochran, WG in 1967. A classic text. Importance: Influence. Principles and Procedures of Statistics with Special Reference to the Biological Sciences. Authors: Steel, R.G.D, and Torrie, J. H.
Founders of statistics. Statistics is the theory and application of mathematics to the scientific method including hypothesis generation, experimental design, sampling, data collection, data summarization, estimation, prediction and inference from those results to the population from which the experimental sample was drawn.
In quantum statistics, Bose–Einstein statistics (B–E statistics) describes one of two possible ways in which a collection of non-interacting identical particles may occupy a set of available discrete energy states at thermodynamic equilibrium. The aggregation of particles in the same state, which is a characteristic of particles obeying ...