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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.
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.
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.
In this example, the dimension, k, equals 2. As another example, suppose that the data consists of points (x, y) that we assume are distributed according to a straight line with i.i.d. Gaussian residuals (with zero mean): this leads to the same statistical model as was used in the example with children's heights. The dimension of the ...
Applied statistics, sometimes referred to as Statistical science, [63] comprises descriptive statistics and the application of inferential statistics. [64] [65] Theoretical statistics concerns the logical arguments underlying justification of approaches to statistical inference, as well as encompassing mathematical statistics.
Taylor diagrams are mathematical diagrams designed to graphically indicate which of several approximate representations (or models) of a system, process, or phenomenon is most realistic. This diagram, invented by Karl E. Taylor in 1994 (published in 2001 [ 1 ] ) facilitates the comparative assessment of different models.
Simple mediation model. The independent variable causes the mediator variable; the mediator variable causes the dependent variable. In statistics, a mediation model seeks to identify and explain the mechanism or process that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third hypothetical variable, known as a mediator ...
In statistics there can be models of mental events as well as models of physical events. For example, a statistical model of customer behavior is a model that is conceptual (because behavior is physical), but a statistical model of customer satisfaction is a model of a concept (because satisfaction is a mental not a physical event).