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Foundations of statistics involves issues in theoretical statistics, its goals and optimization methods to meet these goals, parametric assumptions or lack thereof considered in nonparametric statistics, model selection for the underlying probability distribution, and interpretation of the meaning of inferences made using statistics, related to the philosophy of probability and the philosophy ...
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.
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.
The mythological Judgement of Paris required selecting from three incomparable alternatives (the goddesses shown).. Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses the tools of expected utility and probability to model how individuals would behave rationally under uncertainty.
Per Erik Rutger Martin-Löf (/ l ɒ f /; [2] Swedish: [ˈmǎʈːɪn ˈløːv]; [3] born 8 May 1942) is a Swedish logician, philosopher, and mathematical statistician.He is internationally renowned for his work on the foundations of probability, statistics, mathematical logic, and computer science.
Formal epistemology uses formal methods from decision theory, logic, probability theory and computability theory to model and reason about issues of epistemological interest. Work in this area spans several academic fields, including philosophy , computer science , economics , and statistics .
Wesley Charles Salmon (August 9, 1925 – April 22, 2001) was an American philosopher of science renowned for his work on the nature of scientific explanation. [2] He also worked on confirmation theory, trying to explicate how probability theory via inductive logic might help confirm and choose hypotheses.
The philosophy of probability presents problems chiefly in matters of epistemology and the uneasy interface between mathematical concepts and ordinary language as it is used by non-mathematicians. Probability theory is an established field of study in mathematics.