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Bayesian statistics are based on a different philosophical approach for proof of inference.The mathematical formula for Bayes's theorem is: [|] = [|] [] []The formula is read as the probability of the parameter (or hypothesis =h, as used in the notation on axioms) “given” the data (or empirical observation), where the horizontal bar refers to "given".
The essential tools of the proof besides the definition above are the law of total expectation and the fact that for any random variable Y, E(Y 2) cannot be less than [E(Y)] 2. That inequality is a case of Jensen's inequality, although it may also be shown to follow instantly from the frequently mentioned fact that
This is used in statistical models to prove or disprove research hypotheses. The term "ground truthing" refers to the process of gathering the proper objective (provable) data for this test. Compare with gold standard. For example, suppose we are testing a stereo vision system to see how well it can estimate 3D positions. The "ground truth ...
This category includes articles on basic topics related to mathematical proofs, including terminology and proof techniques.. Related categories: Pages which contain only proofs (of claims made in other articles) should be placed in the subcategory Category:Article proofs.
The expression "statistical proof" may be used technically or colloquially in areas of pure mathematics, such as involving cryptography, chaotic series, and probabilistic number theory or analytic number theory. [23] [24] [25] It is less commonly used to refer to a mathematical proof in the branch of mathematics known as mathematical statistics.
Surrogate data testing [1] (or the method of surrogate data) is a statistical proof by contradiction technique similar to permutation tests [2] and parametric bootstrapping.It is used to detect non-linearity in a time series. [3]
An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of event A taking place in the presence of B, and the odds of A in the absence of B. Due to symmetry, odds ratio reciprocally calculates the ratio of the odds of B occurring in the presence of A, and the odds of B in the absence of A.
Arthur P. Dempster at the Workshop on Theory of Belief Functions (Brest, 1 April 2010).. The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories.