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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".
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 ...
Statistics Indonesia (Indonesian: Badan Pusat Statistik, BPS, lit. 'Central Agency of Statistics'), is a non-departmental government institute of Indonesia that is responsible for conducting statistical surveys. Its main customer is the government, but statistical data is also available to the public.
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
The law of truly large numbers (a statistical adage), attributed to Persi Diaconis and Frederick Mosteller, states that with a large enough number of independent samples, any highly implausible (i.e. unlikely in any single sample, but with constant probability strictly greater than 0 in any sample) result is likely to be observed. [1]
Proof complexity, computational resources required to prove statements; Proof procedure, method for producing proofs in proof theory; Proof theory, a branch of mathematical logic that represents proofs as formal mathematical objects; Statistical proof, demonstration of degree of certainty for a hypothesis
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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.