Kolmogorov in a sentence

If F is continuous then under the null hypothesis converges to the Kolmogorov distribution, which does not depend on F. This result may also be known as the Kolmogorov theorem; see Kolmogorov's theorem for disambiguation.

Induction: From Kolmogorov and Solomonoff to De Finetti and Back to Kolmogorov JJ McCall – Metroeconomica, 2004 – Wiley Online Library.

Kolmogorov randomness seeAlso Kolmogorov randomness defines a string (usually of bits ) as being random if and only if it is shorter than any computer program that can produce that string.

The goodness-of-fit test or the Kolmogorov–Smirnov test is constructed by using the critical values of the Kolmogorov distribution.

The Kolmogorov extension theorem guarantees the existence of a stochastic process with a given family of finite-dimensional probability distributions satisfying the Chapman–Kolmogorov compatibility condition.

These tools are recast into another form that Kolmogorov cites as "Hilbert's four axioms of implication" and "Hilbert's two axioms of negation" (Kolmogorov in van Heijenoort, p. 335).

An example of score function include minimal compression length where a hypothesis with a lowest Kolmogorov complexity has the highest score and is returned.

A. N. Kolmogorov, Three approaches to the quantitative definition of information Problems of Information and Transmission, 1(1):1--7, 1965.

A topological space is Hausdorff if and only if it is both preregular (i.e. topologically distinguishable points are separated by neighbourhoods) and Kolmogorov (i.e. distinct points are topologically distinguishable).

But this method was considered too weak by Alexander Shen who showed that there is a Kolmogorov-Loveland stochastic sequence which does not conform to the general notion of randomness.

Consequences From the Kolmogorov axioms, one can deduce other useful rules for calculating probabilities.

C.S. Wallace and D.L. Dowe (1999) showed a formal connection between MML and algorithmic information theory (or Kolmogorov complexity).

Following Kolmogorov's work in the 1950s, advanced statistics uses approximation theory and functional analysis to quantify the error of approximation.

For example, in the Kolmogorov – Chaitin minimum description length approach, the subject must pick a Turing machine whose operations describe the basic operations believed to represent "simplicity" by the subject.

Gurevich adds the pointer machine model of Kolmogorov and Uspensky (1953, 1958): "..

He gave a more complete description in his 1964 publications, "A Formal Theory of Inductive Inference," Part 1 and Part 2 in Information and Control. citation citation Andrey Kolmogorov later independently published this theorem in Problems Inform.

In 1922, Andrey Kolmogorov published an article entitled "Une série de Fourier-Lebesgue divergente presque partout" in which he gave an example of a Lebesgue-integrable function whose Fourier series diverges almost everywhere.

Indeed, when analysts run across a non-Hausdorff space, it is still probably at least preregular, and then they simply replace it with its Kolmogorov quotient, which is Hausdorff.

It can be shown that the Kolmogorov complexity of any string cannot be more than a few bytes larger than the length of the string itself.

It follows that if a topological group is T 0 ( Kolmogorov ) then it is already T 2 ( Hausdorff ), even T 3½ ( Tychonoff ).