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...such as [[spatial statistics]], [[image analysis]], [[materials science]], and [[mathematical morphology]]. ...math> is the collection of all closed subsets of <math>\mathbb{R}^d</math> and <math>\Sigma</math> is the [[sigma-algebra]] generated over <math>\mathcal{ ...

...\, d\mu</math>.<ref name=Williams>{{cite book|author=David Williams|title=Probability with Martingales|url=https://archive.org/details/probabilitywithm00will_764 ...proof is based fundamentally on an application of the triangle inequality and [[Fatou's lemma]].<ref>{{Cite web |title=Scheffé's Lemma - ProofWiki |url=h ...

...s. This theorem was proved independently by [[Georges Darmois|G. Darmois]] and V. P. Skitovich in 1953.<ref name=darmois>{{cite journal | journal = Review of the International Statistical Institute ...

{{Short description|Statistical rule of thumb}} ...tion lies between the smallest and largest values in any [[random sample]] of five taken from that population. ...

{{Short description|Mathematical index used in Bayesian statistics}} ...yes/#probability-of-direction |website=Georgia State University - Bayesian statistics course |access-date=7 December 2021 |language=en-us}}</ref> ...

{{Short description|Formula in probability theory}} ...a | last = Grigoriu | title = Stochastic Calculus: Applications in Science and Engineering | year = 2002 | pages = 166 | isbn = 978-0-817-64242-6}}</ref> ...

...rt is greater than or equal to the product of the individual probabilities of hitting the circle or the rectangle.]] ...is a [[mathematical theorem]] in the fields of [[mathematical statistics]] and [[convex geometry]]. ...

...]]. This entropy of paths is sometimes called the "caliber" of the system, and is given by the path integral == History == ...

{{short description|Greatest and least values in a statistical data sample}} ...[Box plot]]s of the [[Michelson–Morley experiment]], showing sample maxima and minima]] ...

...rxiv = 1310.0173|last1 = Stigler|first1 = Stephen M|title = The True Title of Bayes's Essay|journal = Statistical Science |volume = 28|issue = 3|pages = ...]], together with a detailed treatment of the problem of setting a [[prior probability]]. ...

...ith [[independent and identically distributed random variables|independent and identically distributed entries]] in the limit ...ally distributed random variables]], all with [[expected value|mean]] zero and [[variance]] equal to {{math|1/''n''}}, the limiting spectral distribution ...

{{Bayesian statistics}} ...er value:<ref>{{cite book | last=van der Vaart|first=A.W.|title=Asymptotic Statistics |year=1998|publisher=Cambridge University Press|isbn=0-521-78450-6|chapter= ...

...yze data such as this, where multiple observations are made on collections of individuals over time.]] ...ate linear model, also known as GMANOVA (Generalized Multivariate Analysis-Of-Variance).<ref>{{cite book ...

{{DISPLAYTITLE:''q''-value (statistics)}} ...very rate: a Bayesian interpretation and the q-value|journal=The Annals of Statistics|volume=31|issue=6|pages=2013–2035|doi=10.1214/aos/1074290335|doi-access=fre ...

....}}</ref> is a way to [[Simulation|simulate]] the [[Ising model]] (a model of [[magnetism]]) on a computer.<ref name="pre0">{{cite journal|url= http://jo .... |last2= Barkema |first2= G.T. |journal= Physica A: Statistical Mechanics and Its Applications |volume= 418 |pages= 78–87 |s2cid= 118589022 }}</ref> ...

{{short description|Discrete probability distribution}} {{Infobox probability distribution ...

{{Short description|Continuous probability distribution}} {{Probability distribution ...

...andom matrices]] in the field of [[nuclear physics]]. The surmise consists of two postulates: ...([[Spin_(physics)|spin]] and [[Parity_(physics)|parity]] are same), the [[probability density function]] for a spacing is given by, ...

{{short description|Branch of econometrics}} ...ased on a degree-of-belief [[probability interpretations|interpretation of probability]], as opposed to a relative-frequency interpretation. ...

...-time Markov process]]es. In particular, they describe how the probability of a continuous-time Markov process in a certain state changes over time. ...e Markov processes, depending on the assumed behavior over small intervals of time: ...