Exchangeable random variables (original) (raw)
Austauschbare Familie von Zufallsvariablen ist ein Begriff aus der Wahrscheinlichkeitstheorie, der die intuitive Vorstellung formalisiert, dass bei der Auswertung gewisser Informationen die Reihenfolge der Auswertung egal ist. Eine der wichtigsten Aussagen über austauschbare Familien ist der Darstellungssatz von de Finetti. Austauschbarkeit ist eine Abschwächung der Forderung, dass Zufallsvariablen unabhängig identisch verteilt sind.
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| dbo:abstract | Austauschbare Familie von Zufallsvariablen ist ein Begriff aus der Wahrscheinlichkeitstheorie, der die intuitive Vorstellung formalisiert, dass bei der Auswertung gewisser Informationen die Reihenfolge der Auswertung egal ist. Eine der wichtigsten Aussagen über austauschbare Familien ist der Darstellungssatz von de Finetti. Austauschbarkeit ist eine Abschwächung der Forderung, dass Zufallsvariablen unabhängig identisch verteilt sind. (de) In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely long) whose joint probability distribution does not change when the positions in the sequence in which finitely many of them appear are altered. Thus, for example the sequences both have the same joint probability distribution. It is closely related to the use of independent and identically distributed random variables in statistical models. Exchangeable sequences of random variables arise in cases of simple random sampling. (en) En teoría de la probabilidad y estadística, una sucesión de variables aleatorias intercambiables es una sucesión tal que las observaciones futuras se comportan igual que las pasadas o, dicho de otra manera, que cualquier reordenación de un subconjunto finito de muestras tiene la misma probabilidad de ocurrir. Este concepto formaliza la noción de "el futuro es predecible a la vista del pasado". Una sucesión de variables aleatorias independientes con la misma distribución es intercambiable. Pero la independencia no es condición necesaria para la intercambiabilidad. La noción es fundamental en el desarrollo de la de Bruno de Finetti y en estadística bayesiana puesto que mientras que los estadísticos frecuentistas usan variables i.i.d. (muestras de una población), los bayesianos utilizan más frecuentemente sucesiones intercambiables. (es) 확률론과 통계학에서 교환 가능 확률 변수족(交換可能確率變數族, 영어: exchangeable family of random variables)은 유한 개를 재배열하여도 결합 확률 분포가 변하지 않는 확률 변수 집합이다. 교환 가능 시그마 대수(交換可能σ代數, 영어: exchangeable sigma-algebra)는 유한 개의 확률 변수를 재배열하여도 발생 여부가 바뀌지 않는 사건들로 구성된 시그마 대수이다. (ko) In de kansrekening formaliseert de eigenschap uitwisselbaarheid van een familie van stochastische variabelen het intuïtieve begrip dat bij de evaluatie van bepaalde informatie de volgorde van de variabelen er niet toe doet. Een van de belangrijkste uitspraken over uitwisselbare families is de Stelling van De Finetti. Uitwisselbaarheid is een afzwakking van de eis dat stochastische variabelen onderling onafhankelijk en gelijkverdeeld zijn. (nl) |
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| rdfs:comment | Austauschbare Familie von Zufallsvariablen ist ein Begriff aus der Wahrscheinlichkeitstheorie, der die intuitive Vorstellung formalisiert, dass bei der Auswertung gewisser Informationen die Reihenfolge der Auswertung egal ist. Eine der wichtigsten Aussagen über austauschbare Familien ist der Darstellungssatz von de Finetti. Austauschbarkeit ist eine Abschwächung der Forderung, dass Zufallsvariablen unabhängig identisch verteilt sind. (de) In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely long) whose joint probability distribution does not change when the positions in the sequence in which finitely many of them appear are altered. Thus, for example the sequences both have the same joint probability distribution. It is closely related to the use of independent and identically distributed random variables in statistical models. Exchangeable sequences of random variables arise in cases of simple random sampling. (en) 확률론과 통계학에서 교환 가능 확률 변수족(交換可能確率變數族, 영어: exchangeable family of random variables)은 유한 개를 재배열하여도 결합 확률 분포가 변하지 않는 확률 변수 집합이다. 교환 가능 시그마 대수(交換可能σ代數, 영어: exchangeable sigma-algebra)는 유한 개의 확률 변수를 재배열하여도 발생 여부가 바뀌지 않는 사건들로 구성된 시그마 대수이다. (ko) In de kansrekening formaliseert de eigenschap uitwisselbaarheid van een familie van stochastische variabelen het intuïtieve begrip dat bij de evaluatie van bepaalde informatie de volgorde van de variabelen er niet toe doet. Een van de belangrijkste uitspraken over uitwisselbare families is de Stelling van De Finetti. Uitwisselbaarheid is een afzwakking van de eis dat stochastische variabelen onderling onafhankelijk en gelijkverdeeld zijn. (nl) En teoría de la probabilidad y estadística, una sucesión de variables aleatorias intercambiables es una sucesión tal que las observaciones futuras se comportan igual que las pasadas o, dicho de otra manera, que cualquier reordenación de un subconjunto finito de muestras tiene la misma probabilidad de ocurrir. Este concepto formaliza la noción de "el futuro es predecible a la vista del pasado". Una sucesión de variables aleatorias independientes con la misma distribución es intercambiable. Pero la independencia no es condición necesaria para la intercambiabilidad. (es) |
| rdfs:label | Austauschbare Familie von Zufallsvariablen (de) Variables aleatorias intercambiables (es) Exchangeable random variables (en) 교환 가능 확률 변수족 (ko) Uitwisselbaarheid (kansrekening) (nl) |
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