"De Finettis sats"@sv . . "1113104644"^^ . "De Finettis sats anv\u00E4nds inom sannolikhetsteori f\u00F6r att f\u00F6rklara varf\u00F6r utbytbara sannolikhetsm\u00E5tt (stokastiska variabler) \u00E4r betingat oberoende som sedan kan tilldelas en Bayesiansk sannolikhetsf\u00F6rdelning. Satsen \u00E4r d\u00F6pt efter Bruno de Finetti. Det vill s\u00E4ga: bara f\u00F6r att en serie \u00E4r utbytbar beh\u00F6ver den inte vara oberoende och likaf\u00F6rdelad, utan det existerar underliggande och ofta icke-observerbara m\u00E4ngder som \u00E4r i.i.d. Dessa utbytbara serier beh\u00F6ver inte vara oberoende och likaf\u00F6rdelade utan best\u00E5r av blandningar av serier som \u00E4r det."@sv . . "Accardi"@en . . . "180835"^^ . . . . . . . . "In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some latent variable. An epistemic probability distribution could then be assigned to this variable. It is named in honor of Bruno de Finetti. For the special case of an exchangeable sequence of Bernoulli random variables it states that such a sequence is a \"mixture\" of sequences of independent and identically distributed (i.i.d.) Bernoulli random variables. A sequence of random variables is called exchangeable if the joint distribution of the sequence is unchanged by any permutation of the indices. While the variables of the exchangeable sequence are not themselves independent, only exchangeable, there is an underlying family of i.i.d. random variables. That is, there are underlying, generally unobservable, quantities that are i.i.d. \u2013 exchangeable sequences are mixtures of i.i.d. sequences."@en . . . . . "Satz von De Finetti"@de . . . . . . . . "Em teoria da probabilidade, o teorema de De Finetti mostra o motivo pelo qual observa\u00E7\u00F5es permut\u00E1veis s\u00E3o condicionalmente independentes, dada alguma vari\u00E1vel latente, para qual uma distribui\u00E7\u00E3o de probabilidade epist\u00EAmica \u00E9 ent\u00E3o atribu\u00EDda. Esse teorema recebe esse nome em homenagem ao matem\u00E1tico e probabilista Bruno de Finetti. Esse teorema afirma que uma sequ\u00EAncia de vari\u00E1veis aleat\u00F3rias com distribui\u00E7\u00E3o de Bernoulli \u00E9 uma \"mistura\" de vari\u00E1veis aleat\u00F3rias Bernoulli independente e identicamente distribu\u00EDdas."@pt . . . . . . . "\u30C7\u30FB\u30D5\u30A3\u30CD\u30C3\u30C6\u30A3\u306E\u5B9A\u7406\uFF08\u82F1: de Finetti's theorem\uFF09\u307E\u305F\u306F\u30C7\u30FB\u30D5\u30A3\u30CD\u30C3\u30C6\u30A3\u306E\u8868\u73FE\u5B9A\u7406\uFF08\u82F1: de Finetti's representation theorem\uFF09\u3068\u306F\u78BA\u7387\u8AD6\u306B\u304A\u3051\u308B\u5B9A\u7406\u3067\u3042\u308A\u3001\u3042\u308B\u6F5C\u5728\u5909\u6570\u306B\u5BFE\u3057\u8A8D\u8B58\u8AD6\u7684\u306A\u78BA\u7387\u5206\u5E03\u304C\u4E0E\u3048\u3089\u308C\u305F\u3068\u3044\u3046\u6761\u4EF6\u306E\u4E0B\u3067\u3001\u306A\u89B3\u6E2C\u5024\u306F\u3067\u3042\u308B\u3068\u3044\u3046\u3053\u3068\u3092\u8FF0\u3079\u308B\u3002\u5B9A\u7406\u306E\u540D\u524D\u306F\u767A\u898B\u8005\u306E\u4E00\u4EBA\u3067\u3042\u308B\u30D6\u30EB\u30FC\u30CE\u30FB\u30C7\u30FB\u30D5\u30A3\u30CD\u30C3\u30C6\u30A3\u306B\u56E0\u3080\u3002 \u4EA4\u63DB\u53EF\u80FD\u306A\u30D9\u30EB\u30CC\u30FC\u30A4\u5909\u6570\u306E\u5217\u306E\u7279\u5225\u306A\u5834\u5408\u3068\u3057\u3066\u3001\u72EC\u7ACB\u540C\u5206\u5E03 (i.i.d.) \u306A\u30D9\u30EB\u30CC\u30FC\u30A4\u5217\u306E\u300C\u6DF7\u5408\u300D\u3057\u305F\u5217\u304C\u3042\u308B\u3002\u4EA4\u63DB\u53EF\u80FD\u306A\u5217\u306E\u500B\u3005\u306E\u78BA\u7387\u5909\u6570\u306F\u305D\u308C\u3089\u81EA\u8EAB\u3067\u306F i.i.d. \u3067\u306F\u306A\u304F\u3001\u4EA4\u63DB\u53EF\u80FD\u306A\u3060\u3051\u3060\u304C\u3001\u305D\u306E\u6839\u5E95\u306B\u306F i.i.d. \u306A\u78BA\u7387\u5909\u6570\u306E\u65CF\u304C\u5B58\u5728\u3059\u308B\u3002 \u3057\u305F\u304C\u3063\u3066\u3001\u5217\u304C\u4EA4\u63DB\u53EF\u80FD\u3067\u3042\u308B\u305F\u3081\u306B\u89B3\u6E2C\u5024\u304C i.i.d. \u3067\u3042\u308B\u5FC5\u8981\u306F\u306A\u3044\u304C\u3001\u305D\u306E\u80CC\u666F\u306B\u306F\u4E00\u822C\u306B\u306F\u89B3\u6E2C\u53EF\u80FD\u3067\u306A\u3044 i.i.d. \u3067\u3042\u308B\u91CF\u304C\u5B58\u5728\u3059\u308B\u3002\u4EA4\u63DB\u53EF\u80FD\u306A\u5217\u306F i.i.d. \u306A\u5217\u306E\u6DF7\u5408\u3067\u3042\u308A\u3001\u305D\u308C\u306F\u5FC5\u305A\u3057\u3082 i.i.d. \u3067\u306F\u306A\u3044\u3002"@ja . . "\u30C7\u30FB\u30D5\u30A3\u30CD\u30C3\u30C6\u30A3\u306E\u5B9A\u7406"@ja . . "\u30C7\u30FB\u30D5\u30A3\u30CD\u30C3\u30C6\u30A3\u306E\u5B9A\u7406\uFF08\u82F1: de Finetti's theorem\uFF09\u307E\u305F\u306F\u30C7\u30FB\u30D5\u30A3\u30CD\u30C3\u30C6\u30A3\u306E\u8868\u73FE\u5B9A\u7406\uFF08\u82F1: de Finetti's representation theorem\uFF09\u3068\u306F\u78BA\u7387\u8AD6\u306B\u304A\u3051\u308B\u5B9A\u7406\u3067\u3042\u308A\u3001\u3042\u308B\u6F5C\u5728\u5909\u6570\u306B\u5BFE\u3057\u8A8D\u8B58\u8AD6\u7684\u306A\u78BA\u7387\u5206\u5E03\u304C\u4E0E\u3048\u3089\u308C\u305F\u3068\u3044\u3046\u6761\u4EF6\u306E\u4E0B\u3067\u3001\u306A\u89B3\u6E2C\u5024\u306F\u3067\u3042\u308B\u3068\u3044\u3046\u3053\u3068\u3092\u8FF0\u3079\u308B\u3002\u5B9A\u7406\u306E\u540D\u524D\u306F\u767A\u898B\u8005\u306E\u4E00\u4EBA\u3067\u3042\u308B\u30D6\u30EB\u30FC\u30CE\u30FB\u30C7\u30FB\u30D5\u30A3\u30CD\u30C3\u30C6\u30A3\u306B\u56E0\u3080\u3002 \u4EA4\u63DB\u53EF\u80FD\u306A\u30D9\u30EB\u30CC\u30FC\u30A4\u5909\u6570\u306E\u5217\u306E\u7279\u5225\u306A\u5834\u5408\u3068\u3057\u3066\u3001\u72EC\u7ACB\u540C\u5206\u5E03 (i.i.d.) \u306A\u30D9\u30EB\u30CC\u30FC\u30A4\u5217\u306E\u300C\u6DF7\u5408\u300D\u3057\u305F\u5217\u304C\u3042\u308B\u3002\u4EA4\u63DB\u53EF\u80FD\u306A\u5217\u306E\u500B\u3005\u306E\u78BA\u7387\u5909\u6570\u306F\u305D\u308C\u3089\u81EA\u8EAB\u3067\u306F i.i.d. \u3067\u306F\u306A\u304F\u3001\u4EA4\u63DB\u53EF\u80FD\u306A\u3060\u3051\u3060\u304C\u3001\u305D\u306E\u6839\u5E95\u306B\u306F i.i.d. \u306A\u78BA\u7387\u5909\u6570\u306E\u65CF\u304C\u5B58\u5728\u3059\u308B\u3002 \u3057\u305F\u304C\u3063\u3066\u3001\u5217\u304C\u4EA4\u63DB\u53EF\u80FD\u3067\u3042\u308B\u305F\u3081\u306B\u89B3\u6E2C\u5024\u304C i.i.d. \u3067\u3042\u308B\u5FC5\u8981\u306F\u306A\u3044\u304C\u3001\u305D\u306E\u80CC\u666F\u306B\u306F\u4E00\u822C\u306B\u306F\u89B3\u6E2C\u53EF\u80FD\u3067\u306A\u3044 i.i.d. \u3067\u3042\u308B\u91CF\u304C\u5B58\u5728\u3059\u308B\u3002\u4EA4\u63DB\u53EF\u80FD\u306A\u5217\u306F i.i.d. \u306A\u5217\u306E\u6DF7\u5408\u3067\u3042\u308A\u3001\u305D\u308C\u306F\u5FC5\u305A\u3057\u3082 i.i.d. \u3067\u306F\u306A\u3044\u3002"@ja . . "De Finetti's theorem"@en . . . "\uB370 \uD53C\uB124\uD2F0 \uC815\uB9AC"@ko . . . "Der Satz von de Finetti (auch Darstellungssatz von de Finetti oder de Finetti\u2019s representation theorem) ist ein Satz aus der Stochastik \u00FCber austauschbare Familien von Zufallsvariablen benannt nach seinem Entdecker Bruno de Finetti. Der Satz sagt, dass die Verteilung einer austauschbaren Folge von Bernoulli-verteilten Zufallsvariablen als ein Integral \u00FCber bedingt unabh\u00E4ngige Bernoulli-verteilte Zufallsvariablen betrachtet werden kann."@de . . . . "De stelling van De Finetti is een wiskundige stelling uit de kansrekening die zegt dat uitwisselbare stochastische variabelen voorwaardelijk onafhankelijk zijn, gegeven een aantal latente variabelen waaraan een subjectieve kansverdeling kan worden toegewezen. De stelling is in 1931 bewezen door Bruno de Finetti, en naar hem genoemd."@nl . . "De_Finetti_theorem"@en . "Stelling van De Finetti"@nl . . . . . . . . . . "In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some latent variable. An epistemic probability distribution could then be assigned to this variable. It is named in honor of Bruno de Finetti. For the special case of an exchangeable sequence of Bernoulli random variables it states that such a sequence is a \"mixture\" of sequences of independent and identically distributed (i.i.d.) Bernoulli random variables."@en . "Der Satz von de Finetti (auch Darstellungssatz von de Finetti oder de Finetti\u2019s representation theorem) ist ein Satz aus der Stochastik \u00FCber austauschbare Familien von Zufallsvariablen benannt nach seinem Entdecker Bruno de Finetti. Der Satz sagt, dass die Verteilung einer austauschbaren Folge von Bernoulli-verteilten Zufallsvariablen als ein Integral \u00FCber bedingt unabh\u00E4ngige Bernoulli-verteilte Zufallsvariablen betrachtet werden kann."@de . . . "L."@en . "Em teoria da probabilidade, o teorema de De Finetti mostra o motivo pelo qual observa\u00E7\u00F5es permut\u00E1veis s\u00E3o condicionalmente independentes, dada alguma vari\u00E1vel latente, para qual uma distribui\u00E7\u00E3o de probabilidade epist\u00EAmica \u00E9 ent\u00E3o atribu\u00EDda. Esse teorema recebe esse nome em homenagem ao matem\u00E1tico e probabilista Bruno de Finetti. Esse teorema afirma que uma sequ\u00EAncia de vari\u00E1veis aleat\u00F3rias com distribui\u00E7\u00E3o de Bernoulli \u00E9 uma \"mistura\" de vari\u00E1veis aleat\u00F3rias Bernoulli independente e identicamente distribu\u00EDdas. Assim, enquanto as observa\u00E7\u00F5es n\u00E3o precisam ser i.d.d. para que uma sequ\u00EAncia seja permut\u00E1vel, existem quantidades subjacentes e geralmente n\u00E3o observ\u00E1veis que s\u00E3o i.i.d. - sequ\u00EAncias permut\u00E1veis s\u00E3o (n\u00E3o necessariamente i.i.d) misturas de sequ\u00EAncias i.i.d."@pt . . . . . "De Finettis sats anv\u00E4nds inom sannolikhetsteori f\u00F6r att f\u00F6rklara varf\u00F6r utbytbara sannolikhetsm\u00E5tt (stokastiska variabler) \u00E4r betingat oberoende som sedan kan tilldelas en Bayesiansk sannolikhetsf\u00F6rdelning. Satsen \u00E4r d\u00F6pt efter Bruno de Finetti. Satsen p\u00E5st\u00E5r att en utbytbar serie av Bernoulliska stokastiska variabler. \u00E4r en blandning av oberoende och likaf\u00F6rdelade (i.i.d. efter det engelska uttrycket Independent and identically distributed) variabler d\u00E4r varje enskild variabel i serien inte sj\u00E4lv n\u00F6dv\u00E4ndigtvis \u00E4r i.i.d. utan endast utbytbar s\u00E5 det finns en underliggande upps\u00E4ttning av stokastiska variabler som \u00E4r i.i.d. Det vill s\u00E4ga: bara f\u00F6r att en serie \u00E4r utbytbar beh\u00F6ver den inte vara oberoende och likaf\u00F6rdelad, utan det existerar underliggande och ofta icke-observerbara m\u00E4ngder som \u00E4r i.i.d. Dessa utbytbara serier beh\u00F6ver inte vara oberoende och likaf\u00F6rdelade utan best\u00E5r av blandningar av serier som \u00E4r det."@sv . "Teorema de De Finetti"@pt . . . "De stelling van De Finetti is een wiskundige stelling uit de kansrekening die zegt dat uitwisselbare stochastische variabelen voorwaardelijk onafhankelijk zijn, gegeven een aantal latente variabelen waaraan een subjectieve kansverdeling kan worden toegewezen. De stelling is in 1931 bewezen door Bruno de Finetti, en naar hem genoemd. Voor het speciale geval van een rij uitwisselbare bernoulli-verdeelde stochastische variabelen zegt de stelling dat een dergelijke rij een \"mengsel\" is van rijen onafhankelijke en gelijkverdeelde bernoulli-variabelen. Terwijl de afzonderlijke variabelen van de uitwisselbare rij zelf niet onafhankelijk en gelijkverdeeld hoeven te zijn, maar alleen uitwisselbaar, is er een onderliggende familie van onafhankelijke en gelijkverdeelde stochastische variabelen."@nl . . . . . "De Finetti theorem"@en . . "12067"^^ . . . .