Oddiy-istakNotation | ![({ boldsymbol mu}, { boldsymbol Lambda}) sim { mathrm {NW}} ({ boldsymbol mu} _ {0}, lambda, { mathbf {W}}, nu)](https://wikimedia.org/api/rest_v1/media/math/render/svg/6b934ecdcbfb1303a5c4979c44543c8455cc4786) |
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Parametrlar | Manzil (ning vektori haqiqiy )
(haqiqiy)
o'lchov matritsasi (pos. def. )
(haqiqiy) |
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Qo'llab-quvvatlash | kovaryans matritsasi (pos. def. ) |
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PDF | ![f ({ boldsymbol mu}, { boldsymbol Lambda} | { boldsymbol mu} _ {0}, lambda, { mathbf {W}}, nu) = { mathcal {N}} ( { boldsymbol mu} | { boldsymbol mu} _ {0}, ( lambda { boldsymbol Lambda}) ^ {{- 1}}) { mathcal {W}} ({ boldsymbol Lambda } | { mathbf {W}}, nu)](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee18e740872ad02698aa9effa54e6d270c3bb65e) |
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Yilda ehtimollik nazariyasi va statistika, normal-Wishart taqsimoti (yoki Gauss-Wishart taqsimoti) ko'p o'zgaruvchan to'rt parametrli doimiy ehtimollik taqsimoti. Bu oldingi konjugat a ko'p o'zgaruvchan normal taqsimot noma'lum bilan anglatadi va aniqlik matritsasi (ning teskarisi kovaryans matritsasi ).[1]
Ta'rif
Aytaylik
![{ displaystyle { boldsymbol { mu}} | { boldsymbol { mu}} _ {0}, lambda, { boldsymbol { Lambda}} sim { mathcal {N}} ({ boldsymbol {) mu}} _ {0}, ( lambda { boldsymbol { Lambda}}) ^ {- 1})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6d2cc90890e646274373a48831e5a34050704536)
bor ko'p o'zgaruvchan normal taqsimot bilan anglatadi
va kovaryans matritsasi
, qayerda
![{ boldsymbol Lambda} | { mathbf {W}}, nu sim { mathcal {W}} ({ boldsymbol Lambda} | { mathbf {W}}, nu)](https://wikimedia.org/api/rest_v1/media/math/render/svg/b1ec50704216114758639181fd3622f8f3d167f6)
bor Istaklarni tarqatish. Keyin
sifatida belgilangan normal-Wishart taqsimotiga ega
![({ boldsymbol mu}, { boldsymbol Lambda}) sim { mathrm {NW}} ({ boldsymbol mu} _ {0}, lambda, { mathbf {W}}, nu) .](https://wikimedia.org/api/rest_v1/media/math/render/svg/d41bd515b4ac2316468a10b0fe9a8d00a259e57d)
Xarakteristikasi
Ehtimollar zichligi funktsiyasi
![f ({ boldsymbol mu}, { boldsymbol Lambda} | { boldsymbol mu} _ {0}, lambda, { mathbf {W}}, nu) = { mathcal {N}} ( { boldsymbol mu} | { boldsymbol mu} _ {0}, ( lambda { boldsymbol Lambda}) ^ {{- 1}}) { mathcal {W}} ({ boldsymbol Lambda } | { mathbf {W}}, nu)](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee18e740872ad02698aa9effa54e6d270c3bb65e)
Xususiyatlari
O'lchov
Marginal taqsimotlar
Qurilish bo'yicha marginal taqsimot ustida
a Istaklarni tarqatish, va shartli taqsimlash ustida
berilgan
a ko'p o'zgaruvchan normal taqsimot. The marginal taqsimot ustida
a ko'p o'zgaruvchan t- tarqatish.
Parametrlarning orqa taqsimlanishi
Qilgandan keyin
kuzatishlar
, parametrlarning orqa taqsimlanishi
![{ displaystyle ({ boldsymbol { mu}}, { boldsymbol { Lambda}}) sim mathrm {NW} ({ boldsymbol { mu}} _ {n}, lambda _ {n}, mathbf {W} _ {n}, nu _ {n}),}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1f783a11ed298e91a6be7b1165b64593d4090dd6)
qayerda
![{ displaystyle lambda _ {n} = lambda + n,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/31bfb2bad6a64dff57ad58381e247ae521ca5b84)
![{ displaystyle { boldsymbol { mu}} _ {n} = { frac { lambda { boldsymbol { mu}} _ {0} + n { boldsymbol { bar {x}}}} { lambda + n}},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/deecd7f55346536467dc46290484c9642fcebe47)
![{ displaystyle nu _ {n} = nu + n,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/69e54e2218b4d3c8ba00031f332764bee6647935)
[2]
Normal-Wishart tasodifiy o'zgarishini yaratish
Tasodifiy o'zgarishni yaratish to'g'ridan-to'g'ri:
- Namuna
dan Istaklarni tarqatish parametrlari bilan
va ![nu](https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468)
- Namuna
dan ko'p o'zgaruvchan normal taqsimot o'rtacha bilan
va dispersiya ![( lambda { boldsymbol Lambda}) ^ {{- 1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0610445dd263f1912dc1e6ce6a561e3810ffcc4b)
Tegishli tarqatishlar
Izohlar
Adabiyotlar
- Bishop, Kristofer M. (2006). Naqshni tanib olish va mashinada o'rganish. Springer Science + Business Media.
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Diskret o'zgaruvchan cheklangan qo'llab-quvvatlash bilan | |
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Diskret o'zgaruvchan cheksiz qo'llab-quvvatlash bilan | |
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Doimiy o'zgaruvchan cheklangan oraliqda qo'llab-quvvatlanadi | |
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Doimiy o'zgaruvchan yarim cheksiz oraliqda qo'llab-quvvatlanadi | |
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Doimiy o'zgaruvchan butun haqiqiy chiziqda qo'llab-quvvatlanadi | |
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Doimiy o'zgaruvchan turi turlicha bo'lgan qo'llab-quvvatlash bilan | |
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Aralashtirilgan uzluksiz diskret bir o'zgaruvchidir | |
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Ko'p o'zgaruvchan (qo'shma) | |
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Yo'naltirilgan | |
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Degeneratsiya va yakka | |
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Oilalar | |
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