Bayesian Analysis of the Independent Multi Normal Process Neither Mean Nor Prec
Bayesian Analysis of the Independent Multi Normal Process Neither Mean Nor Prec
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1 Joint Distribution of (m", y") The joint density of (m", V") is, provided n' > 0, v' > 0, and v > is D(m-, V"|m', V', n', v'> n, v) ot | r-v' -nMm--m' ) (m"-m- )'^ p^'^ (17a) where n*=n'n-/n . ^^^^^ - 16 - and the range of (m", y") is R, „ „, = ((m", y")|-»< m" < -fw and V"-C is PDSj . (17c) Proof : Following the argument of subsections 12. 1. 4 and 12. 6. 1 of [5] we can establish that n (m-ra')*^h(m-m') = n*(m"-m' /h(m"-m' ) (18a) where n*=n'n"/n. The same line of argument allows us to write y"=y'+y+n'(m'm')'^ + n(m m*^) - n"(m"m"'^) = V'+V + n*(m"-m' ) (m"-m' ) '^. (18b) From (7) we have (m, V) = (^ (n"m"-n'm'), V"-V' -n*(m"-m') (m"-m' )'^) . Letting J(m", V"; m, V) denote the Jacobian of the integrand transformation from (m, y) to (m", y")^ we make this transformation in (10b), obtaining (17a). Since J(m", y"; m, y) = J(m", m) J(y", y) and both J(m", m) and J(y", V) are constants involving neither m" nor V", neither does J(m", V"j m, V) . When v<0 and V is singular the numerator in (17a) vanishes, so that the density exists only if v > 0.
What to read after Bayesian Analysis of the Independent Multi Normal Process Neither Mean Nor Prec?
You can find similar books in the "Read Also" column, or choose other free books by Albert Ando to read online
To quickly assess the difficulty of the text, read a short excerpt:
1 Joint Distribution of (m", y") The joint density of (m", V") is, provided n' > 0, v' > 0, and v > is D(m-, V"|m', V', n', v'> n, v) ot | r-v' -nMm--m' ) (m"-m- )'^ p^'^ (17a) where n*=n'n-/n . ^^^^^ - 16 - and the range of (m", y") is R, „ „, = ((m", y")|-»< m" < -fw and V"-C is PDSj . (17c) Proof : Following the argument of subsections 12. 1. 4 and 12. 6. 1 of [5] we can establish that n (m-ra')*^h(m-m') = n*(m"-m' /h(m"-m' ) (18a) where n*=n'n"/n. The same line of argument allows us to write y"=y'+y+n'(m'm')'^ + n(m m*^) - n"(m"m"'^) = V'+V + n*(m"-m' ) (m"-m' ) '^. (18b) From (7) we have (m, V) = (^ (n"m"-n'm'), V"-V' -n*(m"-m') (m"-m' )'^) . Letting J(m", V"; m, V) denote the Jacobian of the integrand transformation from (m, y) to (m", y")^ we make this transformation in (10b), obtaining (17a). Since J(m", y"; m, y) = J(m", m) J(y", y) and both J(m", m) and J(y", V) are constants involving neither m" nor V", neither does J(m", V"j m, V) . When v<0 and V is singular the numerator in (17a) vanishes, so that the density exists only if v > 0.
What to read after Bayesian Analysis of the Independent Multi Normal Process Neither Mean Nor Prec?
You can find similar books in the "Read Also" column, or choose other free books by Albert Ando to read online
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