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June 30th, 2017, 05:20 AM   #1
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Unsolvable Integral?

Is the following integral solvable?

$$P(X) = \int \int P(X|\mu,K)P(\mu|K)P(K) d\mu dK$$

with

$$P(K) = \frac{|K| ^{(v-p-1)/2}}{2^{vd/2}|W|^{v/2}\Gamma_p|\frac{n}{2}|} e^{-tr(V^{-1}K)/2}$$

$$ P(\mu|K) = \frac{|\lambda_0K|^{1/2}}{(2\pi)^{d/2}}e^{-0.5([\mu - \mu_0]^T \lambda_0K[\mu-\mu_0])}$$

$$P(X|\mu,K) = \frac{|K|^{1/2}}{(2\pi)^{d/2}}e^{-0.5([X- \mu]^T K[X-\mu])}$$

with $K$ being a matrix variable and $X$ and $\mu$ being vector variables
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June 30th, 2017, 05:29 AM   #2
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FYI, if you don't get replies to this question (or the previous ones you've asked here), you might have better luck at Cross Validated.
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June 30th, 2017, 06:57 AM   #3
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* edit
Integral should be
$$P(X) = \int^{\infty}_{-\infty} \int^{\infty}_{-\infty} P(X|\mu,K)P(\mu|K)P(K) d\mu dK$$
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June 30th, 2017, 06:59 AM   #4
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*Edit
Integral should be

$$P(X) = \int^{\infty}_{-\infty} \int^{\infty}_{-\infty} P(X|\mu,K)P(\mu|K)P(K) d\mu dK$$
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