The conditional distribution of the joint concomitants can be derived from the above result by comparing the formula in marginal distribution and hence
22.
Joint distribution can be written in terms of univariate marginal distribution functions and a copula which describes the dependence structure between the variables.
23.
By construction, the marginal distribution over \ tau is a gamma distribution, and the conditional distribution over x given \ tau is a Gaussian distribution.
24.
We assume that the statistics of the process are known completely, that is, the marginal distribution of the process seen at each time instant is known.
25.
If X | \ mu has an NEF-QVF distribution and & mu; has a conjugate prior distribution then the marginal distributions are well-known distributions.
26.
Likewise, the estimated joint marginal distribution of the set of variables belonging to one factor is proportional to the product of the factor and the messages from the variables:
27.
The normal-inverse Gaussian distribution can also be seen as the marginal distribution of the normal-inverse Gaussian process which provides an alternative way of explicitly constructing it.
28.
Upon convergence ( if convergence happened ), the estimated marginal distribution of each node is proportional to the product of all messages from adjoining factors ( missing the normalization constant ):
29.
Then the choice of the marginal distribution p _ X ( x ) completely determines the joint distribution p _ { X, Y } ( x, y ) due to the identity
30.
George Seber points out that the Wishart distribution is not called the multivariate chi-squared distribution because the marginal distribution of the off-diagonal elements is not chi-squared.
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