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Fig. 2 Marginal density of eigenvalues of the quotient ensemble.

We first show that the frequency marginal density of the present estimate is bound within [0,1] when using non-identical smoothing operators.

In Fig. 2, we show the marginal density of eigenvalues for n=3, while in Figs. 3 and 4 we display the probability distributions and densities of the extreme eigenvalues.

where (widehat {f} y,mathbf {x)}) is an estimator of the joint density of y and x, and (widehat {mu }(mathbf {x)}) is an estimator of marginal density of x.

Another consequence of normalizing the CSD by the ensemble-averaged PSD is that only the frequency marginal density of the (squared) estimate is bound within [0,1] but the time-resolved estimate itself not.

We carry out the Laplace approximations in the directions orthogonal to the null space of the Jacobian matrix of the data model with respect to the parameters, so that the information gain can be reduced to an integration against the marginal density of the transformed parameters that are not determined by the experiments.

A standard alternative is to use stochastic simulation techniques to approximate the marginal densities of η.

Let and be two random variables with joint density function, assuming that it exists, and denote the (marginal) densities of and by and, respectively.

Because the true coherence between empirically recorded signals is not known, we assess the methods based on the marginal densities of the covariance matrix.

The AC statistic which is based on the measure of the common area under the respective kernel density estimators is used in order to compare the equality among the marginal densities of a k-dimensional random variable.

A key result of this paper is the computation in closed form of the marginal densities of the singular values, leading to a polynomial-time method for the real matrix sample generation problem.