Sentence examples for multivariate normal probabilities from inspiring English sources

A new efficient method is proposed to compute multivariate normal probabilities over rectangles in high dimensions.

Secondly, the probit link also led to a convenient computation of the marginal likelihood in terms of multivariate normal probabilities (Pawitan et al. 2004).

Regression coefficients were assumed to have arisen from a multivariate normal probability distribution [ 30].

Indeed, the CPDF of group i (i = M or N) is given by the well-known multivariate normal probability density as follows: (Where μi is the mean of class i, ∑ is the covariance matrix (which is assumed to be the same for M and N), q is the number of predictor variables used for discrimination and the superscript T indicates matrix transposition).

Under this hypothesis the CPDF of group i (i = M or N) is given by the multivariate normal probability density (6) p (x | i ) = 1 (2 π ) d / 2 | Σ i | − 1 / 2 exp ⁡ { − 1 2 (x − μ i ) ⊤ Σ i − 1 (x − μ i ) } where μ i and Σ i are the mean and the covariance matrix of class i, d the number of predictor variables used for discrimination and superscript T indicates matrix transposition.

Most approaches to maximum likelihood estimation in multivariate probit regression rely on Monte Carlo EM algorithms to avoid computationally intensive evaluations of multivariate normal orthant probabilities.

Quantifying this difference precisely depends on being able to accurately compute cumulative probabilities for multivariate normal distributions with dependence given by (12).

To combine multiple markers, we used a multivariate normal distribution to model the probability density function (pdf) for each class.

Assuming multivariate normal distribution for, we have the following probability density function: where 1 is a vector of n 1 s.

Ward's method joins clusters to maximize the likelihood at each level of the hierarchy under the assumptions of multivariate normal mixtures, spherical covariance matrices, and equal sampling probabilities.

If the test statistics are multivariate normal or t distributed under the null hypotheses, these probabilities can be calculated using, for example, the mvtnorm package in R (Genz and Bretz, 2009).