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We propose a method to generate samples from multivariate distributions that contain far fewer points than reliable Monte Carlo samples, yet retain much of the original distributions' information.
Although only wind power uncertainty modelling is discussed in this paper, the Pair-Copula approach provides a powerful tool for constructing flexible multivariate distributions that it can also be applied to a wide range of statistical analyses and stochastic decision fields of power systems.
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Instead, the pattern of damage must be captured by a high-dimensional multivariate distribution that describes how the presence or absence of damage at every voxel within each brain image is related to damage to all other voxels.
However, this means that the multivariate normal distributions that define each state span this reduced subspace, and are therefore not readily interpretable in terms of the underlying anatomy.
E1 and E2 represent zero-mean, multivariate Gaussian distributions that assume a spatiotemporal factorization into temporal covariance, V, and spatial covariances C(1) and C(2) [Friston et al., 2006].
Using risk adjustment contributions of the year 2011 as a basis we modeled yearly cost increases for all 15 age groups (by drawing random yearly growth rates from a multivariate normal distribution that was informed with observed cost increases for each age group [21]).
The two traits were simulated by drawing the allele substitution effects of each QTL locus from a multivariate normal distribution that followed the simulated genetic correlation.
Azzalini and Dalla Valle (1996) introduced the multivariate skew normal distribution that extends the normal distribution with an additional skewness parameter.
We describe a multivariate wrapped-Gaussian distribution that can be used to model statistical distributions expressed in periodic angular variables even in the presence of significant angle-angle correlations.
These considerations suggest that multivariate distributions of different physiological properties sampled across many cells in a network may contain unique information both about current tuning of this network, and the mechanisms behind this tuning that may act through local recalibration of properties in individual cells (O'Leary et al., 2013).
The Dirichlet distribution is a continuous multivariate distribution over discrete probability distributions (that is, vectors of pre-determined size that contain non-negative elements that sum to one).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com