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As stated by Sklar (1959), copula couples the multivariate distribution to its marginal distributions which are uniformly distributed on [0,1].
And according to the effects of the dependences in application scenes, the corresponding criterion is proposed to map the multivariate distribution to a univariate one, hence facilitating the comparisons between different multivariate models.
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Depending on the experimental set up, we might choose univariate or multivariate distributions to fit our data.
A recent trend of geotechnical correlation analysis is to construct a multivariate distribution model to describe the multiple dependency characteristics of different soil parameters.
The forecast model applies a family of multivariate distribution functions to forecast future drought conditions given the drought status in the past.
Copulas are functions that join multivariate distribution functions to their one-dimensional marginal distribution functions.
Copulas are functions that join or couple multivariate distribution functions to their one-dimensional marginal distribution functions.
For each virtual patient, the fixed effects were sampled from a multivariate normal distribution based on the uncertainty of the fixed effect estimate; the random effects were sampled from a multivariate normal distribution to account for intersubject variability.
One is to use a zero-mean multivariate Gaussian distribution to approximate the student's distribution, which makes the calculation of the prior distribution of a MR image tractable.
GPR is built on Gaussian process, which is a stochastic process that generalizes multivariate Gaussian distribution to infinite-dimensional space such that distributions over function values can be defined.
Seeger et al. [17] suggested that a student's t distribution can be approximated in terms of a Gaussian distribution, we therefore use a zero-mean multivariate Gaussian distribution to approximate the sparse prior of q t, where (q_tsim prod _1^N{mathcal {N}(0,c)}.) The constant value c is determined by the level of variations q t.
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