A copula is a multivariate joint distribution defined on the n-dimensional unit cube [0,1] n in a way that every marginal distribution is uniform in the interval [0,1].
The copula is a commonly used statistical tool to model multivariate joint distribution, it appeared in the early work of Hoeffding, Fréchet and others and formally introduced by Sklar (1959).
Another group of methods employ probabilistic graphical models that analyze multivariate joint probability distributions over the observations, usually with the use of Bayesian Networks (BN) [ 9- 11], or Markov Networks (MN) [ 12].
Using a Bayesian technique, the highly multivariate joint posterior distribution of all transcript concentrations is estimated.
Based on this Markov condition, the multivariate joint probability distribution of the graphical model can be expressed as follows: One of the goals of this study is to infer such BNs from metabolic flux profiles.
The multivariate relationships (joint distribution) between the indices (MP, TE, TMAX, AUC, CMAX and KE), for survivors and non-survivors across descriptors, were displayed using biplots [ 29].
The multivariate normal copula is defined as with density Thus for given marginal distribution functions F1, …, F d and their densities f1, …, f d, the joint distribution function for the multivariate normal copula with these given margins is with density For the distribution in (6), any lower dimensional joint distributions have the same form.
for all joint distributions satisfying.
In an earlier paper the author has defined joint capacity and joint containment functionals which are multivariate set functions describing the joint distribution of random sets.
Although Negative Binomial distributions or other distributions with over-dispersion parameters are often used for modeling *-seq data, they cannot be easily adopted to model the joint distribution of multivariate signals with covariance structures.
