1. A computer-program product tangibly embodied in a non-transitory machine-readable storage medium, the computer-program product including instructions operable to cause a first computing device of a plurality of computing devices to perform operations including: generate a first sample portion of a single random sample from a single posterior probability distribution at least partially in parallel with at least a second computing device of the plurality of computing devices, wherein: the second computing device generates a second sample portion of the single random sample from the single posterior distribution; and the single random sample comprises a plurality of sample portions that comprises the first sample portion and the second sample portion; fit an empirical distribution function to a marginal probability distribution of a variable within the first sample portion of the single random sample to derive a first partial marginal probability distribution approximation of a plurality of partial marginal probability distribution approximations at least partially in parallel with the second computing device, wherein: the second computing device fits the empirical distribution function to a marginal probability distribution of the variable within the second sample portion of the single random sample to derive a second partial marginal probability distribution approximation of the plurality of partial marginal probability distribution approximations; transmit the first partial marginal probability distribution approximation to a coordinating device at least partially in parallel with the second computing device, wherein: the second computing device transmits the second partial marginal probability distribution approximation to the coordinating device; and the coordinating device generates a marginal probability distribution approximation of the single random sample from the plurality of partial marginal probability distribution approximations transmitted to the coordinating device at least partially in parallel by the plurality of computing devices; fit a first portion of a copula function of a plurality of portions of the copula function to a multivariate probability distribution of the first sample portion of the single random sample to generate a first likelihood contribution of a plurality of likelihood contributions at least partially in parallel with the second computing device, wherein: the second computing device fits a second portion of the plurality of portions of the copula function to a multivariate probability distribution of the second sample portion of the single random sample to generate a second likelihood contribution of the plurality of likelihood contributions; transmit an indication of the first likelihood contribution of the first sample portion to the coordinating device at least partially in parallel with the second computing device, wherein: the second computing device transmits an indication of the second likelihood contribution of the second sample portion to the coordinating device; and the coordinating device determines whether the fit of the copula function, performed as the fit of the plurality of portions of the copula function by the plurality of computing devices, meets a predetermined criterion for generation of a reduced size representation of the single random sample that achieves a predetermined degree of fit of the copula function based on the marginal probability distribution approximation and based on the plurality of likelihood contributions to determine whether the fit of the copula function is to be repeated; and in response to receipt of copula coefficients generated and transmitted by the coordinating device in response to a determination by the coordinating device that the fit of the copula function is to be repeated, perform an iteration of operations at least partially in parallel with the second computing device, each iteration comprising: repeat the fitting of the first portion of the copula function to the multivariate probability distribution of the first sample portion based on the copula coefficients to repeat generation of the first likelihood contribution of the first sample; and repeat the transmission of the indication of the first likelihood contribution of the first sample portion to the coordinating device to enable the coordinating device to again determine whether the fit of the copula function meets the predetermined criterion to again determine whether the fit of the copula function is to be again repeated by the plurality of computing devices in another iteration.