Approximate multivariate posterior probability distributions from simulated samples

A computer-implemented method comprising:

• fitting, on a first computing device, an empirical distribution function to a marginal probability distribution of a variable within a first sample portion of a random sample to derive a first partial marginal probability distribution approximation, wherein the random sample is divided into a plurality of sample portions comprising the first sample portion and a second sample portion, and wherein the plurality of sample portions is distributed among a plurality of computing devices;
• fitting, on the first computing device, a first portion of a copula function to a multivariate probability distribution of the first sample portion, wherein the copula function is divided into a plurality of portions comprising the first portion of the copula function and a second portion of the copula function;
• and
• transmitting, from the first computing device, an indication of a first likelihood contribution of the first sample portion to a coordinating device to cause a second computing device to fit the second portion of the copula function to a multivariate probability distribution of the second sample portion.

An apparatus comprising:

• a processor component of a first computing device;
• an empirical function component for execution by the processor component to fit an empirical distribution function to a marginal probability distribution of a variable within a first sample portion of a random sample to derive a first partial marginal probability distribution approximation, wherein the random sample is divided into a plurality of sample portions comprising the first sample portion and a second sample portion, and wherein the plurality of sample portions is distributed among a plurality of computing devices;
• a copula fitting component for execution by the processor component to fit a first portion of a copula function to a multivariate probability distribution of the first sample portion, wherein the copula function is divided into a plurality of portions comprising the first portion of the copula function and a second portion of the copula function;
• and
• a communications component for execution by the processor component to transmit an indication of a first likelihood contribution of the first sample portion to a coordinating device to cause a second computing device to fit the second portion of the copula function to a multivariate probability distribution of the second sample portion.