Interpretation of Monte Carlo Simulations Using Parameter Space Plots

Multimodal distribution functions that result from Monte Carlo simulations can be interpreted by superimposing joint probability density functions onto the contour space of the simulated calculations. The method is demonstrated by analysis of the pathway of a radioactive groundwater contaminant using an analytical solution to the transport equation. Simulated concentrations at a fixed time and distance produce multimodal histograms, which are understood with reference to the parameter space for the two random variables—velocity and dispersivity. Numerical integration under the joint density function up to the contour of the analytical solution gives the probability of contaminant exceeding a target concentration. This technique is potentially more efficient than Monte Carlo simulation for low probability events. Visualization of parameter space is restricted to two random variables. Nevertheless, analyzing the two most pertinent random variables in a simulation might still offer insights into the multimodal nature of output histograms.