7] Monte Carlo Method for determining complete confidence probability distributions of estimated model parameters

Abstract

Publisher Summary The implementation of the Monte Carlo confidence probability determination method requires the initial estimation of the set of most probable parameter values that best characterize some set(s) of experimental observations, according to a suitable mathematical model (that is, one capable of reliably describing the data). The Monte Carlo approach is unique in the sense that it is capable of determining confidence interval probability distributions, in principle, to any desired level of resolution and is conceptually extremely easy to implement. The necessary information for the application of the Monte Carlo method for estimating confidence intervals and probability distribution profiles is two-fold: (1) an accurate estimate of the distribution of experimental uncertainties associated with the data being analyzed and (2) a mathematical model capable of accurately characterizing the experimental observations. The Monte Carlo method is then applied by (1) the analysis of the data for the most probable model parameter values, (2) the generation of “perfect” data as calculated by the model, (3) the superposition of a few hundred sets of simulated noise on the perfect data, (4) the analysis of each of the noise containing, simulated data with subsequent tabulation of each set of most probable parameter values, and (5) an assimilation of the tabulated sets of most probable parameter values by generating histograms. The histograms represent discrete approximations of the model parameter confidence probability distributions as derived from the original data set and the distribution of experimental uncertainty contained therein.