METHODS FOR APPROXIMATING DISTRIBUTION OF UNKNOWN PARAMETER ESTIMATES WITH APPLICATION IN MATERIAL THERMOPHYSICS

摘要

This paper discusses and compares three methods for approximating a joint probability distribution of least-squares estimates of parameters of interest in nonlinear regression. A joint distribution provides complete information about a random fluctuation of the estimates around their true values and can be used for computing arbitrary criterion values in order to assess accuracy of estimates in experimental design problems. Besides an approximate normal distribution and an approximate distribution obtained by numerical optimization of the utility function for the repeatedly simulated model, an approximate probability density derived by a differential geometry is recommended. To demonstrate the computational feasibility of the proposed methods, all three approaches are applied to several simplified versions of a numerical experiment to identify thermophysical parameters using a model with additional random parameters. The examples presented here illustrate how the suggested methods differ, including in terms of computational complexity.