Parameter Identification in a Probabilistic Setting

TL;DR

This paper introduces a deterministic, fast, and reliable method for parameter identification in probabilistic models, capable of handling high-dimensional, nonlinear, and non-Gaussian problems by combining measure updating and functional approximation techniques.

Contribution

It presents a novel deterministic approach that integrates measure updating with functional approximation, eliminating the need for sampling in probabilistic parameter identification.

Findings

Works effectively for highly nonlinear, non-smooth problems

Handles non-Gaussian measures successfully

Outperforms existing methods in speed and reliability

Abstract

Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g. through a measurement, by connecting it to Bayes's theorem. The unknown quantity is modelled as a (may be high-dimensional) random variable. Such a description has two constituents, the measurable function and the measure. One group of methods is identified as updating the measure, the other group changes the measurable function. We connect both groups with the relatively recent methods of functional approximation of stochastic problems, and introduce especially in combination with the second group of methods a new procedure which does not need any sampling, hence works completely deterministically. It also seems to be the fastest and more reliable when compared with other methods. We show by example that it also works for highly nonlinear non-smooth problems with non-Gaussian measures.