In this paper we study statistical inference for certain inverse problems. We go beyond mere estimation purposes and review and develop the construction of confidence intervals and confidence bands in some inverse problems, including deconvolution and the backward heat equation. Further, we discuss the construction of certain hypothesis tests, in particular concerning the number of local maxima...

Abstract—In this paper the influence of errors of function derivatives in initial time which have been obtained by experiment (uncontrollable inaccuracy) to the results of inverse problem solution was investigated. It was shown that these errors distort the inverse problem solution as a rule near the beginning of interval where the solutions are analyzed. Several methods for removing the influe...

We examine the general non-linear inverse problem with a finite number of parameters. In order to permit the incorporation of any a priori information about parameters and any distribution of data (not only of gaussian type) we propose to formulate the problem not using single quantities (such as bounds, means, etc.) but using probability density functions for data and parameters. We also want ...

Let ut −∇2u = f(x) := ∑M m=1 amδ(x− xm) in D × [0,∞), where D ⊂ R3 is a bounded domain with a smooth connected boundary S, am = const, δ(x− xm) is the delta-function. Assume that u(x, 0) = 0, u = 0 on S. Given the extra data u(yk, t) := bk(t), 1 ≤ k ≤ K, can one find M,am, and xm? Here K is some number. An answer to this question and a method for finding M,am, and xm are given.

Author: Pedro Luis Kantek Garcia Navarro Affiliation: CELEPAR Title: AN EVOLUTIONARY APPROACH IN MAGNETOTELLURIC INVERSION Text: Magnetotelluric inversion is the reconstitution of the pattern of underground geolectric conductivities out of an incomplete and noisy set of measurements of the electromagnetic field at various points of the surface, and at various frequencies. In the forward problem...

The inverse geothermal problem consist of estimating the temperature distribution below the earth’s surface using temperature and heat-flux measurements on the earth’s surface. The problem is important since temperature governs a variety of the geological processes including formation of magmas, minerals, fosil fuels and also deformation of rocks. Mathematical this problem is formulated as a Ca...

Abstract. Recent inverse solutions obtained from some geoscience applications are presented. The estimation of the vertical atmospheric temperature from radiaces at infrared wavelenth is computed employing artificial neural networks, where good retrievals are obtained. A source-repector strategy is used for identifying the atmospheric pollutant source, where the Lagrangian particle model is app...

Inverse problems involve estimating parameters or data from inadequate observations; the observations are often noisy and contain incomplete information about the target parameter or data due to physical limitations of the measurement devices. Consequently, solutions to inverse problems are non-unique. To pin down a solution, we must exploit the underlying structure of the desired solution set....

During the past few years the development of experimental techniques has allowed the quantitative analysis of biological systems ranging from neurobiology and molecular biology. This work focuses on the quantitative description of these systems by means of theoretical and numerical tools ranging from statistical physics to probability theory. This dissertation is divided in three parts, each of...