Novel mathematical and statistical approaches to uncertainty evaluation in the context of regression and inverse problems

Abstract

Abstract. The European Metrology Research Programme (EMRP) is currently funding project EMRP-NEW04 on novel mathematical and statistical approaches to uncertainty evaluation. One focus of the project is uncertainty evaluation in the context of regression and parametric inverse problems. The development of methods for such problems will be carried out in close connection with four application examples. Here we outline these application examples, and present some first results.

Overview: Estimating and reporting uncertainties in remotely sensed atmospheric composition and temperature

“…Since this treatment deprives any solution of its claimed optimality (Cressie, 2018), in some cases the measurement noise is artificially "inflated" to account for potential calibration uncertainties. A method to include multiple types of uncertainties in the measurement error covariance matrix is discussed in Marks and Rodgers (1993), Tarantola and Valette (1982), Eriksson (2000), andvon Clarmann et al (2001). These authors discuss the possibility of mapping all relevant error contributions into the measurement space and include them in the S y matrix 5 .…”

“…In the ideal case, when the retrieval vector represents the entire atmospheric state with all its relevant variables, S x, noise covers all uncertainties associated with everything other than the target variable. For example, if one is interested in the error of ozone abundances, any uncertainty in the ozone mixing ratio caused by water vapor uncertainties is implicitly included in S x, noise , as suggested by Marks and Rodgers (1993), Tarantola and Valette (1982), Eriksson (2000; for a different perspective on this issue, see Sect. 4.1.2 in Rodgers (2000).…”

Estimating and Reporting Uncertainties in Remotely Sensed Atmospheric Composition and Temperature

“…Following this, we turn towards error estimation and uncertainty assessment. We preparation), who challenges the principal difference between the error concept and the uncertainty concept; Bich (2012), who, although a Working Group leader of the Joint Committee for Guides in Metrology, claims inconsistencies between the GUM document and its supplements; Grégis (2015), who challenges the position that one can dispense with the notion of 'true value' in metrology as suggested in GUM; or Elster et al (2013) and European Centre for Mathematics and Statistics in Metrology (2019), where the applicability of the GUM concept to inverse problems is critically discussed. Conversely, QA4EO task team 15 (2010), Merchant et al (2017), and Povey and Grainger (2015), e.g., largely endorse the GUM-based uncertainty concept.…”

Novel mathematical and statistical approaches to uncertainty evaluation: introducing a new EMRP research project

“…Further details of this work are given in the related paper: Novel mathematical and statistical approaches to uncertainty evaluation in the context of regression and inverse problems [4].…”

“…The current state of the art for uncertainty evaluation in metrology is provided by the Joint Committee for Guides in Metrology (JCGM) Guide to the expression of uncertainty in measurement (GUM) [1] and its Supplements [2,3]. In addition, a guide to the role of measurement uncertainty in decisionmaking and conformity assessment has recently been published by the JCGM [4]. Existing guidelines are successfully applied across many areas of metrology, but they do not cover some of the new challenges arising from modern measurement systems.…”