The subject of the PhD project was on improving the conceptual basis of environmental decision support, primarily by considering ambiguity of scientific predictions and elicited stakeholder values as part of a formal decision support procedure.
In decision theory, objectives – quantitatively described by attributes – are achieved by taking action in respect of the highest ranked decision alternative(s). This requires: (1) the prediction and (2) the valuation (in the form of utilities) of outcomes that are related to all (possibly conditioned) decision alternatives. In the quantitative specification of attributes it is often unavoidable to elicit knowledge about aleatory or epistemic uncertainties from subject matter experts. Unfortunately, the characterization of subjective degrees of belief in the Bayesian context is ambiguous. We suggested the use of imprecise probabilities to describe ambiguity on uncertainty continuously. In this robust Bayesian concept we evaluated diverse classes of probability distributions. We found the Density Ratio Class the most versatile: (a) being able to adequately represent intersubjective knowledge, describing the actual known state-of-the-art of science and technology, which is typically needed in environmental modeling and (b) having unique conceptual assets that are discussed below. Apart from the advantageous class properties, the Density Ratio Class is known to be difficult to elicit.
1st, we developed a method to construct Density Ratio Classes allowing the expert(s) to state intervals for quantiles or probabilities. To even more enhance the method’s accommodation and practicability we made use of already established elicitation techniques.
2nd, to get deeper insight and a quantitative description of the ambiguity, we introduced generally formulated metrics, applicable to any type of class of probability distributions. The metrics measure, relative to a previously chosen credible interval, the ambiguity of important specific probability distribution attributes such as the width, the shape and the position of the mode.
3rd, we showed that the Density Ratio Class is (i) invariant under Bayesian updating, is (ii) invariant under marginalization, is (iii) invariant if propagated through a deterministic model, and is (iv) embedded again into a Density Ratio Class that might be larger than the set of propagated distributions of the original class – if propagated through a stochastic model. These invariance properties make the class unique with regard to conception and allows for a consistent sequential Bayesian learning process.
We also made a proposition of how to numerically implement all the points mentioned above and developed a generically extendable R software package (freely available) that (I) numerically fits ready-for-use one dimensional Density Ratio Classes according to the proposed elicitation method and that (II) calculates the proposed metrics for non transformed distributions. Finally, we illustrated an exemplary application of these implementation schemes due to a deterministic periphyton model with an additive stochastic error.
Note, the formulation of imprecise utilities is not a specific subject that was explicitly addressed in the thesis.
Keywords: Probability assessment; probability elicitation; expert elicitation; elicitation of vague knowledge; subjective probabilities; inter-subjective probabilities; interval probabilities; imprecise probabilities; qualitative expertise; quantitative expertise; decision analysis, decision theory, robust Bayesian inference; robust Bayesian statistics; quantile elicitation; imprecise probabilities; probability box; quantile class; Density Ratio Class; environmental simulation models; utility functions; integrated assessment
Referee: Prof. Dr. Peter Reichert (Eawag / ETHZ)
Co-Referee: Prof. Dr. Marco Zaffalon (IDSIA, Manno)
Co-Referee: Prof. Dr. Mark E. Borsuk (Thayer School of Engineering at Dartmouth)
Co-Referee: Prof. Dr. Hans Rudolf Künsch (SfS / ETHZ)
Assistant in Modelling of Aquatic Ecosystems | Course 701-0426-00 at ETH Zürich ’09-’11
Assistant in Environmental Systems Analysis | Eawag Summer School ’09 – ’11
Assistant in Introduction to Statistics and Graphics with R | Course at Eawag ’08 and ’09
Attended Summerschools, Conferences and Courses
SIPTA Summer School on Imprecise Probabilities Montpellier, France, ’08
ISIPTA International Symposium on Imprecise Probability: Theories and Applications Durham, United Kingdom, ’09
Course of Eliciting Probability Distributions from Experts with SHELF at the Centre for Bayesian Statistics in Health Economics in Sheffield, United Kingdom, ’10
Assistance to an ETHZ Master Student
Masterthesis “Robust elicitation of imprecise expert knowledge for water infrastructure management” Nov. ’10 – Feb. ’11
Staff Council 2008-2010 | Ph.D.’s at Eawag
Member of “SIPTA” (The Society for Imprecise Probability: Theories and Applications)
MSc Mathematics & Earth Sciences University of Geneva ’07 supervised by:
Dr. Annen Catherine, Prof. Dr. Martin J. Gander and Prof. Dr. Xavier Chillier
BSc Mathematics University of Neuchâtel ’05
R package to fit Density Ratio Classes: fitDRC [zip, 96 KB]
Rinderknecht, Simon L., Nele Schuwirth, Carlo Albert, Mark E. Borsuk, Hans-Rudolf Künsch and Peter Reichert, “The Effect of Imprecise Prior Knowledge on Parameter Estimates and Predictions of a Simple River Periphyton Model”, submitted.
Rinderknecht, Simon L., Mark E. Borsuk and Peter Reichert, 2011. Bridging Uncertain and Ambiguous Knowledge with Imprecise Probabilities, Environmental Modelling & Software, doi:10.1016/j.ensoft.2011.07.022 View Abstract
Rinderknecht, Simon L., Mark E. Borsuk, and Peter Reichert, 2011. Eliciting Density Ratio Classes, International Journal of Approximate Reasoning, 52 (6), 792-804. doi: 10.1016/j.ijar.2011.02.002 View Abstract