Tango- und Milonga-Workshop LiberTango-Baden mit Ricardo Viqueira, Buenos Aires

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Samstag 03. und Sonntag 04. November 2012 Singsaal der Kantonsschule Baden Seminarstrasse 3, 5400 Baden Tango 12.00 bis 14.00 Uhr jeweils Sa und So, Preis: 100.–/Person* Milonga 14.30 bis 16.30 Uhr jeweils Sa und So, Preis: 100.–/Person* * 10% Ermässigung … Continue reading

Monatliche Milonga – Verein LiberTango Baden

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Im Badener Tanzcentrum Martinsbergstrasse 38 5400 Baden Tanzen mit tandas und cortinas in stimmungsvollem Ambiente zur Musik von Marie-Antonine Woutaz und Gast-DJs. Immer am zweiten Samstag im Monat 21.00 bis 01.00 Uhr Samstag 11.08.2012 Samstag 08.09.2012 Samstag 13.10.2012 Samstag 10.11.2012 … Continue reading

TangoTrio Stanzerei Baden um 20h30 am 29. Februar 2012

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Daniel Zisman (vl), Sébastien Fulgido (g), Michael Zisman (band) Das Trio vereint die Reife des grossen Meisters der Tangovioline, Daniel Zisman mit der Jugend der virtuosen Talente Michael Zisman (band) und Sébastien Fulgido (g).
Das Ensemble schlägt die Brücke zwischen dem … Continue reading

Bobby McFerrin hacks your brain with music. Some Expectations. (from TED)

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Bobby McFerrin on Ted in a Pentatonic scale ——–^—— Officially approved Bio of Bobby McFerrin: “There is something almost superhuman about the range and technique of Bobby McFerrin,” says Newsweek. “He sounds, by turns, like a blackbird, a Martian, an … Continue reading

Bridging uncertain and ambiguous knowledge with imprecise probabilities

Bridging uncertain and ambiguous knowledge with imprecise probabilities

  • Simon L. Rinderknechta, b, Corresponding author contact information,
  • Mark E. Borsukc,
  • Peter Reicherta, b, E-mail the corresponding author
  • a Eawag, Swiss Federal Institute of Aquatic Science and Technology, Department of Systems Analysis, Integrated Assessment and Modelling, CH-8600 Dübendorf, Switzerland
  • b ETH Zurich, Department of Environmental Sciences, Institute of Biogeochemistry and Pollutant Dynamics (IBP), CH-8092 Zürich, Switzerland
  • c Dartmouth College, Thayer School of Engineering, Hanover, NH 03755-8000, USA
  • Received 31 July 2010. Revised 25 July 2011. Accepted 27 July 2011. Available online 13 September 2011.

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Abstract

Model-based environmental decision support requires that uncertainty be rigorously evaluated. Whether uncertainty is aleatory or epistemic, we argue that probability is the natural mathematical construct for describing uncertainty in predictions used for decision-making. If expert knowledge is elicited using stated preferences between lotteries, and the experts are rational in the sense of avoiding sure loss, then the resulting knowledge quantifications will be consistent with the axiomatic foundation of probability theory. This idea can be extended to the description of intersubjective knowledge when the intent is to characterize the state of knowledge of the scientific community. Many methods for probability elicitation have been reported, but there is nearly always some degree of ambiguity in translating elicited quantities into probabilistic description. This would include: any lack of fit of a particular distributional form to elicited data; incertitude in the elicited data themselves; and/or disagreement in the elicited data across multiple experts. By replacing a precise probability distribution by a set of distributions, the mathematical concept of imprecise probabilities provides a means for representing this ambiguity. In this way, imprecise probabilities can form a bridge between total ignorance and precisely characterized risk by allowing for a continuous degree of imprecision to represent ambiguity. We introduce three metrics to describe the relative ambiguity of important attributes of probability distributions, namely their width, shape, and mode. These metrics are applicable to sets of distributions characterized by using any available method, and we derive the specific forms of these metrics for the Density Ratio Class, which we have found to have many desirable properties. Based on these metrics and on elicitation data from the literature, we use three examples to demonstrate the wide variety of ambiguity that can be present in elicited knowledge. Imprecise probabilities allow us to quantify this ambiguity and consider it in environmental decision-making. Our examples were implemented using a package we recently developed and made freely available for the R statistical programming environment.

Keywords

  • Expert elicitation;
  • Subjective probabilities;
  • Intersubjective knowledge;
  • Interval probabilities;
  • Qualitative expertise;
  • Quantitative expertise;
  • Robust Bayesian inference;
  • Robust Bayesian statistics;
  • Quantile elicitation;
  • Imprecise probabilities;
  • Probability box;
  • Quantile class;
  • Density Ratio Class

Eliciting density ratio classes

  • Simon L. Rinderknechta, b,
  • Mark E. Borsukc,
  • Peter Reicherta, b, Corresponding author contact information, E-mail the corresponding author
  • a Eawag, Swiss Federal Institute of Aquatic Science and Technology, CH-8600 Dübendorf, Switzerland
  • b ETH Zürich, Institute of Biogeochemistry and Pollutant Dynamics (IBP), CH-8092 Zürich, Switzerland
  • c Dartmouth College, Thayer School of Engineering, Hanover, NH 03755-8000, USA
  • Received 22 April 2010. Revised 8 October 2010. Accepted 11 February 2011. Available online 16 February 2011.

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Abstract

The probability distributions of uncertain quantities needed for predictive modelling and decision support are frequently elicited from subject matter experts. However, experts are often uncertain about quantifying their beliefs using precise probability distributions. Therefore, it seems natural to describe their uncertain beliefs using sets of probability distributions. There are various possible structures, or classes, for defining set membership of continuous random variables. The Density Ratio Class has desirable properties, but there is no established procedure for eliciting this class. Thus, we propose a method for constructing Density Ratio Classes that builds on conventional quantile or probability elicitation, but allows the expert to state intervals for these quantities. Parametric shape functions, ideally also suggested by the expert, are then used to bound the nonparametric set of shapes of densities that belong to the class and are compatible with the stated intervals. This leads to a natural metric for the size of the class based on the ratio of the total areas under upper and lower bounding shape functions. This ratio will be determined by the characteristics of the shape functions, the scatter of the elicited values, and the explicit expert imprecision, as characterized by the width of the stated intervals. We provide some examples, both didactic and real, and conclude with recommendations for the further development and application of the Density Ratio Class.

Keywords

  • Probability assessment;
  • Expert elicitation of vague knowledge;
  • Imprecise probabilities;
  • Robust Bayesian statistics;
  • Quantile elicitation;
  • Density Ratio Class
sciencedirect.com
Corresponding author at: Eawag, Swiss Federal Institute of Aquatic Science and Technology, CH-8600 Dübendorf, Switzerland. Tel.: +41 587655281.

Copyright © 2011 Elsevier Inc. All rights reserved.

676 Nuevo Tango Nonett – Stanzerei Baden, Mittwoch 4. Mai 2011, 20.30 Uhr

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Daniel Zisman (Vl), Michael Zisman (Band), Theo Kapilidis (Git), Richard Pizzorno (P). Wini Holzenkamp (Cb), Franziska Grüter (Vl), Barbara Zisman (Vla), Annapaola Jacomella (Vcl). Tobias Friedli (Perc) Der letzte Abend der LIBERTANGO- Konzerte dieser Saison 2010/2011 wird zugleich der Anfang … Continue reading

“Le Paradoxe de Bertrand” in Deutsch: Das Bertrand-Paradoxon

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Das Bertrand-Paradoxon stammt aus der Wahrscheinlichkeitstheorie. Es verdeutlicht, dass reine Intuition in dieser Disziplin manchmal sehr irreführend ist und zu total verschiedenen Resultaten führen kann. Das Problem wurde erstmals im Jahre 1888 von Joseph Bertrand in seinem Buch “Calcul des … Continue reading