Eliciting Subjective Probability Distributions on Continuous Variables

1975 ◽  
Author(s):  
David A. Seaver ◽  
Detlof v. Winterfeldt ◽  
Ward Edwards
Keyword(s):  
Subjective Probability ◽  
Probability Distributions ◽  
Continuous Variables

Eliciting subjective probability distributions on continuous variables

1978 ◽  
Vol 21 (3) ◽  
pp. 379-391 ◽  
Author(s):  
David A. Seaver ◽  
Detlof von Winterfeldt ◽  
Ward Edwards
Keyword(s):  
Subjective Probability ◽  
Probability Distributions ◽  
Continuous Variables

A Comparison of Subjective and Historical Crop Yield Probability Distributions

1992 ◽  
Vol 24 (2) ◽  
pp. 23-32 ◽  
Author(s):  
James W. Pease
Keyword(s):  
Crop Yield ◽  
Subjective Probability ◽  
Crop Yields ◽  
Probability Distributions ◽  
Geographical Location ◽  
Subjective Expectations ◽  
Grain Farms ◽  
Western Kentucky ◽  
Relative Variability

AbstractForecast distributions based on historical yields and subjective expectations for 1987 expected crop yields were compared for 90 Western Kentucky grain farms. Different subjective probability elicitation techniques were also compared. In many individual cases, results indicate large differences between subjective and empirical moments. Overall, farmer expectations for 1987 corn yields were below those predicted from their past yields, while soybean expectations were above the historical forecast. Geographical location plays a larger role than crop in comparisons of relative variability of yield. Neither elicitation technique nor manager characteristics have significant effects on the comparisons of the forecasts.

Seismic hazard sensitivity analysis: A multi-parameter approach

1991 ◽  
Vol 81 (3) ◽  
pp. 796-817
Author(s):  
Nitzan Rabinowitz ◽  
David M. Steinberg
Keyword(s):  
Sensitivity Analysis ◽  
Seismic Hazard ◽  
Subjective Probability ◽  
Probability Distributions ◽  
Input Parameter ◽  
The Other ◽  
Probabilistic Assessment ◽  
Input Parameters ◽  
Parameter Approach

Abstract We propose a novel multi-parameter approach for conducting seismic hazard sensitivity analysis. This approach allows one to assess the importance of each input parameter at a variety of settings of the other input parameters and thus provides a much richer picture than standard analyses, which assess each input parameter only at the default settings of the other parameters. We illustrate our method with a sensitivity analysis of seismic hazard for Jerusalem. In this example, we find several input parameters whose importance depends critically on the settings of other input parameters. This phenomenon, which cannot be detected by a standard sensitivity analysis, is easily diagnosed by our method. The multi-parameter approach can also be used in the context of a probabilistic assessment of seismic hazard that incorporates subjective probability distributions for the input parameters.

Continuous Random Numbers

2019 ◽  
pp. 54-69
Author(s):  
Robert H. Swendsen
Keyword(s):  
Probability Distributions ◽  
Random Variables ◽  
Delta Function ◽  
Ideal Gas ◽  
Dirac Delta Function ◽  
Bayesian Probability ◽  
Random Numbers ◽  
Continuous Variables ◽  
Dirac Delta ◽  
Discrete Random Variables

The theory of probability developed in Chapter 3 for discrete random variables is extended to probability distributions, in order to treat the continuous momentum variables. The Dirac delta function is introduced as a convenient tool to transform continuous random variables, in analogy with the use of the Kronecker delta for discrete random variables. The properties of the Dirac delta function that are needed in statistical mechanics are presented and explained. The addition of two continuous random numbers is given as a simple example. An application of Bayesian probability is given to illustrate its significance. However, the components of the momenta of the particles in an ideal gas are continuous variables.

scholarly journals SU(2) Symmetry of Qubit States and Heisenberg–Weyl Symmetry of Systems with Continuous Variables in the Probability Representation of Quantum Mechanics

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1099 ◽  
Author(s):  
Peter Adam ◽  
Vladimir A. Andreev ◽  
Margarita A. Man’ko ◽  
Vladimir I. Man’ko ◽  
Matyas Mechler
Keyword(s):  
Probability Distributions ◽  
Star Product ◽  
Kinetic Equations ◽  
Random Variables ◽  
Continuous Variables ◽  
Probability Representation ◽  
Density Operators ◽  
Symmetry Properties ◽  
Weyl Symmetry ◽  
Qubit States

In view of the probabilistic quantizer–dequantizer operators introduced, the qubit states (spin-1/2 particle states, two-level atom states) realizing the irreducible representation of the S U ( 2 ) symmetry group are identified with probability distributions (including the conditional ones) of classical-like dichotomic random variables. The dichotomic random variables are spin-1/2 particle projections m = ± 1 / 2 onto three perpendicular directions in the space. The invertible maps of qubit density operators onto fair probability distributions are constructed. In the suggested probability representation of quantum states, the Schrödinger and von Neumann equations for the state vectors and density operators are presented in explicit forms of the linear classical-like kinetic equations for the probability distributions of random variables. The star-product and quantizer–dequantizer formalisms are used to study the qubit properties; such formalisms are discussed for photon tomographic probability distribution and its correspondence to the Heisenberg–Weyl symmetry properties.

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