Stable Beliefs and Conditional Probability Spaces
... define notions such as Common or Mutual r-stable belief in rationality. A straightforward introduction of an operator in order to express r-stable beliefs syntactically would not be a good idea. This is because such an operator would not satisfy the K-axiom. Therefore, we will introduce two other mo ...
... define notions such as Common or Mutual r-stable belief in rationality. A straightforward introduction of an operator in order to express r-stable beliefs syntactically would not be a good idea. This is because such an operator would not satisfy the K-axiom. Therefore, we will introduce two other mo ...
Stability Analysis of Mean-CVaR Investment Model with Transaction
... If we assume, that all optimal values are finite, the concavity of the objective function in the underlying distribution ensures concavity of the extreme value function. Hence, we can construct the contamination bounds for the extreme value function of the contaminated problem as follows (1 − t)ϕ(0) ...
... If we assume, that all optimal values are finite, the concavity of the objective function in the underlying distribution ensures concavity of the extreme value function. Hence, we can construct the contamination bounds for the extreme value function of the contaminated problem as follows (1 − t)ϕ(0) ...
What is Probability? Patrick Maher August 27, 2010
... It has often been asserted that “probability” means some person’s degrees of belief. Here are a few examples: By degree of probability we really mean, or ought to mean, degree of belief. (de Morgan 1847, 172) Probability measures the confidence that a particular individual has in the truth of a part ...
... It has often been asserted that “probability” means some person’s degrees of belief. Here are a few examples: By degree of probability we really mean, or ought to mean, degree of belief. (de Morgan 1847, 172) Probability measures the confidence that a particular individual has in the truth of a part ...
The origins and legacy of Kolmogorov`s Grundbegriffe
... also in his philosophy of probability—how he proposed to relate the mathematical formalism to the real world. In a 1939 letter to Fréchet, which we reproduce in §A.2, Kolmogorov wrote, “You are also right in attributing to me the opinion that the formal axiomatization should be accompanied by an an ...
... also in his philosophy of probability—how he proposed to relate the mathematical formalism to the real world. In a 1939 letter to Fréchet, which we reproduce in §A.2, Kolmogorov wrote, “You are also right in attributing to me the opinion that the formal axiomatization should be accompanied by an an ...
Symmetry and Probability - Academic Commons
... Still, while, in certain circumstances, an agent's ...
... Still, while, in certain circumstances, an agent's ...
Probabilistic Horn abduction and Bayesian networks
... Determining what is in a system from observations (diagnosis and recognition) is an important part of AI. There have been many logic-based proposals as to what is a diagnosis 17, 57, 13, 45, 12]. One problem with all of these proposals is that for any diagnostic problem of a reasonable size there a ...
... Determining what is in a system from observations (diagnosis and recognition) is an important part of AI. There have been many logic-based proposals as to what is a diagnosis 17, 57, 13, 45, 12]. One problem with all of these proposals is that for any diagnostic problem of a reasonable size there a ...
An evaluation of the Survey of Professional Forecasters probability
... assumed to be independently distributed, so that the joint is the product of the marginals. In section 4.3 we will consider events such as that just described which require the joint density of the two variables, and describe how event probabilities may be recalibrated to remove distortions induced ...
... assumed to be independently distributed, so that the joint is the product of the marginals. In section 4.3 we will consider events such as that just described which require the joint density of the two variables, and describe how event probabilities may be recalibrated to remove distortions induced ...
Detection of Unfaithfulness and Robust Causal Inference
... The Causal Markov Condition is simply that the joint population distribution of V is Markov to the causal DAG over V. But it is only plausible to assume the condition when V is causally sufficient in the following sense: every common direct cause (relative to V) of any pair of variables in V is also ...
... The Causal Markov Condition is simply that the joint population distribution of V is Markov to the causal DAG over V. But it is only plausible to assume the condition when V is causally sufficient in the following sense: every common direct cause (relative to V) of any pair of variables in V is also ...
1-Pass Relative-Error Lp-Sampling with Applications
... which the survivors i in St are heavy hitters with respect to the p-norm, that is, |ai |p ≥ γ 0 ||a(j)||pp , where a(j) denotes the vector a restricted to the survivors in Sj , and γ 0 = poly(ε log−1 n). The heavy hitters in each substream can be found with poly(ε−1 log n) space using known heavy hi ...
... which the survivors i in St are heavy hitters with respect to the p-norm, that is, |ai |p ≥ γ 0 ||a(j)||pp , where a(j) denotes the vector a restricted to the survivors in Sj , and γ 0 = poly(ε log−1 n). The heavy hitters in each substream can be found with poly(ε−1 log n) space using known heavy hi ...
Chap 4 from Ross
... You should carefully check the matrix P, and make sure you understand how it was obtained. ...
... You should carefully check the matrix P, and make sure you understand how it was obtained. ...
Impact of the Three Gorges Dam, the South–North Water Transfer
... + α4 log Qt−7 + α5 (Qt−7 − Qt−8 ) + rt , in which the residuals, rt , are assumed to follow an inverse Gaussian distribution with autocorrelated variance structure, and α0 , . . ., α5 are parameters to be estimated. There are 312 usable observations, since the first day of each sequence is lost thro ...
... + α4 log Qt−7 + α5 (Qt−7 − Qt−8 ) + rt , in which the residuals, rt , are assumed to follow an inverse Gaussian distribution with autocorrelated variance structure, and α0 , . . ., α5 are parameters to be estimated. There are 312 usable observations, since the first day of each sequence is lost thro ...
Case comment—United States v. Copeland, 369
... to express their judgement of the amount of certainty that is required for conviction of crime under the reasonable doubt standard.15 To the extent that the actual language of Fatico and Vargas is a true barometer of Weinstein’s motivations for conducting those surveys, Weinstein was investigating h ...
... to express their judgement of the amount of certainty that is required for conviction of crime under the reasonable doubt standard.15 To the extent that the actual language of Fatico and Vargas is a true barometer of Weinstein’s motivations for conducting those surveys, Weinstein was investigating h ...
Probability box
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A probability box (or p-box) is a characterization of an uncertain number consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modeling where numerical calculations must be performed. Probability bounds analysis is used to make arithmetic and logical calculations with p-boxes.An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x. The bounds are coincident for values of x below 0 and above 24. The bounds may have almost any shapes, including step functions, so long as they are monotonically increasing and do not cross each other. A p-box is used to express simultaneously incertitude (epistemic uncertainty), which is represented by the breadth between the left and right edges of the p-box, and variability (aleatory uncertainty), which is represented by the overall slant of the p-box.