A Bayesian Method for the Induction of Probabilistic Networks from
... system, and that x2 and x3, represent two findings. Given the database, what are the qualitative dependency relationships among the variables? For example, do x1 and x3 influence each other directly, or do they do so only through x2? What is the probability that x3 will be present if x1 is present? ...
... system, and that x2 and x3, represent two findings. Given the database, what are the qualitative dependency relationships among the variables? For example, do x1 and x3 influence each other directly, or do they do so only through x2? What is the probability that x3 will be present if x1 is present? ...
Significance testing as perverse probabilistic reasoning
... it may be more informative to consider a range of possible value for the strength of the effect, and to compute a probability distribution over this range of possible effect sizes, from which we could also ‘read off’ the credibility of the hypothesis that the effect size is equal to or close to zero ...
... it may be more informative to consider a range of possible value for the strength of the effect, and to compute a probability distribution over this range of possible effect sizes, from which we could also ‘read off’ the credibility of the hypothesis that the effect size is equal to or close to zero ...
regular conditional probability, disintegration of probability
... in Faden (1985) for the case of separable probability space. In the context of separable probability space, existence of RCP is guaranteed via the property of either perfectness or compactness, see e.g. Hoffmann-Jörgensen (1971), Sazonov (1965) and Faden (1985). More recently we proved a necessary a ...
... in Faden (1985) for the case of separable probability space. In the context of separable probability space, existence of RCP is guaranteed via the property of either perfectness or compactness, see e.g. Hoffmann-Jörgensen (1971), Sazonov (1965) and Faden (1985). More recently we proved a necessary a ...
March 26, 2013 Palmetto Lecture on Comparative Inference
... Bayes estimates, relative to their individually elicited beta priors, of the proportion of “long words” among the first words appearing on the 758 pages of a copy of Maugham’s novel Of Human Bondage. We mentioned that a strong majority of the Bayes estimators tend to outperform pb. We now examine th ...
... Bayes estimates, relative to their individually elicited beta priors, of the proportion of “long words” among the first words appearing on the 758 pages of a copy of Maugham’s novel Of Human Bondage. We mentioned that a strong majority of the Bayes estimators tend to outperform pb. We now examine th ...
Decision making in an uncertain environment - Marco Campi
... where the parameter ² ∈ (0, 1) represents the admissible probabilistic risk of violating the constraint f (x, δ) ≤ 0. It is clear that allowing for a probability ² of violation results in an optimal solution that outperforms the optimal robust solution for the uncertainty instances that are indeed f ...
... where the parameter ² ∈ (0, 1) represents the admissible probabilistic risk of violating the constraint f (x, δ) ≤ 0. It is clear that allowing for a probability ² of violation results in an optimal solution that outperforms the optimal robust solution for the uncertainty instances that are indeed f ...
Population recovery and partial identification
... k log k ) and performs the same task3 even without knowing the noise parameter ν. With an appropriate definition of noise, one can generalize this theorem to every alphabet Σ. Moreover, it can also be generalized to the case that a different (but known) noise probability is applied in every coordina ...
... k log k ) and performs the same task3 even without knowing the noise parameter ν. With an appropriate definition of noise, one can generalize this theorem to every alphabet Σ. Moreover, it can also be generalized to the case that a different (but known) noise probability is applied in every coordina ...
Decision Support for Offering Load-Side Regulation Service Reserves in Competitive Power Markets
... [8]). This paper adopts optimal real time demand management by Smart Building Operators (SBO) proposed in [5] to reflect upon a related but longer time scale decision, namely the optimal bid of RS capacity by SBOs in the Hour Ahead Markets where Energy and RS capacity offers are co-optimized. More s ...
... [8]). This paper adopts optimal real time demand management by Smart Building Operators (SBO) proposed in [5] to reflect upon a related but longer time scale decision, namely the optimal bid of RS capacity by SBOs in the Hour Ahead Markets where Energy and RS capacity offers are co-optimized. More s ...
Combining Labeled and Unlabeled Data with Co
... examples with non-zero probability under D are consistent with some target function f1 2 C1, and are also consistent with some target function f2 2 C2. In other words, if f denotes the combined target concept over the entire example, then for any example x = (x1 x2) observed with label `, we have f( ...
... examples with non-zero probability under D are consistent with some target function f1 2 C1, and are also consistent with some target function f2 2 C2. In other words, if f denotes the combined target concept over the entire example, then for any example x = (x1 x2) observed with label `, we have f( ...
cern_stat_4
... Confidence intervals for a parameter q can be found by defining a test of the hypothesized value q (do this for all q): Specify values of the data that are ‘disfavoured’ by q (critical region) such that P(data in critical region) ≤ a for a prespecified a, e.g., 0.05 or 0.1. If data observed in the c ...
... Confidence intervals for a parameter q can be found by defining a test of the hypothesized value q (do this for all q): Specify values of the data that are ‘disfavoured’ by q (critical region) such that P(data in critical region) ≤ a for a prespecified a, e.g., 0.05 or 0.1. If data observed in the c ...
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.