Conditionals and Conditional Probabilities: Three Triviality Theorems

1990 ◽  
pp. 287-306 ◽  
Author(s):  
Hugues Leblanc ◽  
Peter Roeper
Keyword(s):  
Conditional Probabilities

The dependence of the majority voting decision-making probabilities on a multi-expert binary system experts number

2020 ◽  
pp. 7-14
Author(s):  
E. D. Avedyan ◽  
Le Thi Trang Linh
Keyword(s):  
Decision Making ◽  
Binary System ◽  
Conditional Probability ◽  
Majority Voting ◽  
Correct Solution ◽  
Conditional Probabilities ◽  
Analytical Results ◽  
Independent Expert ◽  
Mutually Independent

The article presents the analytical results of the decision-making by the majority voting algorithm (MVA). Particular attention is paid to the case of an even number of experts. The conditional probabilities of the MVA for two hypotheses are given for an even number of experts and their properties are investigated depending on the conditional probability of decision-making by independent experts of equal qualifications and on their number. An approach to calculating the probabilities of the correct solution of the MVA with unequal values of the conditional probabilities of accepting hypotheses of each statistically mutually independent expert is proposed. The findings are illustrated by numerical and graphical calculations.

Minimal distributions in a stochastic partial ordering and bounds for Gaussian processes

1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Partial Ordering ◽  
Boundary Crossing ◽  
Conditional Probabilities ◽  
Life Distribution ◽  
Life Distributions ◽  
Bounded Below ◽  
Crossing Probabilities

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.

scholarly journals Conditional probabilities via line arrangements and point configurations

2021 ◽  
pp. 1-33
Author(s):  
Oliver Clarke ◽  
Fatemeh Mohammadi ◽  
Harshit J. Motwani
Keyword(s):  
Conditional Probabilities ◽  
Line Arrangements ◽  
Point Configurations

scholarly journals H. L. Wagner's Unbiased Hit Rate and the Assessment of Categorical Forecasting Accuracy

2013 ◽  
Vol 28 (3) ◽  
pp. 802-814 ◽  
Author(s):  
Timothy W. Armistead
Keyword(s):  
Weather Forecasting ◽  
Skill Score ◽  
Conditional Probabilities ◽  
Paper Briefly ◽  
Forecasting Accuracy ◽  
Hit Rate ◽  
History Of ◽  
The Difference ◽  
Measure Of Association ◽  
Accuracy Rates

Abstract The paper briefly reviews measures that have been proposed since the 1880s to assess accuracy and skill in categorical weather forecasting. The majority of the measures consist of a single expression, for example, a proportion, the difference between two proportions, a ratio, or a coefficient. Two exemplar single-expression measures for 2 × 2 categorical arrays that chronologically bracket the 130-yr history of this effort—Doolittle's inference ratio i and Stephenson's odds ratio skill score (ORSS)—are reviewed in detail. Doolittle's i is appropriately calculated using conditional probabilities, and the ORSS is a valid measure of association, but both measures are limited in ways that variously mirror all single-expression measures for categorical forecasting. The limitations that variously affect such measures include their inability to assess the separate accuracy rates of different forecast–event categories in a matrix, their sensitivity to the interdependence of forecasts in a 2 × 2 matrix, and the inapplicability of many of them to the general k × k (k ≥ 2) problem. The paper demonstrates that Wagner's unbiased hit rate, developed for use in categorical judgment studies with any k × k (k ≥ 2) array, avoids these limitations while extending the dual-measure Bayesian approach proposed by Murphy and Winkler in 1987.

PREDICTION OF WEATHER-RELATED FAILURES OF OVERHEAD DISTRIBUTION FEEDERS

2005 ◽  
Vol 20 (1) ◽  
pp. 117-125 ◽  
Author(s):  
Yujia Zhou ◽  
Anil Pahwa ◽  
Sanjoy Das
Keyword(s):  
Linear Regression ◽  
Bayesian Network ◽  
Regression Function ◽  
Conditional Probabilities ◽  
Weather Factors ◽  
Distribution Feeder

This article presents two methods for predicting weather-related overhead distribution feeder failures. The first model is based on linear regression, which uses a regression function to determine the correlation between the weather factors and overhead feeder failures. The second method is based on a one-layer Bayesian network, which uses conditional probabilities to model the correlation. Both methods are discussed and followed by tests to assess their performance. The results obtained using these methods are discussed and compared.

scholarly journals Communicative efficiency and differential case marking: a reverse-engineering approach

2021 ◽  
Vol 7 (s3) ◽  
Author(s):  
Natalia Levshina
Keyword(s):  
Reverse Engineering ◽  
Conditional Probabilities ◽  
Case Marking ◽  
Poisson Models ◽  
Linguistic Patterns ◽  
Cue Reliability ◽  
Communicative Efficiency ◽  
Cue Availability ◽  
Probabilistic Measures ◽  
Better Than

Abstract The use of differential case marking of A and P has been explained in terms of efficiency (economy) and markedness. The present study tests predictions based on these accounts, using conditional probabilities of a particular feature given the syntactic role (cue availability), and conditional probabilities of a particular syntactic role given the feature in question (cue reliability). Cue availability serves as a measure of markedness, whereas cue reliability is central for the efficiency account. Similar to reverse engineering, we determine which of the probabilistic measures could have been responsible for the recurrent cross-linguistic patterns described in the literature. The probabilities are estimated from spontaneous informal dialogues in English and Russian (Indo-European), Lao (Tai-Kadai), N||ng (Tuu) and Ruuli (Bantu). The analyses, which involve a series of mixed-effects Poisson models, clearly demonstrate that cue reliability matches the observed cross-linguistic patterns better than cue availability. Thus, the results support the efficiency account of differential marking.

The dependence of sojourn times on service times in tandem queues

1984 ◽  
Vol 21 (3) ◽  
pp. 661-667 ◽  
Author(s):  
Xi-Ren Cao
Keyword(s):  
Sojourn Time ◽  
Past History ◽  
Interarrival Time ◽  
Conditional Probabilities ◽  
Tandem Queues ◽  
Sojourn Times ◽  
Distributed Service ◽  
Service Times

In this paper we study a series of servers with exponentially distributed service times. We find that the sojourn time of a customer at any server depends on the customer's past history only through the customer's interarrival time to that server. A method of calculating the conditional probabilities of sojourn times is developed.

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