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Journal articles on the topic 'Imprecise Probability'

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1

de Cooman, Gert, and Filip Hermans. "Imprecise probability trees: Bridging two theories of imprecise probability." Artificial Intelligence 172, no. 11 (2008): 1400–1427. http://dx.doi.org/10.1016/j.artint.2008.03.001.

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2

Coolen, Frank, Thomas Fetz, Serafín Moral, and Michael Oberguggenberger. "Editorial – Imprecise probability." International Journal of Approximate Reasoning 53, no. 8 (2012): 1107–9. http://dx.doi.org/10.1016/j.ijar.2012.06.016.

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3

Peressini, Anthony F. "Imprecise Probability and Chance." Erkenntnis 81, no. 3 (2015): 561–86. http://dx.doi.org/10.1007/s10670-015-9755-9.

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4

Zaffalon, Marco. "Credibility via imprecise probability." International Journal of Approximate Reasoning 39, no. 2-3 (2005): 115–21. http://dx.doi.org/10.1016/j.ijar.2004.11.001.

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5

Kozine, Igor O., and Lev V. Utkin. "Constructing imprecise probability distributions." International Journal of General Systems 34, no. 4 (2005): 401–8. http://dx.doi.org/10.1080/03081070500201701.

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6

Ding, Yifeng, Wesley H. Holliday, and Thomas F. Icard. "Logics of imprecise comparative probability." International Journal of Approximate Reasoning 132 (May 2021): 154–80. http://dx.doi.org/10.1016/j.ijar.2021.02.004.

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7

Ferson, Scott, and William L. Oberkampf. "Validation of imprecise probability models." International Journal of Reliability and Safety 3, no. 1/2/3 (2009): 3. http://dx.doi.org/10.1504/ijrs.2009.026832.

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8

Augustin, Thomas, Serena Doria, and Mássimo Marinacci. "Imprecise probability: Theories and applications." International Journal of Approximate Reasoning 84 (May 2017): 39–40. http://dx.doi.org/10.1016/j.ijar.2017.03.001.

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9

Regoli, G. "Inference under imprecise probability assessments." Soft Computing - A Fusion of Foundations, Methodologies and Applications 3, no. 3 (1999): 181–86. http://dx.doi.org/10.1007/s005000050067.

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10

Galvan, Bruno. "Quantum Mechanics and Imprecise Probability." Journal of Statistical Physics 131, no. 6 (2008): 1155–67. http://dx.doi.org/10.1007/s10955-008-9530-2.

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11

Viertl, R., and D. Hareter. "Fuzzy information and imprecise probability." ZAMM 84, no. 10-11 (2004): 731–39. http://dx.doi.org/10.1002/zamm.200410152.

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12

Rinard, Susanna. "Imprecise Probability and Higher Order Vagueness." Res Philosophica 94, no. 2 (2017): 1–17. http://dx.doi.org/10.11612/resphil.1538.

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13

Allahverdyan, Armen E. "Imprecise probability for non-commuting observables." New Journal of Physics 17, no. 8 (2015): 085005. http://dx.doi.org/10.1088/1367-2630/17/8/085005.

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14

Stojaković, Mila. "Imprecise set and fuzzy valued probability." Journal of Computational and Applied Mathematics 235, no. 16 (2011): 4524–31. http://dx.doi.org/10.1016/j.cam.2010.01.016.

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15

Augustin, Thomas, Enrique Miranda, and Jiřina Vejnarová. "Imprecise probability models and their applications." International Journal of Approximate Reasoning 50, no. 4 (2009): 581–82. http://dx.doi.org/10.1016/j.ijar.2009.02.009.

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16

George Benson, P., and Kathleen M. Whitcomb. "The effectiveness of imprecise probability forecasts." Journal of Forecasting 12, no. 2 (1993): 139–59. http://dx.doi.org/10.1002/for.3980120207.

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17

Chung, Won Sang, and Abdullah Algin. "Imprecise probability through f-probability and its statistical physical implications." Chaos, Solitons & Fractals 139 (October 2020): 110020. http://dx.doi.org/10.1016/j.chaos.2020.110020.

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18

Walley, Peter. "Towards a unified theory of imprecise probability." International Journal of Approximate Reasoning 24, no. 2-3 (2000): 125–48. http://dx.doi.org/10.1016/s0888-613x(00)00031-1.

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19

Cozman, Fabio, Sébastien Destercke, and Teddy Seidenfeld. "Imprecise Probability: Theories and Applications (ISIPTA'13)." International Journal of Approximate Reasoning 56 (January 2015): 157–58. http://dx.doi.org/10.1016/j.ijar.2014.11.001.

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20

Hable, Robert. "Minimum distance estimation in imprecise probability models." Journal of Statistical Planning and Inference 140, no. 2 (2010): 461–79. http://dx.doi.org/10.1016/j.jspi.2009.07.025.

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21

Zaffalon, Marco, and Gert de Cooman. "Editorial: Imprecise probability perspectives on artificial intelligence." Annals of Mathematics and Artificial Intelligence 45, no. 1-2 (2005): 1–4. http://dx.doi.org/10.1007/s10472-005-9009-7.

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22

Möller, B. "Fuzzy randomness - a contribution to imprecise probability." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 84, no. 10-11 (2004): 754–64. http://dx.doi.org/10.1002/zamm.200410153.

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23

Rinard, Susanna. "The Principle of Indifference and Imprecise Probability." Thought: A Journal of Philosophy 3, no. 2 (2014): 110–14. http://dx.doi.org/10.1002/tht3.118.

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24

Pérez-Castro, Rubisel, and Francisco L. Silva-González. "Environmental contours based on imprecise probability distributions." Ocean Engineering 281 (August 2023): 114742. http://dx.doi.org/10.1016/j.oceaneng.2023.114742.

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25

Reichert, Peter. "On the necessity of using imprecise probabilities for modelling environmental systems." Water Science and Technology 36, no. 5 (1997): 149–56. http://dx.doi.org/10.2166/wst.1997.0186.

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One of the most important problems in the application of methods of parametric statistics to environmental systems is the impossibility of verifying the assumptions on probability distributions (e.g. the assumption of normally distributed measurements is usual but hardly exactly true). If Bayesian techniques are applied, the knowledge of probability distributions is even worse, because also vague prior knowledge (typical in modelling environmental systems) must be formulated in the form of (precise) prior probability distributions of model parameters or model structures. These two examples dem
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26

Modares, Mehdi, and Joshua Bergerson. "Buckling Analysis of Uncertain Structures Using Imprecise Probability." SAE International Journal of Passenger Cars - Mechanical Systems 8, no. 2 (2015): 421–25. http://dx.doi.org/10.4271/2015-01-0485.

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27

Modares, Mehdi, and Joshua Bergerson. "Dynamic analysis of uncertain structures using imprecise probability." International Journal of Reliability and Safety 9, no. 2/3 (2015): 203. http://dx.doi.org/10.1504/ijrs.2015.072720.

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28

Modares, Mehdi, and Joshua Bergerson. "Frequency analysis of uncertain structures using imprecise probability." International Journal of Reliability and Safety 9, no. 4 (2015): 235. http://dx.doi.org/10.1504/ijrs.2015.073126.

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29

Hall, Jim W. "Uncertainty-based sensitivity indices for imprecise probability distributions." Reliability Engineering & System Safety 91, no. 10-11 (2006): 1443–51. http://dx.doi.org/10.1016/j.ress.2005.11.042.

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30

Augustin, Thomas, Frank Coolen, Serafín Moral, and Matthias Troffaes. "Imprecise probability in statistical inference and decision making." International Journal of Approximate Reasoning 51, no. 9 (2010): 1011–13. http://dx.doi.org/10.1016/j.ijar.2010.08.001.

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31

Cozman, Fabio Gagliardi. "Learning imprecise probability models: Conceptual and practical challenges." International Journal of Approximate Reasoning 55, no. 7 (2014): 1594–96. http://dx.doi.org/10.1016/j.ijar.2014.04.016.

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32

Pelessoni, Renato, and Paolo Vicig. "The Goodman–Nguyen relation within imprecise probability theory." International Journal of Approximate Reasoning 55, no. 8 (2014): 1694–707. http://dx.doi.org/10.1016/j.ijar.2014.06.002.

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33

Oberguggenberger, M., G. I. Schuëller, and K. Marti. "Fuzzy sets, imprecise probability, and stochastics in engineering." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 84, no. 10-11 (2004): n/a. http://dx.doi.org/10.1002/zamm.200490025.

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34

Suo, Bin, Yong-sheng Cheng, Chao Zeng, and Jun Li. "Calculation of Failure Probability of Series and Parallel Systems for Imprecise Probability." International Journal of Engineering and Manufacturing 2, no. 2 (2012): 79–85. http://dx.doi.org/10.5815/ijem.2012.02.12.

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35

Liell-Cock, Jack, and Sam Staton. "Compositional Imprecise Probability: A Solution from Graded Monads and Markov Categories." Proceedings of the ACM on Programming Languages 9, POPL (2025): 1596–626. https://doi.org/10.1145/3704890.

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Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our desiderata are that we would like our model to support all kinds of composition, categorical and monoidal; in other words, guided by dataflow diagrams. Another equivalent perspective is that we would like a model of synthetic probability in the sense of Markov categories. Imprecise probability can be modelled in various ways, with the leading monad-based approach usi
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36

Derr, Rabanus, and Robert C. Williamson. "Systems of Precision: Coherent Probabilities on Pre-Dynkin Systems and Coherent Previsions on Linear Subspaces." Entropy 25, no. 9 (2023): 1283. http://dx.doi.org/10.3390/e25091283.

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In the literature on imprecise probability, little attention is paid to the fact that imprecise probabilities are precise on a set of events. We call these sets systems of precision. We show that, under mild assumptions, the system of precision of a lower and upper probability form a so-called (pre-)Dynkin system. Interestingly, there are several settings, ranging from machine learning on partial data over frequential probability theory to quantum probability theory and decision making under uncertainty, in which, a priori, the probabilities are only desired to be precise on a specific underly
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37

Suo, Bin, Chao Zeng, Yong Sheng Cheng, and Jun Li. "Reliability Model of Series and Parallel Systems under Imperfect Information." Applied Mechanics and Materials 204-208 (October 2012): 4932–35. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.4932.

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In the situation that unit failure probability is imprecise when calculation the failure probability of system, classical probability method is not applicable, and the analysis result of interval method is coarse. To calculate the reliability of series and parallel systems in above situation, D-S evidence theory was used to represent the unit failure probability. Multi-sources information was fused, and belief and plausibility function were used to calculate the reliability of series and parallel systems by evidential reasoning. By this mean, lower and upper bounds of probability distribution
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38

Wasserman, Larry, and Peter Walley. "Statistical Reasoning With Imprecise Probabilities." Journal of the American Statistical Association 88, no. 422 (1993): 700. http://dx.doi.org/10.2307/2290362.

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39

Hand, David J., and P. Walley. "Statistical Reasoning with Imprecise Probabilities." Applied Statistics 42, no. 1 (1993): 237. http://dx.doi.org/10.2307/2347427.

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40

Karge, Jonas. "A Modified Supervaluationist Framework for Decision-Making." Logos & Episteme 12, no. 2 (2021): 175–91. http://dx.doi.org/10.5840/logos-episteme202112212.

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How strongly an agent beliefs in a proposition can be represented by her degree of belief in that proposition. According to the orthodox Bayesian picture, an agent's degree of belief is best represented by a single probability function. On an alternative account, an agent’s beliefs are modeled based on a set of probability functions, called imprecise probabilities. Recently, however, imprecise probabilities have come under attack. Adam Elga claims that there is no adequate account of the way they can be manifested in decision-making. In response to Elga, more elaborate accounts of the imprecis
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41

Qi, Xianjun, and Qiao Cheng. "Imprecise reliability assessment of generating systems involving interval probability." IET Generation, Transmission & Distribution 11, no. 17 (2017): 4332–37. http://dx.doi.org/10.1049/iet-gtd.2017.0874.

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42

Cano, Andrés, and Serafín Moral. "Using probability trees to compute marginals with imprecise probabilities." International Journal of Approximate Reasoning 29, no. 1 (2002): 1–46. http://dx.doi.org/10.1016/s0888-613x(01)00046-9.

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43

Ognjanovic, Zoran, Zoran Markovic, and Miodrag Raskovic. "Completeness theorem for a logic with imprecise and conditional probabilities." Publications de l'Institut Math?matique (Belgrade) 78, no. 92 (2005): 35–49. http://dx.doi.org/10.2298/pim0578035o.

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We present a prepositional probability logic which allows making formulas that speak about imprecise and conditional probabilities. A class of Kripke-like probabilistic models is defined to give semantics to probabilistic formulas. Every possible world of such a model is equipped with a probability space. The corresponding probabilities may have nonstandard values. The proposition "the probability is close to r" means that there is an infinitesimal ?, such that the probability is equal to r ? ? (or r + ?). We provide an infinitary axiomatization and prove the corresponding extended completenes
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44

Kinney, David. "Imprecise Bayesian Networks as Causal Models." Information 9, no. 9 (2018): 211. http://dx.doi.org/10.3390/info9090211.

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This article considers the extent to which Bayesian networks with imprecise probabilities, which are used in statistics and computer science for predictive purposes, can be used to represent causal structure. It is argued that the adequacy conditions for causal representation in the precise context—the Causal Markov Condition and Minimality—do not readily translate into the imprecise context. Crucial to this argument is the fact that the independence relation between random variables can be understood in several different ways when the joint probability distribution over those variables is imp
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45

Smithson, Michael, David V. Budescu, Stephen B. Broomell, and Han-Hui Por. "Never say “not”: Impact of negative wording in probability phrases on imprecise probability judgments." International Journal of Approximate Reasoning 53, no. 8 (2012): 1262–70. http://dx.doi.org/10.1016/j.ijar.2012.06.019.

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46

Feng, Naidan, and Yongquan Liang. "A new rough set based bayesian classifier prior assumption." Journal of Intelligent & Fuzzy Systems 39, no. 3 (2020): 2647–55. http://dx.doi.org/10.3233/jifs-190517.

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Aiming at the imprecise and uncertain data and knowledge, this paper proposes a novel prior assumption by the rough set theory. The performance of the classical Bayesian classifier is improved through this study. We applied the operations of approximations to represent the imprecise knowledge accurately, and the concept of approximation quality is first applied in this method. Thus, this paper provides a novel rough set theory based prior probability in classical Bayesian classifier and the corresponding rough set prior Bayesian classifier. And we chose 18 public datasets to evaluate the perfo
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47

Utkin, Lev V. "Imprecise Second-Order Hierarchical Uncertainty Model." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 11, no. 03 (2003): 301–17. http://dx.doi.org/10.1142/s0218488503002090.

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A hierarchical uncertainty model for combining different evidence is studied in the paper. The model is general enough for many applications. The presented approach for dealing with the model allows us to combine the available heterogeneous information in the following ways: computing new probability bounds for some predefined interval of previsions, computing an "average" interval of first-order previsions, and updating the second-order probabilities after observing new events. Numerical examples illustrate this approach.
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48

Utkin, Lev V., and Yulia A. Zhuk. "Robust Classifiers Using Imprecise Probability Models and Importance of Classes." International Journal on Artificial Intelligence Tools 24, no. 01 (2015): 1550008. http://dx.doi.org/10.1142/s0218213015500086.

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A framework for constructing robust classification models is proposed in the paper. An assumption about importance of one of the classes in comparison with other classes is incorporated into the models. It often takes place in the real application, for example, in reliability, in medical diagnostic, etc. A main idea underlying the models is to consider a set of probability distributions on training examples produced by the imprecise probability models such as linear-vacuous mixture and constant odd-ratio contaminated models. Extreme points of the sets of probability distributions are a main to
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49

Kriegler, E., J. W. Hall, H. Held, R. Dawson, and H. J. Schellnhuber. "Imprecise probability assessment of tipping points in the climate system." Proceedings of the National Academy of Sciences 106, no. 13 (2009): 5041–46. http://dx.doi.org/10.1073/pnas.0809117106.

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50

Bayrak, Oben K., and John D. Hey. "Expected utility theory with imprecise probability perception: explaining preference reversals." Applied Economics Letters 24, no. 13 (2016): 906–10. http://dx.doi.org/10.1080/13504851.2016.1240332.

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