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Journal articles on the topic 'Bayes's theorem'

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Published: 25 July 2024

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1

Utyuganova, V. V., V. S. Serdyuk, and A. I. Fomin. "Prediction and Assessment of the Occupational Risks in the Mining Industry Using the Bayess Theorem." Occupational Safety in Industry, no. 1 (January 2021): 79–87. http://dx.doi.org/10.24000/0409-2961-2021-1-79-87.

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The analysis of existing methods for assessing occupational risks is carried out, and the need for searchinga fundamentally new approach to the assessment and prediction of risks in the mining industry is substantiated. Based on the results of the analysis of modern methods and technologies, it is established that the development of the methodology for assessment and prediction of the occupational risks using Bayes's theorem has significant advantages: simplicity and accessibility for the occupational safety specialists, reproducibility considering many factors of working conditions, as well as the possibility of preventive measures prediction and development. The application of Bayes's theorem is promising in determining cause-and-effect relationships and predicting the occupational morbidity of the employees, which is also an advantage of this methodology for managing occupational risks in the mining industry. Bayes's approaches to modeling are characterized by high performance, intuitively clear in the form of a graph. The example is given concerning the application of Bayes's theorem to assess the risk of a fatal incident taking into account the statistics on the mining industry. Also, the simplest types of Bayes’s trust networks were developed reflecting the possibility of establishing cause-and-effect relationships (both for assessment and prediction), and are the basis for further modeling.

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2

Eells, E. "Review: Bayes's Theorem." Mind 113, no. 451 (July 1, 2004): 591–96. http://dx.doi.org/10.1093/mind/113.451.591.

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3

McGrew, T. "Two cheers for Bayes's theorem." Analysis 55, no. 2 (April 1, 1995): 123–25. http://dx.doi.org/10.1093/analys/55.2.123.

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4

CadwalladerOlsker, Todd D. "When 95% Accurate Isn't: Exploring Bayes's Theorem." Mathematics Teacher 104, no. 6 (February 2011): 426–31. http://dx.doi.org/10.5951/mt.104.6.0426.

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Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Shaughnessy (1992) has commented, “There is a good deal of cognitive strain involved in reading the problem and keeping everything straight; it is difficult for students to interpret exactly what they are being asked to do” (p. 471).

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5

CadwalladerOlsker, Todd D. "When 95% Accurate Isn't: Exploring Bayes's Theorem." Mathematics Teacher 104, no. 6 (February 2011): 426–31. http://dx.doi.org/10.5951/mt.104.6.0426.

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Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Shaughnessy (1992) has commented, “There is a good deal of cognitive strain involved in reading the problem and keeping everything straight; it is difficult for students to interpret exactly what they are being asked to do” (p. 471).

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6

Zellner, Arnold. "Optimal Information Processing and Bayes's Theorem." American Statistician 42, no. 4 (November 1988): 278. http://dx.doi.org/10.2307/2685143.

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7

Zellner, Arnold. "Optimal Information Processing and Bayes's Theorem." American Statistician 42, no. 4 (November 1988): 278–80. http://dx.doi.org/10.1080/00031305.1988.10475585.

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8

Jaynes, E. T. "[Optimal Information Processing and Bayes's Theorem]: Comment." American Statistician 42, no. 4 (November 1988): 280. http://dx.doi.org/10.2307/2685144.

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9

Hill, Bruce M. "[Optimal Information Processing and Bayes's Theorem]: Comment." American Statistician 42, no. 4 (November 1988): 281. http://dx.doi.org/10.2307/2685145.

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10

Zellner, Arnold. "[Optimal Information Processing and Bayes's Theorem]: Reply." American Statistician 42, no. 4 (November 1988): 283. http://dx.doi.org/10.2307/2685148.

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11

Walters, D. E. "Bayes's Theorem and the Analysis of Binomial Random Variables." Biometrical Journal 30, no. 7 (1988): 817–25. http://dx.doi.org/10.1002/bimj.4710300710.

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12

Grove, William M. "Bootstrapping diagnoses using Bayes's theorem: It's not worth the trouble." Journal of Consulting and Clinical Psychology 53, no. 2 (1985): 261–63. http://dx.doi.org/10.1037/0022-006x.53.2.261.

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13

Gilat, Sharon, Joachim Meyer, Ibo Erev, and Daniel Gopher. "Beyond Bayes's theorem: Effect of base-rate information in consensus games." Journal of Experimental Psychology: Applied 3, no. 2 (1997): 83–104. http://dx.doi.org/10.1037/1076-898x.3.2.83.

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14

Wood, James M. "Weighing Evidence in Sexual Abuse Evaluations: An Introduction to Bayes's Theorem." Child Maltreatment 1, no. 1 (February 1996): 25–36. http://dx.doi.org/10.1177/1077559596001001004.

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15

O'Gradaigh, D., and P. Merry. "A diagnostic algorithm for carpal tunnel syndrome based on Bayes's theorem." Rheumatology 39, no. 9 (September 1, 2000): 1040–41. http://dx.doi.org/10.1093/rheumatology/39.9.1040.

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16

Zellner, Arnold. "Generalizing the standard product rule of probability theory and Bayes's Theorem." Journal of Econometrics 138, no. 1 (May 2007): 14–23. http://dx.doi.org/10.1016/j.jeconom.2006.05.013.

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17

Miller, Steven I., and Marcel Fredericks. "Hearing Discordant Voices: Some Notes on Using Bayes's Theorem in Interpretive Inquiry." Qualitative Health Research 8, no. 3 (May 1998): 393–98. http://dx.doi.org/10.1177/104973239800800309.

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18

Trafimow, David. "Hypothesis testing and theory evaluation at the boundaries: Surprising insights from Bayes's theorem." Psychological Review 110, no. 3 (2003): 526–35. http://dx.doi.org/10.1037/0033-295x.110.3.526.

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19

Zellner, Arnold. "Erratum to “Generalizing the standard product rule of probability theory and Bayes's Theorem”." Journal of Econometrics 141, no. 2 (December 2007): 1419. http://dx.doi.org/10.1016/j.jeconom.2007.04.001.

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20

IRANZO, Valeriano. "Bayesianism and inference to the best explanation." THEORIA 23, no. 1 (2008): 89–106. http://dx.doi.org/10.1387/theoria.11.

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Bayesianism and Inference to the best explanation (IBE) are two different models of inference. Recently there has been some debate about the possibility of "bayesianizing" IBE. Firstly I explore several alternatives to include explanatory considerations in Bayes's Theorem. Then I distinguish two different interpretations of prior probabilities: "IBE-Bayesianism" (IBE-Bay) and "frequentist-Bayesianism" (Freq-Bay). After detailing the content of the latter, I propose a rule for assessing the priors. I also argue that Freq-Bay: (i) endorses a role for explanatory value in the assessment of scientific hypotheses; (ii) avoids a purely subjectivist reading of prior probabilities; and (iii) fits better than IBE-Bayesianism with two basic facts about science, i.e., the prominent role played by empirical testing and the existence of many scientific theories in the past that failed to fulfil their promises and were subsequently abandoned.

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21

Wahyunita, Laili. "Klasifikasi Penyebab Penyalahgunaan Narkoba Dari Berita Online Dengan Menggunakan Naive Bayes." Jurnal ELTIKOM 1, no. 1 (June 12, 2017): 23–30. http://dx.doi.org/10.31961/eltikom.v1i1.12.

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This research conducted the classification process by applying the method of classification of Naive Bayes. News article document is one form of text data that is not structured so that requires the process of cleaning data and pre-processing first. The Naive Bayes approach is an approach that refers to Bayes's Theorem, where it uses the principle of statistical opportunity to combine previous knowledge. The use of this technique is based on the need of the system to know the probability value of the data to be classified. Waterfall method was used for built this classificaiton system. Accuracy rate up to 60 % with the highest precision and recall is 80% and 90%.

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22

Bickel, David R. "Pseudo-Likelihood, Explanatory Power, and Bayes's Theorem [Comment on “A Likelihood Paradigm for Clinical Trials”]." Journal of Statistical Theory and Practice 7, no. 2 (January 2013): 178–82. http://dx.doi.org/10.1080/15598608.2013.771546.

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23

Bartha, Paul, and Christopher Hitchcock. "No One Knows the Date or the Hour: An Unorthodox Application of Rev. Bayes's Theorem." Philosophy of Science 66 (September 1999): S339—S353. http://dx.doi.org/10.1086/392736.

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24

Moens, H. J., and J. K. van der Korst. "Development and validation of a computer program using Bayes's theorem to support diagnosis of rheumatic disorders." Annals of the Rheumatic Diseases 51, no. 2 (February 1, 1992): 266–71. http://dx.doi.org/10.1136/ard.51.2.266.

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25

Van Laarhoven, P. J. M., C. G. E. Boender, E. H. L. Aarts, and A. H. G. Rinnooy Kan. "A Bayesian Approach to Simulated Annealing." Probability in the Engineering and Informational Sciences 3, no. 4 (October 1989): 453–75. http://dx.doi.org/10.1017/s0269964800001327.

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Simulated annealing is a probabilistic algorithm for approximately solving large combinatorial optimization problems. The algorithm can mathematically be described as the generation of a series of Markov chains, in which each Markov chain can be viewed as the outcome of a random experiment with unknown parameters (the probability of sampling a cost function value). Assuming a probability distribution on the values of the unknown parameters (the prior distribution) and given the sequence of configurations resulting from the generation of a Markov chain, we use Bayes's theorem to derive the posterior distribution on the values of the parameters. Numerical experiments are described which show that the posterior distribution can be used to predict accurately the behavior of the algorithm corresponding to the next Markov chain. This information is also used to derive optimal rules for choosing some of the parameters governing the convergence of the algorithm.

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26

Yuen, Jonathan. "Bayesian Approaches to Plant Disease Forecasting." Plant Health Progress 4, no. 1 (January 2003): 20. http://dx.doi.org/10.1094/php-2003-1113-06-rv.

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Prediction of disease occurrence is a well known historical theme, and has begun to receive new interest due to internet-based prediction systems. The evaluation of these systems in a quantitative manner is an important step if they are to be used in modern agricultural production. Bayes's theorem is one way in which the performance of such predictors can be studied. In this way, the conditional probability of pest occurrence after a positive or negative prediction can be compared with the unconditional probability of pest occurrence. Both the specificity and the sensitivity of the predictive system are needed, along with the unconditional probability of pest occurrence, in order to make a Bayesian analysis. If there is little information on the prior probability of disease, most predictors will be useful, but for extremely common or extremely rare diseases, a Bayesian analysis indicates that a system predicting disease occurrence or non-occurrence will have limited usefulness. Accepted for publication 29 January 2002. Published 13 November 2003.

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27

Donaldson, Theodore, and Richard Wollert. "A Mathematical Proof and Example That Bayes's Theorem Is Fundamental to Actuarial Estimates of Sexual Recidivism Risk." Sexual Abuse: A Journal of Research and Treatment 20, no. 2 (June 2008): 206–17. http://dx.doi.org/10.1177/1079063208317734.

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28

Anand, Paul. "Bayes's Theorem (Proceedings of the British Academy, vol. 113), edited by Richard Swinburne, Oxford University Press, 2002, 160 pages." Economics and Philosophy 21, no. 1 (April 2005): 139–42. http://dx.doi.org/10.1017/s026626710422051x.

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29

Osherson, Daniel N., Michael Stob, and Scott Weinstein. "Mechanical learners pay a price for Bayesianism." Journal of Symbolic Logic 53, no. 4 (December 1988): 1245–51. http://dx.doi.org/10.1017/s0022481200028073.

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The price is failure on a class of inductive inference problems that are easily solved, in contrast, by nonBayesian mechanical learners. By “mechanical” is meant “simulable by Turing machine”.One of the central tenets of Bayesianism, which is common to the heterogeneous collection of views which fall under this rubric, is that hypothesis change proceeds via conditionalization on accumulated evidence, the posterior probability of a given hypothesis on the evidence being computed using Bayes's theorem. We show that this strategy for hypothesis change precludes the solution of certain problems of inductive inference by mechanical means—problems which are solvable by mechanical means when the restriction to this Bayesian strategy is lifted. Our discussion proceeds as follows. After some technical preliminaries, the concept of (formal) learner is introduced along with a criterion of inferential success. Next we specify a class of inductive inference problems, and then define the notion of “Bayesian behavior” on those problems. Finally, we exhibit an inductive inference problem from the specified class such that (a) some nonmechanical Bayesian learner solves the problem, (b) some nonBayesian mechanical learner solves the problem, (c) some mechanical learner manifests Bayesian behavior on the problem, but (d) no mechanical Bayesian learner solves the problem.Insofar as possible terminology and notation are drawn from Osherson, Stob, and Weinstein [1986].

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30

Wollert, Richard. "Low base rates limit expert certainty when current actuarials are used to identify sexually violent predators: An application of Bayes's theorem." Psychology, Public Policy, and Law 12, no. 1 (February 2006): 56–85. http://dx.doi.org/10.1037/1076-8971.12.1.56.

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31

Peter, Justin R., Alan Seed, and Peter J. Steinle. "Application of a Bayesian Classifier of Anomalous Propagation to Single-Polarization Radar Reflectivity Data." Journal of Atmospheric and Oceanic Technology 30, no. 9 (September 1, 2013): 1985–2005. http://dx.doi.org/10.1175/jtech-d-12-00082.1.

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Abstract A naïve Bayes classifier (NBC) was developed to distinguish precipitation echoes from anomalous propagation (anaprop). The NBC is an application of Bayes's theorem, which makes its classification decision based on the class with the maximum a posteriori probability. Several feature fields were input to the Bayes classifier: texture of reflectivity (TDBZ), a measure of the reflectivity fluctuations (SPIN), and vertical profile of reflectivity (VPDBZ). Prior conditional probability distribution functions (PDFs) of the feature fields were constructed from training sets for several meteorological scenarios and for anaprop. A Box–Cox transform was applied to transform these PDFs to approximate Gaussian distributions, which enabled efficient numerical computation as they could be specified completely by their mean and standard deviation. Combinations of the feature fields were tested on the training datasets to evaluate the best combination for discriminating anaprop and precipitation, which was found to be TDBZ and VPDBZ. The NBC was applied to a case of convective rain embedded in anaprop and found to be effective at distinguishing the echoes. Furthermore, despite having been trained with data from a single radar, the NBC was successful at distinguishing precipitation and anaprop from two nearby radars with differing wavelength and beamwidth characteristics. The NBC was extended to implement a strength of classification index that provides a metric to quantify the confidence with which data have been classified as precipitation and, consequently, a method to censor data for assimilation or quantitative precipitation estimation.

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32

Harries, R. W. J. "A Rational Approach to Radiological Screening in Von Hippel-Lindau Disease." Journal of Medical Screening 1, no. 2 (April 1994): 88–95. http://dx.doi.org/10.1177/096914139400100205.

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Objectives— To optimise radiological screening in von Hippel-Lindau disease (VHL) while minimising cost and morbidity. Methods— A model of VHL was based on retrospective studies, and Bayes's theorem used to calculate the probability of the gene's presence and the likelihood of further lesions in affected families. A six year follow up was conducted to test the validity of the model. Results— Follow up confirmed the accuracy and validity of the model. Posterior fossa haemangioblastomas occur in 79·2% of VHL cases, supratentorial, retinal and spinal haemangioblastomas in 6·9%, 42·8%, and 22·0%, phaeochromocytomas in 5·2%, and renal carcinomas in 14·5%. Population incidences are 1:15 700 live births (posterior fossa), 1:780 000 (supratentorial), and 1:116 000 (spinal). The birth rate of subjects with VHL is 1:43 000; new mutations occur in 1:178 000 live births. Penetrance is 90%; 40% present with multiple lesions and 6·4% die within two years after diagnosis. Conclusions— For most patients presenting with a VHL-type lesion, with sufficient clinical and pedigree data, the presence or absence of the VHL gene, and the probability of further lesions occurring, can be assessed with a high degree of accuracy using the method described in this paper. Those cases in the non-VHL group do not require long term radiological follow up, nor do their relatives require radiological screening. Subjects in the VHL group should be screened for renal carcinoma indefinitely from the age of 20 years, and all clinically unaffected relatives should be screened genetically for the VHL gene. (Those found negative for the gene do not require further screening, but those found positive should be screened.)

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33

Rhoda, Alan R. "Bayes’s Theorem." International Philosophical Quarterly 45, no. 2 (2005): 269–70. http://dx.doi.org/10.5840/ipq200545215.

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34

Lewis, Nicholas. "An Objective Bayesian Improved Approach for Applying Optimal Fingerprint Techniques to Estimate Climate Sensitivity*." Journal of Climate 26, no. 19 (September 24, 2013): 7414–29. http://dx.doi.org/10.1175/jcli-d-12-00473.1.

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Abstract A detailed reanalysis is presented of a “Bayesian” climate parameter study (as exemplified by Forest et al.) that estimates climate sensitivity (ECS) jointly with effective ocean diffusivity and aerosol forcing, using optimal fingerprints to compare multidecadal observations with simulations by the Massachusetts Institute of Technology 2D climate model at varying settings of the three climate parameters. Use of improved methodology primarily accounts for the 90% confidence bounds for ECS reducing from 2.1–8.9 K to 2.0–3.6 K. The revised methodology uses Bayes's theorem to derive a probability density function (PDF) for the whitened (made independent using an optimal fingerprint transformation) observations, for which a uniform prior is known to be noninformative. A dimensionally reducing change of variables onto the parameter surface is then made, deriving an objective joint PDF for the climate parameters. The PDF conversion factor from the whitened variables space to the parameter surface represents a noninformative joint parameter prior, which is far from uniform. The noninformative prior prevents more probability than data uncertainty distributions warrant being assigned to regions where data respond little to parameter changes, producing better-constrained PDFs. Incorporating 6 years of unused model simulation data and revising the experimental design to improve diagnostic power reduces the best-fit climate sensitivity. Employing the improved methodology, preferred 90% bounds of 1.2–2.2 K for ECS are then derived (mode and median 1.6 K). The mode is identical to those from Aldrin et al. and [using the same Met Office Hadley Centre Climate Research Unit temperature, version 4 (HadCRUT4), observational dataset] from Ring et al. Incorporating nonaerosol forcing and observational surface temperature uncertainties, unlike in the original study, widens the 90% range to 1.0–3.0 K.

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35

Koehler, Jonathan J. "The base rate fallacy reconsidered: Descriptive, normative, and methodological challenges." Behavioral and Brain Sciences 19, no. 1 (March 1996): 1–17. http://dx.doi.org/10.1017/s0140525x00041157.

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AbstractWe have been oversold on the base rate fallacy in probabilistic judgment from an empirical, normative, and methodological standpoint. At the empirical level, a thorough examination of the base rate literature (including the famous lawyer–engineer problem) does not support the conventional wisdom that people routinely ignore base rates. Quite the contrary, the literature shows that base rates are almost always used and that their degree of use depends on task structure and representation. Specifically, base rates play a relatively larger role in tasks where base rates are implicitly learned or can be represented in frequentist terms. Base rates are also used more when they are reliable and relatively more diagnostic than available individuating information. At the normative level, the base rate fallacy should be rejected because few tasks map unambiguously into the narrow framework that is held up as the standard of good decision making. Mechanical applications of Bayes's theorem to identify performance errors are inappropriate when (1) key assumptions of the model are either unchecked or grossly violated, and (2) no attempt is made to identify the decision maker's goals, values, and task assumptions. Methodologically, the current approach is criticized for its failure to consider how the ambiguous, unreliable, and unstable base rates of the real world are and should be used. Where decision makers' assumptions and goals vary, and where performance criteria are complex, the traditional Bayesian standard is insufficient. Even where predictive accuracy is the goal in commonly defined problems, there may be situations (e.g., informationally redundant environments) in which base rates can be ignored with impunity. A more ecologically valid research program is called for. This program should emphasize the development of prescriptive theory in rich, realistic decision environments.

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36

McCullagh, Peter, and Han Han. "On Bayes’s theorem for improper mixtures." Annals of Statistics 39, no. 4 (August 2011): 2007–20. http://dx.doi.org/10.1214/11-aos892.

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37

Szreder, Mirosław. "Twierdzenie Bayesa po 250 latach." Wiadomości Statystyczne. The Polish Statistician 2013, no. 12 (December 30, 2013): 23–36. http://dx.doi.org/10.59139/ws.2013.12.1.

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The author recalls that 250 years ago in the British scientific circles appeared theorem of probability of causes, now called Bayes’ theorem (formulated in 1763 by Thomas Bayes). It refers to the situation where there has been some events and once need to assess the probability of another incident which was the reason, i.e. what is cause and what is the effect of this event. Despite the passing years Bayes’ approach in statistical surveys for the conditional probability of occurrence is constantly confirmed and important.

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38

Rudge, David Wyss. "A Bayesian Analysis of Strategies in Evolutionary Biology." Perspectives on Science 6, no. 4 (1998): 341–60. http://dx.doi.org/10.1162/posc_a_00555.

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Most work done in philosophy of experiment has focused on experiments taken from the domain of physics. The present essay tests whether Allan Franklin’s (1984, 1986, 1989, 1990) philosophy of experiment developed in the context of high energy physics can be extended to include examples from evolutionary biology, such as H. B. D. Kettlewell’s (1935, 1956, 1958) famous studies of industrial melanism in the peppered moth, Biston betularia. The analysis demonstrates that many of the techniques used by evolutionary biologists exemplify the strategies Franklin lists, and identifies an additional strategy that can likewise be justified by appeal to Bayes’s Theorem.

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39

Guo, Chen. "Implementation and improvement of Bayes’s theorem for indoor visible light positioning system." Optical Engineering 58, no. 02 (February 20, 2019): 1. http://dx.doi.org/10.1117/1.oe.58.2.026110.

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40

Dhondutatya, Mathpati, Memon Simran, Kesgire Akash, and Karande Siddharth. "Healthcare Portal System using Iterative Search, K-Nn, Differential Diagnosis, Baye's Theorem." IJARCCE 6, no. 3 (March 30, 2017): 470–73. http://dx.doi.org/10.17148/ijarcce.2017.63109.

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41

Sadashiv, Naidila, and Dilip Kumar S M. "A Baye's Theorem Based Node Selection for Load Balancing in Cloud Environment." International Journal on Cloud Computing: Services and Architecture 7, no. 1 (February 28, 2017): 01–08. http://dx.doi.org/10.5121/ijccsa.2017.7101.

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42

Tijani, Ahmed, Richard Molyet, and Mansoor Alam. "Collision Warning System Using Naïve Bayes Classifier." Technium: Romanian Journal of Applied Sciences and Technology 4, no. 5 (June 4, 2022): 39–56. http://dx.doi.org/10.47577/technium.v4i5.6653.

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Motor vehicle crashes can lead to traumatic experiences. High-impact collisions usually cause severe injuries or fatalities. A collision warning system that analyzes driving behaviors and warns drivers of impending crashes can prevent road collisions and save lives, so increasing traffic safety. An application of the Naïve Bayes classifier model to determine the potential for rear-end collisions between highway vehicles is presented. The Naïve Bayes classifier is a supervised machine-learning model based on Bayes’s theorem. Two vehicles are utilized, with one vehicle following the other. The parameters studied are speed, distance, acceleration, and deceleration. Training examples involving over 100 potential collision scenarios have been evaluated. Simulation results show that the model successfully responds to and correctly predicts potential collisions.

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43

Villejoubert, Gaëlle, and David R. Mandel. "The inverse fallacy: An account of deviations from Bayes’s theorem and the additivity principle." Memory & Cognition 30, no. 2 (March 2002): 171–78. http://dx.doi.org/10.3758/bf03195278.

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44

Barrenechea, Rodrigo, and James Mahoney. "A Set-Theoretic Approach to Bayesian Process Tracing." Sociological Methods & Research 48, no. 3 (July 25, 2017): 451–84. http://dx.doi.org/10.1177/0049124117701489.

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This article develops a set-theoretic approach to Bayes’s theorem and Bayesian process tracing. In the approach, hypothesis testing is the procedure whereby one updates beliefs by narrowing the range of states of the world that are regarded as possible, thus diminishing the domain in which the actual world can reside. By explicitly connecting Bayesian analysis to its set-theoretic foundations, the approach makes process tracing more intuitive and thus easier to apply for qualitative researchers. Moreover, the set-theoretic approach provides new tools for assessing both the consequentialness and expectedness of evidence when conducting process tracing. It also provides a new way to classify and interpret process-tracing tests, such as hoop tests and smoking gun tests, by viewing them as zones in a continuous space whose dimensions reflect the magnitude of changes in sets. The article shows that Bayesian process tracing and set-theoretic process tracing are not alternatives to each other but rather two sides of the same coin.

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45

Villejoubert, Gaëlle, and David R. Mandel. "Erratum to: The inverse fallacy: An account of deviations from Bayes’s theorem and the additivity principle." Memory & Cognition 30, no. 2 (March 2002): 1. http://dx.doi.org/10.3758/bf03195277.

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46

Canepa-Anson, R., M. R. Freeman, L. MacMillan, and P. W. Armstrong. "Baye'S Theorem and Test Performance. Should Women with Unstable Ischaemic Syndromes be Investigated Differently from Men?" Clinical Science 72, s16 (January 1, 1987): 57P—58P. http://dx.doi.org/10.1042/cs072057pb.

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47

Scheuerer, Michael, Scott Gregory, Thomas M. Hamill, and Phillip E. Shafer. "Probabilistic Precipitation-Type Forecasting Based on GEFS Ensemble Forecasts of Vertical Temperature Profiles." Monthly Weather Review 145, no. 4 (March 21, 2017): 1401–12. http://dx.doi.org/10.1175/mwr-d-16-0321.1.

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Abstract A Bayesian classification method for probabilistic forecasts of precipitation type is presented. The method considers the vertical wet-bulb temperature profiles associated with each precipitation type, transforms them into their principal components, and models each of these principal components by a skew normal distribution. A variance inflation technique is used to de-emphasize the impact of principal components corresponding to smaller eigenvalues, and Bayes’s theorem finally yields probability forecasts for each precipitation type based on predicted wet-bulb temperature profiles. This approach is demonstrated with reforecast data from the Global Ensemble Forecast System (GEFS) and observations at 551 METAR sites, using either the full ensemble or the control run only. In both cases, reliable probability forecasts for precipitation type being either rain, snow, ice pellets, freezing rain, or freezing drizzle are obtained. Compared to the model output statistics (MOS) approach presently used by the National Weather Service, the skill of the proposed method is comparable for rain and snow and significantly better for the freezing precipitation types.

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48

Shagidullin, A. R., Yu A. Tunakova, S. V. Novikova, and V. S. Valiev. "Modeling the integral risk assessment for air pollution in the areas of highways by probabilistic methods." Journal of Physics: Conference Series 2134, no. 1 (December 1, 2021): 012001. http://dx.doi.org/10.1088/1742-6596/2134/1/012001.

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Abstract A methodology for calculating the integral risk of atmospheric pollution using Bayes’s theorem is proposed to take into account the action of mobile and stationary emission sources in the influence zones of highways, the response to the impact in the form of accumulation of emission components in depositing media and biological media of the population. At the first stage, the clustering of experimental data arrays was carried out, homogeneous road sections (clusters) were identified. The integral risk was calculated for the selected clusters. The risks of contamination of the investigated media have been calculated. A multiple regression model has been built to assess the level of integral risk with a high degree of reliability when compared with experimental data. The significance of the aerogenic factor in the formation of the level of integral risk is shown. A reduced model for assessing the integral risk by the level of risk of atmospheric air pollution is proposed. Grades of risk levels are given according to the degree of acceptability. It is possible to determine the contribution of the road transport component to the level of integral risk based on the obtained values of the final risk.

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Bishop, Craig H., and Kevin T. Shanley. "Bayesian Model Averaging’s Problematic Treatment of Extreme Weather and a Paradigm Shift That Fixes It." Monthly Weather Review 136, no. 12 (December 1, 2008): 4641–52. http://dx.doi.org/10.1175/2008mwr2565.1.

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Abstract Methods of ensemble postprocessing in which continuous probability density functions are constructed from ensemble forecasts by centering functions around each of the ensemble members have come to be called Bayesian model averaging (BMA) or “dressing” methods. Here idealized ensemble forecasting experiments are used to show that these methods are liable to produce systematically unreliable probability forecasts of climatologically extreme weather. It is argued that the failure of these methods is linked to an assumption that the distribution of truth given the forecast can be sampled by adding stochastic perturbations to state estimates, even when these state estimates have a realistic climate. It is shown that this assumption is incorrect, and it is argued that such dressing techniques better describe the likelihood distribution of historical ensemble-mean forecasts given the truth for certain values of the truth. This paradigm shift leads to an approach that incorporates prior climatological information into BMA ensemble postprocessing through Bayes’s theorem. This new approach is shown to cure BMA’s ill treatment of extreme weather by providing a posterior BMA distribution whose probabilistic forecasts are reliable for both extreme and nonextreme weather forecasts.

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Leroy, Stephen S., Gianluca Redaelli, and Barbara Grassi. "Prioritizing Data for Improving the Multidecadal Predictive Capability of Atmospheric Models." Journal of Climate 28, no. 13 (July 1, 2015): 5077–90. http://dx.doi.org/10.1175/jcli-d-14-00444.1.

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Abstract The prioritization accorded to observation types currently being considered for a space-based climate observing system is extended from a previous study. Hindcast averages and trends from 1970 through 2005 of longitude–latitude maps of 200-hPa geopotential height and of net downward shortwave and longwave radiation at the top of the atmosphere are investigated as relevant tests of climate models for predicting multidecadal surface air temperature change. To discover the strongest tests of climate models, Bayes’s theorem is applied to the output provided by phase 5 of the Coupled Model Intercomparison, and correlations of hindcasts and multidecadal climate prediction are used to rank the observation types and long-term averages versus long-term trends. Spatial patterns in data are shown to contain more information for improving climate prediction than do global averages of data, but no statistically significant test is found by considering select locations on the globe. Eigenmodes of intermodel differences in hindcasts may likely serve as tests of climate models that can improve interdecadal climate prediction, in particular the rate of Arctic tropospheric expansion, which is measurable by Earth radio occultation.

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