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Relevant bibliographies by topics / Bayes's theorem

Academic literature on the topic 'Bayes's theorem'

Author: Grafiati

Published: 25 July 2024

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Journal articles on the topic "Bayes's theorem"

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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Bayes's theorem"

1

Portugal, Agnaldo Cuoco. "Theism, Bayes's theorem and religious experience : an examination of Richard Swinburnes's religious epistemology." Thesis, King's College London (University of London), 2003. https://kclpure.kcl.ac.uk/portal/en/theses/theism-bayess-theorem-and-religious-experience--an-examination-of-richard-swinburness-religious-epistemology(f6ab0fd9-9277-41d7-9997-ecad803c54ae).html.

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Rogers, David M. "Using Bayes' theorem for free energy calculations." Cincinnati, Ohio : University of Cincinnati, 2009. http://rave.ohiolink.edu/etdc/view.cgi?acc_num=ucin1251832030.

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Thesis (Ph. D.)--University of Cincinnati, 2009.
Advisor: Thomas L. Beck. Title from electronic thesis title page (viewed Jan. 21, 2010). Keywords: Bayes; probability; statistical mechanics; free energy. Includes abstract. Includes bibliographical references.

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Jones, Martin K. "Bayes' Theorem and positive confirmation : an experimental economic analysis." Thesis, University of East Anglia, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300072.

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Fletcher, Douglas. "Generalized Empirical Bayes: Theory, Methodology, and Applications." Diss., Temple University Libraries, 2019. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/546485.

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Statistics
Ph.D.
The two key issues of modern Bayesian statistics are: (i) establishing a principled approach for \textit{distilling} a statistical prior distribution that is \textit{consistent} with the given data from an initial believable scientific prior; and (ii) development of a \textit{consolidated} Bayes-frequentist data analysis workflow that is more effective than either of the two separately. In this thesis, we propose generalized empirical Bayes as a new framework for exploring these fundamental questions along with a wide range of applications spanning fields as diverse as clinical trials, metrology, insurance, medicine, and ecology. Our research marks a significant step towards bridging the ``gap'' between Bayesian and frequentist schools of thought that has plagued statisticians for over 250 years. Chapters 1 and 2---based on \cite{mukhopadhyay2018generalized}---introduces the core theory and methods of our proposed generalized empirical Bayes (gEB) framework that solves a long-standing puzzle of modern Bayes, originally posed by Herbert Robbins (1980). One of the main contributions of this research is to introduce and study a new class of nonparametric priors ${\rm DS}(G, m)$ that allows exploratory Bayesian modeling. However, at a practical level, major practical advantages of our proposal are: (i) computational ease (it does not require Markov chain Monte Carlo (MCMC), variational methods, or any other sophisticated computational techniques); (ii) simplicity and interpretability of the underlying theoretical framework which is general enough to include almost all commonly encountered models; and (iii) easy integration with mainframe Bayesian analysis that makes it readily applicable to a wide range of problems. Connections with other Bayesian cultures are also presented in the chapter. Chapter 3 deals with the topic of measurement uncertainty from a new angle by introducing the foundation of nonparametric meta-analysis. We have applied the proposed methodology to real data examples from astronomy, physics, and medical disciplines. Chapter 4 discusses some further extensions and application of our theory to distributed big data modeling and the missing species problem. The dissertation concludes by highlighting two important areas of future work: a full Bayesian implementation workflow and potential applications in cybersecurity.
Temple University--Theses

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Conlon, Erin Marie. "Estimation and flexible correlation structures in spatial hierarchical models of disease mapping /." Diss., ON-CAMPUS Access For University of Minnesota, Twin Cities Click on "Connect to Digital Dissertations", 1999. http://www.lib.umn.edu/articles/proquest.phtml.

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Chadwick, Thomas Jonathan. "A general Bayes theory of nested model comparisons." Thesis, University of Newcastle Upon Tyne, 2002. http://hdl.handle.net/10443/641.

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We propose a general Bayes analysis for nested model comparisons which does not suffer from Lindley's paradox. It does not use Bayes factors, but uses the posterior distribution of the likelihood ratio between the models evaluated at the true values of the nuisance parameters. This is obtained directly from the posterior distribution of the full model parameters. The analysis requires only conventional uninformative or flat priors, and prior odds on the models. The conclusions from the posterior distribution of the likelihood ratio are in general in conflict with Bayes factor conclusions, but are in agreement with frequentist likelihood ratio test conclusions. Bayes factor conclusions and those from the BIC are, even in simple cases, in conflict with conclusions from HPD intervals for the same parameters, and appear untenable in general. Examples of the new analysis are given, with comparisons to classical P-values and Bayes factors.

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Zhang, Shunpu. "Some contributions to empirical Bayes theory and functional estimation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq23100.pdf.

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Yang, Ying. "Discretization for Naive-Bayes learning." Monash University, School of Computer Science and Software Engineering, 2003. http://arrow.monash.edu.au/hdl/1959.1/9393.

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Liu, Ka-yee. "Bayes and empirical Bayes estimation for the panel threshold autoregressive model and non-Gaussian time series." Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B30706166.

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Liu, Ka-yee, and 廖家怡. "Bayes and empirical Bayes estimation for the panel threshold autoregressive model and non-Gaussian time series." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B30706166.

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Books on the topic "Bayes's theorem"

1

Richard, Swinburne, and British Academy, eds. Bayes's theorem. Oxford: Published for The British Academy by Oxford University Press, 2002.

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Proving history: Bayes's theorem and the quest for the historical Jesus. Amherst, N.Y: Prometheus Books, 2012.

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Kuo, Lynn. Bayesian computations in survival models via the Gibbs sampler. Monterey, Calif: Naval Postgraduate School, 1991.

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Kucsma, András I. Bidding for contract games: Applying game theory to analyze first price sealed bid auctions. Monterey, Calif: Naval Postgraduate School, 1997.

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Gaver, Donald Paul. Regression analysis of hierarchical Poisson-like event rate data: Superpopulation model effect on predictions. Monterey, Calif: Naval Postgraduate School, 1990.

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ERIC Clearinghouse on Assessment and Evaluation., ed. Bayes' theorem: An old tool applicable to today's classroom measurement needs. [College Park, MD: ERIC Clearinghouse on Assessment and Evaluation, University of Maryland, 2000.

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Carlin, Bradley P. Bayes and empirical Bayes methods for data analysis. Boca Raton: Chapman & Hall/CRC, 1998.

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Carlin, Bradley P. Bayes and Empirical Bayes methods for data analysis. 2nd ed. Boca Raton: Chapman & Hall/CRC, 2000.

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1944-, Louis Thomas A., ed. Bayes and empirical Bayes methods for data analysis. London: Chapman & Hall, 1996.

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Large-scale inference: Empirical Bayes methods for estimation, testing, and prediction. Cambridge: Cambridge University Press, 2010.

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Book chapters on the topic "Bayes's theorem"

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Modis, Konstantinos. "Bayes’s Theorem." In Encyclopedia of Mathematical Geosciences, 1–4. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-26050-7_440-1.

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Modis, Konstantinos. "Bayes’s Theorem." In Encyclopedia of Mathematical Geosciences, 61–65. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-030-85040-1_440.

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O’Hagan, Anthony. "Bayes’ theorem." In Probability, 45–61. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-1211-3_3.

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Harney, Hanns Ludwig. "Bayes’ Theorem." In Bayesian Inference, 11–25. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-41644-1_2.

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Petroianu, Georg, and Peter Michael Osswald. "Bayes-Theorem." In Anästhesie in Frage und Antwort, 31–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-05715-5_11.

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Harney, Hanns L. "Bayes’ Theorem." In Bayesian Inference, 8–18. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-06006-3_2.

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Hoang, Lê Nguyên. "Bayes’ Theorem." In The Equation of Knowledge, 17–32. Boca Raton : C&H/CRC Press, 2020. | Translation of: La formule du savoir : une philosophie unifiée du savoir fondée sur le théorème de Bayes: Chapman and Hall/CRC, 2020. http://dx.doi.org/10.1201/9780367855307-2.

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Koch, Karl-Rudolf. "Bayes’ Theorem." In Bayesian Inference with Geodetic Applications, 4–8. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0048702.

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Kadane, Joseph B. "Bayes’ Theorem." In International Encyclopedia of Statistical Science, 89–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-04898-2_141.

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Gooch, Jan W. "Bayes’ Theorem." In Encyclopedic Dictionary of Polymers, 970. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6247-8_15157.

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Conference papers on the topic "Bayes's theorem"

1

Dezert, Jean, Albena Tchamova, and Deqiang Han. "Total Belief Theorem and Generalized Bayes' Theorem." In 2018 International Conference on Information Fusion (FUSION). IEEE, 2018. http://dx.doi.org/10.23919/icif.2018.8455351.

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Price, Harold J. "Uninformative priors for Bayes’ theorem." In BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING. AIP, 2002. http://dx.doi.org/10.1063/1.1477060.

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Ballesteros-Pérez, Pablo, Mª Carmen González-Cruz, and Daniel Mora-Melià. "EXPLAINING THE BAYES’ THEOREM GRAPHICALLY." In 12th International Technology, Education and Development Conference. IATED, 2018. http://dx.doi.org/10.21125/inted.2018.0028.

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Josang, Audun. "Generalising Bayes' theorem in subjective logic." In 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI). IEEE, 2016. http://dx.doi.org/10.1109/mfi.2016.7849531.

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Kosko, Bart. "Bayes Theorem Extends to Overlapping Hypotheses." In 2019 International Conference on Computational Science and Computational Intelligence (CSCI). IEEE, 2019. http://dx.doi.org/10.1109/csci49370.2019.00106.

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Qu, Guangzhi, Hui Zhang, and Craig T. Hartrick. "Multi-label classification with Bayes' theorem." In 2011 4th International Conference on Biomedical Engineering and Informatics (BMEI). IEEE, 2011. http://dx.doi.org/10.1109/bmei.2011.6098780.

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Xiao, Mi, Qiangzhuang Yao, Liang Gao, Haihong Xiong, and Fengxiang Wang. "Metamodel Uncertainty Quantification by Using Bayes’ Theorem." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46746.

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In complex engineering systems, approximation models, also called metamodels, are extensively constructed to replace the computationally expensive simulation and analysis codes. With different sample data and metamodeling methods, different metamodels can be constructed to describe the behavior of an engineering system. Then, metamodel uncertainty will arise from selecting the best metamodel from a set of alternative ones. In this study, a method based on Bayes’ theorem is used to quantify this metamodel uncertainty. With some mathematical examples, metamodels are built by six metamodeling methods, i.e., polynomial response surface, locally weighted polynomials (LWP), k-nearest neighbors (KNN), radial basis functions (RBF), multivariate adaptive regression splines (MARS), and kriging methods, and under four sampling methods, i.e., parameter study (PS), Latin hypercube sampling (LHS), optimal LHS and full factorial design (FFD) methods. The uncertainty of metamodels created by different metamodeling methods and under different sampling methods is quantified to demonstrate the process of implementing the method.

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Liu, Hongze, Zhengjiang Liu, Xin Wang, and Yao Cai. "Bayes' Theorem based maritime safety information classifier." In 2018 Chinese Control And Decision Conference (CCDC). IEEE, 2018. http://dx.doi.org/10.1109/ccdc.2018.8407588.

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Li, Jiandun, Dingyu Yang, and Chunlei Ji. "Mine weighted network motifs via Bayes' theorem." In 2017 4th International Conference on Systems and Informatics (ICSAI). IEEE, 2017. http://dx.doi.org/10.1109/icsai.2017.8248334.

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Dezert, Jean, Albena Tchamova, Deqiang Han, and Thanuka Wickramarathne. "A Simplified Formulation of Generalized Bayes' Theorem." In 2019 22th International Conference on Information Fusion (FUSION). IEEE, 2019. http://dx.doi.org/10.23919/fusion43075.2019.9011357.

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Reports on the topic "Bayes's theorem"

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Smith, A. F., and A. E. Gelfand. Bayes Theorem from a Sampling-Resampling Perspective. Fort Belvoir, VA: Defense Technical Information Center, July 1991. http://dx.doi.org/10.21236/ada239515.

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Smith, Donald L., Denise Neudecker, and Roberto Capote Noy. Investigation of the Effects of Probability Density Function Kurtosis on Evaluated Data Results. IAEA Nuclear Data Section, May 2018. http://dx.doi.org/10.61092/iaea.yxma-3y50.

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In two previous investigations that are documented in this IAEA report series, we examined the effects of non-Gaussian, non-symmetric probability density functions (PDFs) on the outcomes of data evaluations. Most of this earlier work involved considering just two independent input data values and their respective uncertainties. They were used to generate one evaluated data point. The input data are referred to, respectively, as the mean value and standard deviation pair (y0,s0) for a prior PDF p0(y) and a second mean value and standard deviation pair (ye,se) for a likelihood PDF pe(y). Conceptually, these input data could be viewed as resulting from theory (subscript “0”) and experiment (subscript “e”). In accordance with Bayes Theorem, the evaluated mean value and standard deviation pair (ysol,ssol) corresponds to the posterior PDF p(y) which is related to p0(y) and pe(y) by p(y) = Cp0(y)pe(y). The prior and likelihood PDFs are both assumed to be normalized so that they integrate to unity for all y ≥ 0. Negative values of y are viewed as non-physical so they are not permitted. The product function p0(y)pe(y) is not normalized, so a positive multiplicative constant C is required to normalize p(y). In the earlier work, both normal (Gaussian) and lognormal functions were considered for the prior PDF. The likelihood functions were all taken to be Gaussians. Gaussians are symmetric, with zero skewness, and they always possess a fixed kurtosis of 3. Lognormal functions are inherently skewed, with widely varying values of skewness and kurtosis that depend on the function parameters. In order to explore the effects of kurtosis, distinct from skewness, the present work constrains the likelihood function to be Gaussian, and it considers three distinct, inherently symmetric prior PDF types: Gaussian (kurtosis = 3), Continuous Uniform (kurtosis = 1.8), and Laplace (kurtosis = 6). A product of two Gaussians produces a Gaussian even if ye ≠ y0. The product of a Gaussian PDF and a Uniform PDF, or a Laplace PDF, yields a symmetric PDF with zero skewness only when ye = y0. A pure test of the effect of kurtosis on an evaluation is provided by considering combinations of s0 and se with ye = y0. The present work also investigates the extent to which p(y) exhibits skewness when ye ≠ y0, again by considering various values for s0 and se. The Bayesian results from numerous numerical examples have been compared with corresponding least-squares solutions in order to arrive at some general conclusions regarding how the evaluated result (ysol,ssol) depends on various combinations of the input data y0, s0, ye, and se as well as on prior-likelihood PDF combinations: Gaussian-Gaussian, Uniform-Gaussian, and Laplace-Gaussian.

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Smith, Donald L., Denise Neudecker, and Roberto Capote Noy. Investigation of the Effects of Probability Density Function Kurtosis on Evaluated Data Results. IAEA Nuclear Data Section, May 2020. http://dx.doi.org/10.61092/iaea.nqsh-f02d.

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In two previous investigations that are documented in this IAEA report series, we examined the effects of non-Gaussian, non-symmetric probability density functions (PDFs) on the outcomes of data evaluations. Most of this earlier work involved considering just two independent input data values and their respective uncertainties. They were used to generate one evaluated data point. The input data are referred to, respectively, as the mean value and standard deviation pair (y0,s0) for a prior PDF p0(y) and a second mean value and standard deviation pair (ye,se) for a likelihood PDF pe(y). Conceptually, these input data could be viewed as resulting from theory (subscript “0”) and experiment (subscript “e”). In accordance with Bayes Theorem, the evaluated mean value and standard deviation pair (ysol,ssol) corresponds to the posterior PDF p(y) which is related to p0(y) and pe(y) by p(y) = Cp0(y)pe(y). The prior and likelihood PDFs are both assumed to be normalized so that they integrate to unity for all y ≥ 0. Negative values of y are viewed as non-physical so they are not permitted. The product function p0(y)pe(y) is not normalized, so a positive multiplicative constant C is required to normalize p(y). In the earlier work, both normal (Gaussian) and lognormal functions were considered for the prior PDF. The likelihood functions were all taken to be Gaussians. Gaussians are symmetric, with zero skewness, and they always possess a fixed kurtosis of 3. Lognormal functions are inherently skewed, with widely varying values of skewness and kurtosis that depend on the function parameters. In order to explore the effects of kurtosis, distinct from skewness, the present work constrains the likelihood function to be Gaussian, and it considers three distinct, inherently symmetric prior PDF types: Gaussian (kurtosis = 3), Continuous Uniform (kurtosis = 1.8), and Laplace (kurtosis = 6). A product of two Gaussians produces a Gaussian even if ye ≠ y0. The product of a Gaussian PDF and a Uniform PDF, or a Laplace PDF, yields a symmetric PDF with zero skewness only when ye = y0. A pure test of the effect of kurtosis on an evaluation is provided by considering combinations of s0 and se with ye = y0. The present work also investigates the extent to which p(y) exhibits skewness when ye ≠ y0, again by considering various values for s0 and se. The Bayesian results from numerous numerical examples have been compared with corresponding least-squares solutions in order to arrive at some general conclusions regarding how the evaluated result (ysol,ssol) depends on various combinations of the input data y0, s0, ye, and se as well as on prior-likelihood PDF combinations: Gaussian-Gaussian, Uniform-Gaussian, and Laplace-Gaussian.

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Smith, D. L., D. Neudecker, and R. Capote Noy. Investigation of the Effects of Probability Density Function Kurtosis on Evaluated Data Results. IAEA Nuclear Data Section, May 2020. http://dx.doi.org/10.61092/iaea.3ar5-xmp8.

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In two previous investigations that are documented in this IAEA report series, we examined the effects of non-Gaussian, non-symmetric probability density functions (PDFs) on the outcomes of data evaluations. Most of this earlier work involved considering just two independent input data values and their respective uncertainties. They were used to generate one evaluated data point. The input data are referred to, respectively, as the mean value and standard deviation pair (y0,s0) for a prior PDF p0(y) and a second mean value and standard deviation pair (ye,se) for a likelihood PDF pe(y). Conceptually, these input data could be viewed as resulting from theory (subscript “0”) and experiment (subscript “e”). In accordance with Bayes Theorem, the evaluated mean value and standard deviation pair (ysol,ssol) corresponds to the posterior PDF p(y) which is related to p0(y) and pe(y) by p(y) = Cp0(y)pe(y). The prior and likelihood PDFs are both assumed to be normalized so that they integrate to unity for all y ≥ 0. Negative values of y are viewed as non-physical so they are not permitted. The product function p0(y)pe(y) is not normalized, so a positive multiplicative constant C is required to normalize p(y). In the earlier work, both normal (Gaussian) and lognormal functions were considered for the prior PDF. The likelihood functions were all taken to be Gaussians. Gaussians are symmetric, with zero skewness, and they always possess a fixed kurtosis of 3. Lognormal functions are inherently skewed, with widely varying values of skewness and kurtosis that depend on the function parameters. In order to explore the effects of kurtosis, distinct from skewness, the present work constrains the likelihood function to be Gaussian, and it considers three distinct, inherently symmetric prior PDF types: Gaussian (kurtosis = 3), Continuous Uniform (kurtosis = 1.8), and Laplace (kurtosis = 6). A product of two Gaussians produces a Gaussian even if ye ≠ y0. The product of a Gaussian PDF and a Uniform PDF, or a Laplace PDF, yields a symmetric PDF with zero skewness only when ye = y0. A pure test of the effect of kurtosis on an evaluation is provided by considering combinations of s0 and se with ye = y0. The present work also investigates the extent to which p(y) exhibits skewness when ye ≠ y0, again by considering various values for s0 and se. The Bayesian results from numerous numerical examples have been compared with corresponding least-squares solutions in order to arrive at some general conclusions regarding how the evaluated result (ysol,ssol) depends on various combinations of the input data y0, s0, ye, and se as well as on prior-likelihood PDF combinations: Gaussian-Gaussian, Uniform-Gaussian, and Laplace-Gaussian.

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