Articoli di riviste: "Bayesian statistical decision theory"

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Wijayanti, Rina. "PENAKSIRAN PARAMETER ANALISIS REGRESI COX DAN ANALISIS SURVIVAL BAYESIAN." PRISMATIKA: Jurnal Pendidikan dan Riset Matematika 1, no. 2 (June 1, 2019): 16–26. http://dx.doi.org/10.33503/prismatika.v1i2.427.

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In the theory of estimation, there are two approaches, namely the classical statistical approach and global statistical approach (Bayesian). Classical statistics are statistics in which the procedure is the decision based only on the data samples taken from the population. While Bayesian statistics in making decisions based on new information from the observed data (sample) and prior knowledge. At this writing Cox Regression Analysis will be taken as an example of parameter estimation by the classical statistical approach Survival Analysis and Bayesian statistical approach as an example of global (Bayesian). Survival Bayesial parameter estimation using MCMC algorithms for model complex / complicated and difficult to resolve while the Cox regression models using the method of partial likelihood. Results of the parameter estimates do not close form that needs to be done by the method of Newton-Raphson iteration.

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de la Horra, Julián. "Bayesian robustness of the quantile loss in statistical decision theory." Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 107, no. 2 (May 16, 2012): 451–58. http://dx.doi.org/10.1007/s13398-012-0070-x.

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Luce, Bryan R., Ya-Chen Tina Shih, and Karl Claxton. "INTRODUCTION." International Journal of Technology Assessment in Health Care 17, no. 1 (January 2001): 1–5. http://dx.doi.org/10.1017/s0266462301104010.

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Until the mid-1980s, most economic analyses of healthcare technologies were based on decision theory and used decision-analytic models. The goal was to synthesize all relevant clinical and economic evidence for the purpose of assisting decision makers to efficiently allocate society's scarce resources. This was true of virtually all the early cost-effectiveness evaluations sponsored and/or published by the U.S. Congressional Office of Technology Assessment (OTA) (15), Centers of Disease Control and Prevention (CDC), the National Cancer Institute, other elements of the U.S. Public Health Service, and of healthcare technology assessors in Europe and elsewhere around the world. Methodologists routinely espoused, or at minimum assumed, that these economic analyses were based on decision theory (8;24;25). Since decision theory is rooted in—in fact, an informal application of—Bayesian statistical theory, these analysts were conducting studies to assist healthcare decision making by appealing to a Bayesian rather than a classical, or frequentist, inference approach. But their efforts were not so labeled. Oddly, the statistical training of these decision analysts was invariably classical, not Bayesian. Many were not—and still are not—conversant with Bayesian statistical approaches.

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Procaccia, H., R. Cordier, and S. Muller. "Application of Bayesian statistical decision theory for a maintenance optimization problem." Reliability Engineering & System Safety 55, no. 2 (February 1997): 143–49. http://dx.doi.org/10.1016/s0951-8320(96)00006-3.

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Reinhardt, Howard E. "Statistical Decision Theory and Bayesian Analysis. Second Edition (James O. Berger)." SIAM Review 29, no. 3 (September 1987): 487–89. http://dx.doi.org/10.1137/1029095.

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Laedermann, Jean-Pascal, Jean-François Valley, and François O. Bochud. "Measurement of radioactive samples: application of the Bayesian statistical decision theory." Metrologia 42, no. 5 (September 13, 2005): 442–48. http://dx.doi.org/10.1088/0026-1394/42/5/015.

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Martín, Jacinto, David Ríos Insua, and Fabrizio Ruggeri. "Joint sensitivity in bayesian decision theory." Test 12, no. 1 (June 2003): 173–94. http://dx.doi.org/10.1007/bf02595818.

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Ghosh, Malay, and James Berger. "Stastical Decision Theory and Bayesian Analysis." Journal of the American Statistical Association 83, no. 401 (March 1988): 266. http://dx.doi.org/10.2307/2288950.

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Abraham, Christophe, and Benoît Cadre. "Asymptotic global robustness in bayesian decision theory." Annals of Statistics 32, no. 4 (August 2004): 1341–66. http://dx.doi.org/10.1214/009053604000000562.

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Corander, Jukka. "Bayesian graphical model determination using decision theory." Journal of Multivariate Analysis 85, no. 2 (May 2003): 253–66. http://dx.doi.org/10.1016/s0047-259x(02)00033-7.

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Geisler, Wilson S., and Randy L. Diehl. "Bayesian natural selection and the evolution of perceptual systems." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 357, no. 1420 (April 29, 2002): 419–48. http://dx.doi.org/10.1098/rstb.2001.1055.

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In recent years, there has been much interest in characterizing statistical properties of natural stimuli in order to better understand the design of perceptual systems. A fruitful approach has been to compare the processing of natural stimuli in real perceptual systems with that of ideal observers derived within the framework of Bayesian statistical decision theory. While this form of optimization theory has provided a deeper understanding of the information contained in natural stimuli as well as of the computational principles employed in perceptual systems, it does not directly consider the process of natural selection, which is ultimately responsible for design. Here we propose a formal framework for analysing how the statistics of natural stimuli and the process of natural selection interact to determine the design of perceptual systems. The framework consists of two complementary components. The first is a maximum fitness ideal observer, a standard Bayesian ideal observer with a utility function appropriate for natural selection. The second component is a formal version of natural selection based upon Bayesian statistical decision theory. Maximum fitness ideal observers and Bayesian natural selection are demonstrated in several examples. We suggest that the Bayesian approach is appropriate not only for the study of perceptual systems but also for the study of many other systems in biology.

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Borysova, Valentyna I., and Bohdan P. Karnaukh. "Standard of proof in common law: Mathematical explication and probative value of statistical data." Journal of the National Academy of Legal Sciences of Ukraine 28, no. 2 (June 25, 2021): 171–80. http://dx.doi.org/10.37635/jnalsu.28(2).2021.171-180.

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As a result of recent amendments to the procedural legislation of Ukraine, one may observe a tendency in judicial practice to differentiate the standards of proof depending on the type of litigation. Thus, in commercial litigation the so-called standard of “probability of evidence” applies, while in criminal proceedings – “beyond a reasonable doubt” standard applies. The purpose of this study was to find the rational justification for the differentiation of the standards of proof applied in civil (commercial) and criminal cases and to explain how the same fact is considered proven for the purposes of civil lawsuit and not proven for the purposes of criminal charge. The study is based on the methodology of Bayesian decision theory. The paper demonstrated how the principles of Bayesian decision theory can be applied to judicial fact-finding. According to Bayesian theory, the standard of proof applied depends on the ratio of the false positive error disutility to false negative error disutility. Since both types of error have the same disutility in a civil litigation, the threshold value of conviction is 50+ percent. In a criminal case, on the other hand, the disutility of false positive error considerably exceeds the disutility of the false negative one, and therefore the threshold value of conviction shall be much higher, amounting to 90 percent. Bayesian decision theory is premised on probabilistic assessments. And since the concept of probability has many meanings, the results of the application of Bayesian theory to judicial fact-finding can be interpreted in a variety of ways. When dealing with statistical evidence, it is crucial to distinguish between subjective and objective probability. Statistics indicate objective probability, while the standard of proof refers to subjective probability. Yet, in some cases, especially when statistical data is the only available evidence, the subjective probability may be roughly equivalent to the objective probability. In such cases, statistics cannot be ignored

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Majeed, Nasir, Amjad Hilal, and Tabinda Rani. "UNDERSTANDING BAYES’ THEOREM AND ITS APPLICATION IN JUDICIAL DECISION MAKING." Pakistan Journal of Social Research 05, no. 02 (June 30, 2023): 449–57. http://dx.doi.org/10.52567/pjsr.v5i02.1096.

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The Bayes’ theorem is a mathematical formula to gauge and describe the probability of an event by employing prior knowledge and evidence relevant to the event. The objective of the present study was to understand the Bayesian theorem and its application in judicial trials by deploying doctrinal research methodology. After consulting authoritative writings of prominent researchers and judicial decisions, study found that the Bayesian Probability in legal context used in odds version, likelihood ratio and in the form of Bayesian networks. The study also found that the application of the theorem in judicial proceedings was controversial since various researchers condemned, and numerous analysts advocated its application in real time court cases. Moreover, the study found that the theorem has been and advocated to be used to measure the probative force of statistical and non-statistical evidence, and to infer the causes of any event by observing its effects. It is expected that the present study will enable the legal fraternity to understand the working mechanism and various uses of Bayes’ theorem in legal context. Keywords: Application of Bayesian theorem, Bayesian Probability, Judicial decisions, Uses of Bayesian theory in judicial trials.

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Johnson, Richard A., and Abderrahmane Mouhab. "A Bayesian Decision Theory Approach to Classification Problems." Journal of Multivariate Analysis 56, no. 2 (February 1996): 232–44. http://dx.doi.org/10.1006/jmva.1996.0012.

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Abraham, Christophe, and Jean-Pierre Daurès. "Robust Bayesian decision theory applied to optimal dosage." Statistics in Medicine 23, no. 7 (2004): 1055–73. http://dx.doi.org/10.1002/sim.1690.

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De Waal, D. J. "Summary on Bayes estimation and hypothesis testing." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 7, no. 1 (March 17, 1988): 28–32. http://dx.doi.org/10.4102/satnt.v7i1.896.

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Although Bayes’ theorem was published in 1764, it is only recently that Bayesian procedures were used in practice in statistical analyses. Many developments have taken place and are still taking place in the areas of decision theory and group decision making. Two aspects, namely that of estimation and tests of hypotheses, will be looked into. This is the area of statistical inference mainly concerned with Mathematical Statistics.

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Girtler, Jerzy. "Limiting Distribution of the Three-State Semi-Markov Model of Technical State Transitions of Ship Power Plant Machines and its Applicability in Operational Decision-Making." Polish Maritime Research 27, no. 2 (June 1, 2020): 136–44. http://dx.doi.org/10.2478/pomr-2020-0035.

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AbstractThe article presents the three-state semi-Markov model of the process {W(t): t ≥ 0} of state transitions of a ship power plant machine, with the following interpretation of these states: s1 – state of full serviceability, s2 – state of partial serviceability, and s3 – state of unserviceability. These states are precisely defined for the ship main engine (ME). A hypothesis is proposed which explains the possibility of application of this model to examine models of real state transitions of ship power plant machines. Empirical data concerning ME were used for calculating limiting probabilities for the process {W(t): t ≥ 0}. The applicability of these probabilities in decision making with the assistance of the Bayesian statistical theory is demonstrated. The probabilities were calculated using a procedure included in the computational software MATHEMATICA, taking into consideration the fact that the random variables representing state transition times of the process {W(t): t ≥ 0} have gamma distributions. The usefulness of the Bayesian statistical theory in operational decision-making concerning ship power plants is shown using a decision dendrite which maps ME states and consequences of particular decisions, thus making it possible to choose between the following two decisions: d1 – first perform a relevant preventive service of the engine to restore its state and then perform the commissioned task within the time limit determined by the customer, and d2 – omit the preventive service and start performing the commissioned task.

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Alho, Juha M., and Jyrki Kangas. "Analyzing Uncertainties in Experts' Opinions of Forest Plan Performance." Forest Science 43, no. 4 (November 1, 1997): 521–28. http://dx.doi.org/10.1093/forestscience/43.4.521.

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Abstract Multi-objective forestry requires new decision support systems to aid the forest owner and foresters in the planning of future treatment schedules. The analytic hierarchy process (AHP), based on pairwise comparison data and Saaty's eigenvector method, is one technique that has been proposed to make such qualitatively different objectives as income from timber sales and scenic beauty of forest landscape commensurable. A weak point of the methodology has been the lack of a statistical theory behind it. We have earlier shown how classical regression techniques can be used to provide a statistical assessment of the uncertainty of the estimated ratio-scales. In this paper we extend the results to a multi-level decision hierarchy commonly used in forest planning. We also provide a Bayesian extension of the regression technique. The advantage of the Bayesian approach is that it provides summaries of expert views that are easily understood by decision makers who may not have extensive understanding of statistical concepts. On the basis of the Bayesian analysis, one can calculate, for example, how likely it is that (in the view of the expert) a given forest plan is better than any other plan being compared. For. Sci. 43(4):521-528.

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Galvani, Marta, Chiara Bardelli, Silvia Figini, and Pietro Muliere. "A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap." Algorithms 14, no. 1 (January 3, 2021): 11. http://dx.doi.org/10.3390/a14010011.

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Bootstrap resampling techniques, introduced by Efron and Rubin, can be presented in a general Bayesian framework, approximating the statistical distribution of a statistical functional ϕ(F), where F is a random distribution function. Efron’s and Rubin’s bootstrap procedures can be extended, introducing an informative prior through the Proper Bayesian bootstrap. In this paper different bootstrap techniques are used and compared in predictive classification and regression models based on ensemble approaches, i.e., bagging models involving decision trees. Proper Bayesian bootstrap, proposed by Muliere and Secchi, is used to sample the posterior distribution over trees, introducing prior distributions on the covariates and the target variable. The results obtained are compared with respect to other competitive procedures employing different bootstrap techniques. The empirical analysis reports the results obtained on simulated and real data.

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Gelman, Andrew. "Some Class-Participation Demonstrations for Decision Theory and Bayesian Statistics." American Statistician 52, no. 2 (May 1998): 167. http://dx.doi.org/10.2307/2685476.

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Gelman, Andrew. "Some Class-Participation Demonstrations for Decision Theory and Bayesian Statistics." American Statistician 52, no. 2 (May 1998): 167–74. http://dx.doi.org/10.1080/00031305.1998.10480557.

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Abraham, Christophe. "Asymptotics in Bayesian decision theory with applications to global robustness." Journal of Multivariate Analysis 95, no. 1 (July 2005): 50–65. http://dx.doi.org/10.1016/j.jmva.2004.07.001.

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Mukha, V. S., and N. F. Kako. "The integrals and integral transformations connected with the joint vector Gaussian distribution." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 57, no. 2 (July 16, 2021): 206–16. http://dx.doi.org/10.29235/1561-2430-2021-57-2-206-216.

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In many applications it is desirable to consider not one random vector but a number of random vectors with the joint distribution. This paper is devoted to the integral and integral transformations connected with the joint vector Gaussian probability density function. Such integral and transformations arise in the statistical decision theory, particularly, in the dual control theory based on the statistical decision theory. One of the results represented in the paper is the integral of the joint Gaussian probability density function. The other results are the total probability formula and Bayes formula formulated in terms of the joint vector Gaussian probability density function. As an example the Bayesian estimations of the coefficients of the multiple regression function are obtained. The proposed integrals can be used as table integrals in various fields of research.

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North, D. W. "Analysis of Uncertainty and Reaching Broad Conclusions." Journal of the American College of Toxicology 7, no. 5 (September 1988): 583–90. http://dx.doi.org/10.3109/10915818809019535.

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Probability theory can provide a general way of reasoning about uncertainty, even when data are sparse or absent. The idea that probabilities can represent judgment is a basic principle for decision analysis and for the Bayesian school of statistics. The use of judgmental probabilities and Bayesian statistical methods for the analysis of toxicological data appears to be promising in reaching broad conclusions for policy and for research planning. Illustrative examples are given using quantal dose-response data from carcinogenicity bioassays for two chemicals, perchloroethylene and alachlor.

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Shao, Jun, and Shein-Chung Chow. "Constructing Release Targets for Drug Products: A Bayesian Decision Theory Approach." Applied Statistics 40, no. 3 (1991): 381. http://dx.doi.org/10.2307/2347518.

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Fang, Chih-Chiang, Chin-Chia Hsu, and Je-Hung Liu. "Bayesian Statistical Method Enhance the Decision-Making for Imperfect Preventive Maintenance with a Hybrid Competing Failure Mode." Axioms 11, no. 12 (December 15, 2022): 734. http://dx.doi.org/10.3390/axioms11120734.

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The study aims to provide a Bayesian statistical method with natural conjugate for facilities’ preventive maintenance scheduling related to the hybrid competing failure mode. An effective preventive maintenance strategy not only can improve a system’s health condition but also can increase a system’s efficiency, and therefore a firm needs to make an appropriate strategy for increasing the utilization of a system with reasonable costs. In the last decades, preventive maintenance issues of deteriorating systems have been studied in the related literature, and hundreds of maintenance/replacement models have been created. However, few studies focused on the issue of hybrid deteriorating systems which are composed of maintainable and non-maintainable failure modes. Moreover, due to the situations of the scarcity of historical failure data, the related analyses of preventive maintenance would be difficult to perform. Based on the above two reasons, this study proposed a Bayesian statistical method to deal with such preventive maintenance problems. Non-homogeneous Poisson processes (NHPP) with power law failure intensity functions are employed to describe the system’s deterioration behavior. Accordingly, the study can provide useful ways to help managers to make effective decisions for preventive maintenance. To apply the proposed models in actual cases, the study provides solution algorithms and a computerized architecture design for decision-makers to realize the computerization of decision-making.

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Ma, Rui, Long Han, and Hujun Geng. "Implementation and Error Analysis of MNIST Handwritten Dataset Classification Based on Bayesian Decision Classifier." Journal of Physics: Conference Series 2171, no. 1 (January 1, 2022): 012049. http://dx.doi.org/10.1088/1742-6596/2171/1/012049.

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Abstract In recent years, with the continuous development of computer technology, pattern recognition technology has gradually entered people’s life and learning, and people’s demand for pattern recognition technology is also growing.In order to adapt to people’s life and study, the application of pattern recognition theory is more and more, such as speech recognition, character recognition, face recognition and so on.The main methods of pattern recognition are statistics, clustering,neural network and artificial intelligence.Statistical method is one of the most classic methods, and Bayesian classification is widely used in statistical method because of its convenience and good classification effect.

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Lee, Michael D. "Bayesian methods for analyzing true-and-error models." Judgment and Decision Making 13, no. 6 (November 2018): 622–35. http://dx.doi.org/10.1017/s193029750000663x.

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AbstractBirnbaum and Quispe-Torreblanca (2018) evaluated a set of six models developed under true-and-error theory against data in which people made choices in repeated gambles. They concluded the three models based on expected utility theory were inadequate accounts of the behavioral data, and argued in favor of the simplest of the remaining three more general models. To reach these conclusions, they used non-Bayesian statistical methods: frequentist point estimation of parameters, bootstrapped confidence intervals of parameters, and null hypothesis significance testing of models. We address the same research goals, based on the same models and the same data, using Bayesian methods. We implement the models as graphical models in JAGS to allow for computational Bayesian analysis. Our results are based on posterior distribution of parameters, posterior predictive checks of descriptive adequacy, and Bayes factors for model comparison. We compare the Bayesian results with those of Birnbaum and Quispe-Torreblanca (2018). We conclude that, while the very general conclusions of the two approaches agree, the Bayesian approach offers better detailed answers, especially for the key question of the evidence the data provide for and against the competing models. Finally, we discuss the conceptual and practical advantages of using Bayesian methods in judgment and decision making research highlighted by this case study.

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Brunier, Hazel C., and John Whitehead. "Sample sizes for phase ii clinical trials derived from Bayesian decision theory." Statistics in Medicine 13, no. 23-24 (December 15, 1994): 2493–502. http://dx.doi.org/10.1002/sim.4780132312.

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Garrett, K. A., L. V. Madden, G. Hughes, and W. F. Pfender. "New Applications of Statistical Tools in Plant Pathology." Phytopathology® 94, no. 9 (September 2004): 999–1003. http://dx.doi.org/10.1094/phyto.2004.94.9.999.

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The series of papers introduced by this one address a range of statistical applications in plant pathology, including survival analysis, nonparametric analysis of disease associations, multivariate analyses, neural networks, meta-analysis, and Bayesian statistics. Here we present an overview of additional applications of statistics in plant pathology. An analysis of variance based on the assumption of normally distributed responses with equal variances has been a standard approach in biology for decades. Advances in statistical theory and computation now make it convenient to appropriately deal with discrete responses using generalized linear models, with adjustments for overdispersion as needed. New nonparametric approaches are available for analysis of ordinal data such as disease ratings. Many experiments require the use of models with fixed and random effects for data analysis. New or expanded computing packages, such as SAS PROC MIXED, coupled with extensive advances in statistical theory, allow for appropriate analyses of normally distributed data using linear mixed models, and discrete data with generalized linear mixed models. Decision theory offers a framework in plant pathology for contexts such as the decision about whether to apply or withhold a treatment. Model selection can be performed using Akaike's information criterion. Plant pathologists studying pathogens at the population level have traditionally been the main consumers of statistical approaches in plant pathology, but new technologies such as microarrays supply estimates of gene expression for thousands of genes simultaneously and present challenges for statistical analysis. Applications to the study of the landscape of the field and of the genome share the risk of pseudoreplication, the problem of determining the appropriate scale of the experimental unit and of obtaining sufficient replication at that scale.

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Lepora, Nathan F., and Kevin N. Gurney. "The Basal Ganglia Optimize Decision Making over General Perceptual Hypotheses." Neural Computation 24, no. 11 (November 2012): 2924–45. http://dx.doi.org/10.1162/neco_a_00360.

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The basal ganglia are a subcortical group of interconnected nuclei involved in mediating action selection within cortex. A recent proposal is that this selection leads to optimal decision making over multiple alternatives because the basal ganglia anatomy maps onto a network implementation of an optimal statistical method for hypothesis testing, assuming that cortical activity encodes evidence for constrained gaussian-distributed alternatives. This letter demonstrates that this model of the basal ganglia extends naturally to encompass general Bayesian sequential analysis over arbitrary probability distributions, which raises the proposal to a practically realizable theory over generic perceptual hypotheses. We also show that the evidence in this model can represent either log likelihoods, log-likelihood ratios, or log odds, all leading proposals for the cortical processing of sensory data. For these reasons, we claim that the basal ganglia optimize decision making over general perceptual hypotheses represented in cortex. The relation of this theory to cortical encoding, cortico-basal ganglia anatomy, and reinforcement learning is discussed.

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Thapa, Samudrajit, Seongyu Park, Yeongjin Kim, Jae-Hyung Jeon, Ralf Metzler, and Michael A. Lomholt. "Bayesian inference of scaled versus fractional Brownian motion." Journal of Physics A: Mathematical and Theoretical 55, no. 19 (April 12, 2022): 194003. http://dx.doi.org/10.1088/1751-8121/ac60e7.

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Abstract We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion. We include the possibility of measurement noise in both models. We find that for trajectories of a few hundred time points the procedure is able to resolve well the true model and parameters. Using the prior of the synthetic data generation process also for the inference, the approach is optimal based on decision theory. We include a comparison with inference using a prior different from the data generating one.

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Liu, Shun, Qin Xu, and Pengfei Zhang. "Identifying Doppler Velocity Contamination Caused by Migrating Birds. Part II: Bayes Identification and Probability Tests." Journal of Atmospheric and Oceanic Technology 22, no. 8 (August 1, 2005): 1114–21. http://dx.doi.org/10.1175/jtech1758.1.

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Abstract Based on the Bayesian statistical decision theory, a probabilistic quality control (QC) technique is developed to identify and flag migrating-bird-contaminated sweeps of level II velocity scans at the lowest elevation angle using the QC parameters presented in Part I. The QC technique can use either each single QC parameter or all three in combination. The single-parameter QC technique is shown to be useful for evaluating the effectiveness of each QC parameter based on the smallness of the tested percentages of wrong decision by using the ground truth information (if available) or based on the smallness of the estimated probabilities of wrong decision (if there is no ground truth information). The multiparameter QC technique is demonstrated to be much better than any of the three single-parameter QC techniques, as indicated by the very small value of the tested percentages of wrong decision for no-flag decisions (not contaminated by migrating birds). Since the averages of the estimated probabilities of wrong decision are quite close to the tested percentages of wrong decision, they can provide useful information about the probability of wrong decision when the multiparameter QC technique is used for real applications (with no ground truth information).

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Charlton, Julie A., Wiktor F. Młynarski, Yoon H. Bai, Ann M. Hermundstad, and Robbe L. T. Goris. "Environmental dynamics shape perceptual decision bias." PLOS Computational Biology 19, no. 6 (June 8, 2023): e1011104. http://dx.doi.org/10.1371/journal.pcbi.1011104.

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To interpret the sensory environment, the brain combines ambiguous sensory measurements with knowledge that reflects context-specific prior experience. But environmental contexts can change abruptly and unpredictably, resulting in uncertainty about the current context. Here we address two questions: how should context-specific prior knowledge optimally guide the interpretation of sensory stimuli in changing environments, and do human decision-making strategies resemble this optimum? We probe these questions with a task in which subjects report the orientation of ambiguous visual stimuli that were drawn from three dynamically switching distributions, representing different environmental contexts. We derive predictions for an ideal Bayesian observer that leverages knowledge about the statistical structure of the task to maximize decision accuracy, including knowledge about the dynamics of the environment. We show that its decisions are biased by the dynamically changing task context. The magnitude of this decision bias depends on the observer’s continually evolving belief about the current context. The model therefore not only predicts that decision bias will grow as the context is indicated more reliably, but also as the stability of the environment increases, and as the number of trials since the last context switch grows. Analysis of human choice data validates all three predictions, suggesting that the brain leverages knowledge of the statistical structure of environmental change when interpreting ambiguous sensory signals.

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Yang, Jen-Jen, Yen-Ching Chuang, Huai-Wei Lo, and Ting-I. Lee. "A Two-Stage MCDM Model for Exploring the Influential Relationships of Sustainable Sports Tourism Criteria in Taichung City." International Journal of Environmental Research and Public Health 17, no. 7 (March 30, 2020): 2319. http://dx.doi.org/10.3390/ijerph17072319.

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Many countries advocate sports for all to cultivate people’s interest in sports. In cities, cross-industry alliances between sports and tourism are one of the common practices. The following two important issues need to be discussed, namely, what factors should be paid attention to in the development of sports tourism, and what are the mutual influential relationships among these factors. This study proposes a novel two-stage multi-criteria decision-making (MCDM) model to incorporate the concept of sustainable development into sports tourism. First, the Bayesian best–worst method (Bayesian BWM) is used to screen out important criteria. Bayesian BWM solves the problem of expert opinion integration of conventional BWM. It is based on the statistical probability to estimate the optimal group criteria weights. Secondly, the rough decision making trial and evaluation laboratory (rough DEMATEL) technique is used to map out complex influential relationships. The introduction of DEMATEL from the rough set theory has better practicality. In the calculation program, interval types are used to replace crisp values in order to retain more expert information. A city in central Taiwan was used to demonstrate the effectiveness of the model. The results show that the quality of urban security, government marketing, business sponsorship and mass transit planning are the most important criteria. In addition, in conjunction with local festivals is the most influential factor for the overall evaluation system.

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Scales, John A., and Luis Tenorio. "Prior information and uncertainty in inverse problems." GEOPHYSICS 66, no. 2 (March 2001): 389–97. http://dx.doi.org/10.1190/1.1444930.

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Solving any inverse problem requires understanding the uncertainties in the data to know what it means to fit the data. We also need methods to incorporate data‐independent prior information to eliminate unreasonable models that fit the data. Both of these issues involve subtle choices that may significantly influence the results of inverse calculations. The specification of prior information is especially controversial. How does one quantify information? What does it mean to know something about a parameter a priori? In this tutorial we discuss Bayesian and frequentist methodologies that can be used to incorporate information into inverse calculations. In particular we show that apparently conservative Bayesian choices, such as representing interval constraints by uniform probabilities (as is commonly done when using genetic algorithms, for example) may lead to artificially small uncertainties. We also describe tools from statistical decision theory that can be used to characterize the performance of inversion algorithms.

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Huang, Yi Hu, Jin Li Wang, and Xi Mei Jia. "Research of Soccer Robot Target Tracking Algorithm Based on Improved CAMShift." Advanced Materials Research 221 (March 2011): 610–14. http://dx.doi.org/10.4028/www.scientific.net/amr.221.610.

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According to the vision needs of robot soccer and CAMShift tracking inefficient in dynamic background, a new tracking algorithm is brought forward to improve the CAMShift in this paper. A real-time updating background model is build, by traversing the search area for all target pixels to statistic and calculate the color probability distribution of the color target, statistical principles and minimum error rate of Bayesian decision theory are used to achieve a more accurate distinction between the target and the background. By comparing with the CAMShift, the new algorithm provides a better robustness in the soccer robot game and can meet the purposes of fast and accurate tracking.

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Chow, Siu L. "The null-hypothesis significance-test procedure is still warranted." Behavioral and Brain Sciences 21, no. 2 (April 1998): 228–35. http://dx.doi.org/10.1017/s0140525x98591169.

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Entertaining diverse assumptions about empirical research, commentators give a wide range of verdicts on the NHSTP defence in Statistical significance. The null-hypothesis significance-test procedure (NHSTP) is defended in a framework in which deductive and inductive rules are deployed in theory corroboration in the spirit of Popper's Conjectures and refutations (1968b). The defensible hypothetico-deductive structure of the framework is used to make explicit the distinctions between (1) substantive and statistical hypotheses, (2) statistical alternative and conceptual alternative hypotheses, and (3) making statistical decisions and drawing theoretical conclusions. These distinctions make it easier to show that (1) H0 can be true, (2) the effect size is irrelevant to theory corroboration, and (3) “strong” hypotheses make no difference to NHSTP. Reservations about statistical power, meta-analysis, and the Bayesian approach are still warranted.

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Stallard, Nigel. "Sample Size Determination for Phase II Clinical Trials Based on Bayesian Decision Theory." Biometrics 54, no. 1 (March 1998): 279. http://dx.doi.org/10.2307/2534014.

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40

Brown, B. "The choice of variables in multivariate regression: a non-conjugate Bayesian decision theory approach." Biometrika 86, no. 3 (September 1, 1999): 635–48. http://dx.doi.org/10.1093/biomet/86.3.635.

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41

Vasiliev, O. V., E. S. Boyarenko, and K. I. Galaeva. "Substantiation of source data on the parametric algorithms for the classification of weather hazards." Civil Aviation High Technologies 26, no. 6 (December 25, 2023): 8–21. http://dx.doi.org/10.26467/2079-0619-2023-26-6-8-21.

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The meteorological situation is one of the decisive factors determining the safety and frequency of civil aviation flights. Weather hazards (WH), associated with cumulonimbus clouds, such as a heavy shower, thunderstorm, hail, combined with high atmosphere turbulence, quite often lead to aviation events and even accidents. Currently, a domestic weather radar system of the near airfield zone (WR) “Monocle” has been developed and successfully operated. The criteria for the classification of meteorological phenomena (MP), used in the WR, have been developed individually for each phenomenon and have some heuristic character. These criteria are cumbersome and complicate the process of automating the WH classification. In this case, there is a natural desire to generalize the criteria and optimize them in accordance with the theory of distinguishing statistical hypotheses. This article discusses the application of the Bayesian approach to the WH classification. The statistical Bayesian decision theory assumes decision-making in terms of the probability theory when all significant probabilistic values, so-called sufficient statistics, are known. In order to obtain statistical descriptions of the probability distributions of reflectivity and the eddy dissipation rate (EDR), an analysis of radar signals, reflected from such MP as a rain shower, thunderstorm, hail was carried out. The article provides brief descriptions of the methods of conducting experiments to form statistical database and its analysis. Based on the above methods, the statistical parameter H(EDRmax) analysis for a rain shower, the amplitude distribution of reflectivity parameters and the EDR (Zmax, EDRmax) for thunderstorms and hail was carried out, which showed the low distinguishing ability of each individual parameter when solving the problem to classify MP within the assigned alphabet. The obvious solution is dictated by the theory of recognition. To increase the classification confidence, it is essential to share information parameters, for example, in the form of multidimensional distribution densities of the probabilities of random parameters. The article presents a parametric description of the MP “rain shower-thunderstorm-hail” classification features. An analysis to evaluate the probabilistic characteristics of the WH classification for the adopted empirical classification criteria in the WR shows that the adopted criteria are far from optimal in terms of the probabilities of the correct classification, especially in the rain shower case. It is obvious that a problem solution of the assigned classification confidence is associated with the optimization of the feature space and classification criteria. Based on the data obtained, it is necessary to build an algorithm to classify the WH “rain shower-thunderstorm-hail”.

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Mukha, V. S., and N. F. Kako. "Integrals and integral transformations related to the vector Gaussian distribution." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 4 (January 7, 2020): 457–66. http://dx.doi.org/10.29235/1561-2430-2019-55-4-457-466.

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This paper is dedicated to the integrals and integral transformations related to the probability density function of the vector Gaussian distribution and arising in probability applications. Herein, we present three integrals that permit to calculate the moments of the multivariate Gaussian distribution. Moreover, the total probability formula and Bayes formula for the vector Gaussian distribution are given. The obtained results are proven. The deduction of the integrals is performed on the basis of the Gauss elimination method. The total probability formula and Bayes formula are obtained on the basis of the proven integrals. These integrals and integral transformations could be used, for example, in the statistical decision theory, particularly, in the dual control theory, and as table integrals in various areas of research. On the basis of the obtained results, Bayesian estimations of the coefficients of the multiple regression function are calculated.

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Rue, Håvard, and Anne Randi Syversveen. "Bayesian object recognition with baddeley's delta loss." Advances in Applied Probability 30, no. 01 (March 1998): 64–84. http://dx.doi.org/10.1017/s0001867800008089.

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A common problem in Bayesian object recognition using marked point process models is to produce a point estimate of the true underlying object configuration: the number of objects and the size, location and shape of each object. We use decision theory and the concept of loss functions to design a more reasonable estimator for this purpose, rather than using the common zero-one loss corresponding to the maximum a posteriori estimator. We propose to use the squared Δ-metric of Baddeley (1992) as our loss function and demonstrate that the corresponding optimal Bayesian estimator can be well approximated by combining Markov chain Monte Carlo methods with simulated annealing into a two-step algorithm. The proposed loss function is tested using a marked point process model developed for locating cells in confocal microscopy images.

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Domanov, Aleksey. "The Basics of Bayesian Approach to Quantitative Analysis (at the Example of Euroscepticism)." Political Science (RU), no. 1 (2021): 301–21. http://dx.doi.org/10.31249/poln/2021.01.13.

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This article attempts to identify the main assumptions, prerequisites and techniques of the methods developed by some modern statisticians on the basis of T. Bayes' theorem for the purposes of social variables interactions assessment. The author underlined several advantages of the given approach as compared to more traditional quantitative methods and highlighted key research areas subject to evaluation by Bayesian estimates. First of all, this approach is compatible with game and decision theory, event analysis, hidden Markov chains, prediction using neural networks and other predictive algorithms of artificial intelligence. The Bayesian approach differs significantly from traditional statistical methods (first of all, it is focused on finding the most probable, rather than the only true value of the feature coupling coefficient), hence a graphical interpretation was provided for such basic concepts and techniques as probabilistic inference, maximum likelihood estimation and Bayesian confidence network. The described tools were used to test the hypothesis about the impact of life quality decrease on rise in Euroscepticism of EU citizens. ANOVA and correlation analysis of 27 thousand people’s responses to Eurobarometer questions addressed in November-December 2019 attributed strong likelihood to this assumption. Moreover, Bayesian approach allowed for a probabilistic conclusion that this hypothesis is more plausible than the link between Euroscepticism and respondents’ current financial situation (explanatory power of comparison to the past is relatively greater).

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Nemykin, O. I. "ALGORITHM FOR SELECTION OF LAUNCH ELEMENTS IN THE PRESENCE OF A PRIORI INFORMATION ABOUT ITS COMPOSITION AND STRUCTURE." Issues of radio electronics, no. 3 (March 20, 2018): 114–19. http://dx.doi.org/10.21778/2218-5453-2018-3-114-119.

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Traditional methods of the theory of statistical solutions are developed for cases of making single-valued two-alternative or multialternative solutions about the class of an object. Assuming the possibility of ambiguous multi-alternative (in the case of solving the problem of selection of space objects of three-alternative) decisions on the classification of of space objects at the stages of the selection process, a modification of the traditional statistical decision making algorithm is required. Such a modification of the algorithm can be carried out by appropriate selection of the loss function. In the framework of the Bayes approach, an additive loss function is proposed, the structure of which takes into account a priori information on the structure and composition of launch elements in relation to the classes «Launch vehicle» and «spacecraft». The algorithm of decision making is synthesized under the conditions of a priori certainty regarding the probabilistic description of the analyzed situation. It is shown that the problem of verifying three-alternative hypotheses can be reduced to an independent verification of three two-alternative hypotheses, which makes it possible to take particular solutions in the solution process and use a different set of the signs of selection for the formation of solutions for individual classes of space objects. The peculiarities of the implementation of the selection algorithm are discussed in the presence of a priori information and measurement information on starts of a limited volume. The synthesized Bayesian decision making algorithm has the properties necessary to solve the problem of selection of space objects at launch in real conditions in the presence of measuring information specified in the form of a training sample. Its architecture allows to form unambiguous and ambiguous decisions about each space object in the launch.

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Braun, Marie. "The Effectiveness of Actuarial Models in Predicting Insurance Claims in Germany." Journal of Statistics and Actuarial Research 8, no. 2 (July 5, 2024): 42–52. http://dx.doi.org/10.47604/jsar.2763.

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Purpose: The aim of the study was to analyze the effectiveness of actuarial models in predicting insurance claims in Germany. Methodology: This study adopted a desk methodology. A desk study research design is commonly known as secondary data collection. This is basically collecting data from existing resources preferably because of its low cost advantage as compared to a field research. Our current study looked into already published studies and reports as the data was easily accessed through online journals and libraries. Findings: Actuarial models in Germany effectively predict insurance claims by leveraging extensive historical data and advanced statistical techniques. They assess risks like mortality, morbidity, and catastrophic events crucial for pricing and underwriting decisions. Challenges include continuous recalibration for changing conditions and regulatory shifts. Integration of technologies like machine learning enhances their predictive power against complex risk scenarios. Unique Contribution to Theory, Practice and Policy: Theory of Bayesian statistics, theory of generalized linear models (GLMs) & theory of machine learning may be used to anchor future studies on analyze the effectiveness of actuarial models in predicting insurance claims in Germany. Insurers should prioritize investments in data governance frameworks to ensure data accuracy, completeness, and timeliness. Robust data quality assurance practices are essential for optimizing actuarial model effectiveness and decision-making processes. Policymakers should collaborate with industry stakeholders to develop regulatory frameworks that support the adoption of advanced modeling techniques.

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Maiworm, Mario, Peter König, and Brigitte Röder. "Integrative Processing of Perception and Reward in an Auditory Localization Paradigm." Experimental Psychology 58, no. 3 (November 1, 2011): 217–26. http://dx.doi.org/10.1027/1618-3169/a000088.

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Under natural conditions, human beings routinely have to choose among multiple alternatives which are associated with specific outcomes of varying desirability. Typically, decisions are based upon the processing of perceptual input, which introduces additional noise to the system. Bayesian decision theory (BDT) allows us to formalize decision under risk and to predict statistically optimal choice behavior. In the present study, human observers performed a classification task characterized by an extensive amount of perceptual uncertainty (auditory localization). In addition, a spatial reward function was imposed on the task. We set up a BDT model with no free parameters to serve as a benchmark for statistically optimal choices, and tested it against a purely perceptual model and a hybrid, heuristic model. In addition, we tested these three models with free rather than fixed parameters for the perceptual uncertainty and the peak of the reward function. The log likelihoods of the models given the empirical data were determined by means of Monte Carlo simulations. Bayesian model comparison (BMC) revealed that the BDT model with two free parameters was the most plausible among the tested models. The fitted parameter values for the peak of the reward function were consistently smaller than the actual peak reward communicated to the participants. The results are discussed in the context of an internal underweighting of the reward function.

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FELGAER, PABLO, PAOLA BRITOS, and RAMÓN GARCÍA-MARTÍNEZ. "PREDICTION IN HEALTH DOMAIN USING BAYESIAN NETWORKS OPTIMIZATION BASED ON INDUCTION LEARNING TECHNIQUES." International Journal of Modern Physics C 17, no. 03 (March 2006): 447–55. http://dx.doi.org/10.1142/s0129183106008558.

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A Bayesian network is a directed acyclic graph in which each node represents a variable and each arc a probabilistic dependency; they are used to provide: a compact form to represent the knowledge and flexible methods of reasoning. Obtaining it from data is a learning process that is divided in two steps: structural learning and parametric learning. In this paper we define an automatic learning method that optimizes the Bayesian networks applied to classification, using a hybrid method of learning that combines the advantages of the induction techniques of the decision trees (TDIDT-C4.5) with those of the Bayesian networks. The resulting method is applied to prediction in health domain.

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STAUFFER, HOWARD B. "APPLICATION OF BAYESIAN STATISTICAL INFERENCE AND DECISION THEORY TO A FUNDAMENTAL PROBLEM IN NATURAL RESOURCE SCIENCE: THE ADAPTIVE MANAGEMENT OF AN ENDANGERED SPECIES." Natural Resource Modeling 21, no. 2 (April 29, 2008): 264–84. http://dx.doi.org/10.1111/j.1939-7445.2008.00007.x.

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Kilpatrick, Zachary P., Jacob D. Davidson, and Ahmed El Hady. "Uncertainty drives deviations in normative foraging decision strategies." Journal of The Royal Society Interface 18, no. 180 (July 2021): 20210337. http://dx.doi.org/10.1098/rsif.2021.0337.

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Nearly all animals forage to acquire energy for survival through efficient search and resource harvesting. Patch exploitation is a canonical foraging behaviour, but there is a need for more tractable and understandable mathematical models describing how foragers deal with uncertainty. To provide such a treatment, we develop a normative theory of patch foraging decisions, proposing mechanisms by which foraging behaviours emerge in the face of uncertainty. Our model foragers statistically and sequentially infer patch resource yields using Bayesian updating based on their resource encounter history. A decision to leave a patch is triggered when the certainty of the patch type or the estimated yield of the patch falls below a threshold. The time scale over which uncertainty in resource availability persists strongly impacts behavioural variables like patch residence times and decision rules determining patch departures. When patch depletion is slow, as in habitat selection, departures are characterized by a reduction of uncertainty, suggesting that the forager resides in a low-yielding patch. Uncertainty leads patch-exploiting foragers to overharvest (underharvest) patches with initially low (high) resource yields in comparison with predictions of the marginal value theorem. These results extend optimal foraging theory and motivate a variety of behavioural experiments investigating patch foraging behaviour.

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