Articles de revues : « Bayesian-Entropy method »

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Orton, T. G., et R. M. Lark. « The Bayesian maximum entropy method for lognormal variables ». Stochastic Environmental Research and Risk Assessment 23, n^o 3 (6 février 2008) : 319–28. http://dx.doi.org/10.1007/s00477-008-0217-7.

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Yu, Jiao, Wenhao Gui et Yuqi Shan. « Statistical Inference on the Shannon Entropy of Inverse Weibull Distribution under the Progressive First-Failure Censoring ». Entropy 21, n^o 12 (10 décembre 2019) : 1209. http://dx.doi.org/10.3390/e21121209.

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Entropy is an uncertainty measure of random variables which mathematically represents the prospective quantity of the information. In this paper, we mainly focus on the estimation for the parameters and entropy of an Inverse Weibull distribution under progressive first-failure censoring using classical (Maximum Likelihood) and Bayesian methods. For Bayesian approaches, the Bayesian estimates are obtained based on both asymmetric (General Entropy, Linex) and symmetric (Squared Error) loss functions. Due to the complex form of Bayes estimates, we cannot get an explicit solution. Therefore, the Lindley method as well as Importance Sampling procedure is applied. Furthermore, using Importance Sampling method, the Highest Posterior Density credible intervals of entropy are constructed. As a comparison, the asymptotic intervals of entropy are also gained. Finally, a simulation study is implemented and a real data set analysis is performed to apply the previous methods.

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Liao, Kuo-Wei, Jia-Jun Guo, Jen-Chen Fan, Chien Huang et Shao-Hua Chang. « Estimation of Soil Depth Using Bayesian Maximum Entropy Method ». Entropy 21, n^o 1 (15 janvier 2019) : 69. http://dx.doi.org/10.3390/e21010069.

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Soil depth plays an important role in landslide disaster prevention and is a key factor in slopeland development and management. Existing soil depth maps are outdated and incomplete in Taiwan. There is a need to improve the accuracy of the map. The Kriging method, one of the most frequently adopted estimation approaches for soil depth, has room for accuracy improvements. An appropriate soil depth estimation method is proposed, in which soil depth is estimated using Bayesian Maximum Entropy method (BME) considering space distribution of measured soil depth and impact of physiographic factors. BME divides analysis data into groups of deterministic and probabilistic data. The deterministic part are soil depth measurements in a given area and the probabilistic part contains soil depth estimated by a machine learning-based soil depth estimation model based on physiographic factors including slope, aspect, profile curvature, plan curvature, and topographic wetness index. Accuracy of estimates calculated by soil depth grading, very shallow (<20 cm), shallow (20–50 cm), deep (50–90 cm), and very deep (>90 cm), suggests that BME is superior to the Kriging method with estimation accuracy up to 82.94%. The soil depth distribution map of Hsinchu, Taiwan made by BME with a soil depth error of ±5.62 cm provides a promising outcome which is useful in future applications, especially for locations without soil depth data.

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Wang, Xinjing, et Wenhao Gui. « Bayesian Estimation of Entropy for Burr Type XII Distribution under Progressive Type-II Censored Data ». Mathematics 9, n^o 4 (5 février 2021) : 313. http://dx.doi.org/10.3390/math9040313.

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With the rapid development of statistics, information entropy is proposed as an important indicator used to quantify information uncertainty. In this paper, maximum likelihood and Bayesian methods are used to obtain the estimators of the entropy for a two-parameter Burr type XII distribution under progressive type-II censored data. In the part of maximum likelihood estimation, the asymptotic confidence intervals of entropy are calculated. In Bayesian estimation, we consider non-informative and informative priors respectively, and asymmetric and symmetric loss functions are both adopted. Meanwhile, the posterior risk is also calculated to evaluate the performances of the entropy estimators against different loss functions. In a numerical simulation, the Lindley approximation and the Markov chain Monte Carlo method were used to obtain the Bayesian estimates. In turn, the highest posterior density credible intervals of the entropy were derived. Finally, average absolute bias and mean square error were used to evaluate the estimators under different methods, and a real dataset was selected to illustrate the feasibility of the above estimation model.

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Shi, Yingni, Xuan Zhou, Xiaofeng Yang, Lijian Shi et Sheng Ma. « Merging Satellite Ocean Color Data With Bayesian Maximum Entropy Method ». IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 8, n^o 7 (juillet 2015) : 3294–304. http://dx.doi.org/10.1109/jstars.2015.2425691.

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Shi, Xiaolin, Yimin Shi et Kuang Zhou. « Estimation for Entropy and Parameters of Generalized Bilal Distribution under Adaptive Type II Progressive Hybrid Censoring Scheme ». Entropy 23, n^o 2 (8 février 2021) : 206. http://dx.doi.org/10.3390/e23020206.

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Entropy measures the uncertainty associated with a random variable. It has important applications in cybernetics, probability theory, astrophysics, life sciences and other fields. Recently, many authors focused on the estimation of entropy with different life distributions. However, the estimation of entropy for the generalized Bilal (GB) distribution has not yet been involved. In this paper, we consider the estimation of the entropy and the parameters with GB distribution based on adaptive Type-II progressive hybrid censored data. Maximum likelihood estimation of the entropy and the parameters are obtained using the Newton–Raphson iteration method. Bayesian estimations under different loss functions are provided with the help of Lindley’s approximation. The approximate confidence interval and the Bayesian credible interval of the parameters and entropy are obtained by using the delta and Markov chain Monte Carlo (MCMC) methods, respectively. Monte Carlo simulation studies are carried out to observe the performances of the different point and interval estimations. Finally, a real data set has been analyzed for illustrative purposes.

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Li, Yuanbin. « Bayesian System Reliability Assessment Method with Maximum Entropy as Prior Distribution ». Journal of Information and Computational Science 11, n^o 4 (1 mars 2014) : 1271–79. http://dx.doi.org/10.12733/jics20103002.

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Abe, Sumiyoshi. « Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics ». EPL (Europhysics Letters) 108, n^o 4 (1 novembre 2014) : 40008. http://dx.doi.org/10.1209/0295-5075/108/40008.

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Yari, G., et A. R. Chaji. « Maximum Bayesian entropy method for determining ordered weighted averaging operator weights ». Computers & ; Industrial Engineering 63, n^o 1 (août 2012) : 338–42. http://dx.doi.org/10.1016/j.cie.2012.03.010.

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Liu, Shuhan, et Wenhao Gui. « Estimating the Entropy for Lomax Distribution Based on Generalized Progressively Hybrid Censoring ». Symmetry 11, n^o 10 (1 octobre 2019) : 1219. http://dx.doi.org/10.3390/sym11101219.

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As it is often unavoidable to obtain incomplete data in life testing and survival analysis, research on censoring data is becoming increasingly popular. In this paper, the problem of estimating the entropy of a two-parameter Lomax distribution based on generalized progressively hybrid censoring is considered. The maximum likelihood estimators of the unknown parameters are derived to estimate the entropy. Further, Bayesian estimates are computed under symmetric and asymmetric loss functions, including squared error, linex, and general entropy loss function. As we cannot obtain analytical Bayesian estimates directly, the Lindley method and the Tierney and Kadane method are applied. A simulation study is conducted and a real data set is analyzed for illustrative purposes.

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Granziol, Diego, Binxin Ru, Stefan Zohren, Xiaowen Dong, Michael Osborne et Stephen Roberts. « MEMe : An Accurate Maximum Entropy Method for Efficient Approximations in Large-Scale Machine Learning ». Entropy 21, n^o 6 (31 mai 2019) : 551. http://dx.doi.org/10.3390/e21060551.

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Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally efficient approximations. We showcase the usefulness of the proposed method, its equivalence to constrained Bayesian variational inference and demonstrate its superiority over existing approaches in two applications, namely, fast log determinant estimation and information-theoretic Bayesian optimisation.

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Cheng, Yin-bao, Xiao-huai Chen, Hong-li Li, Zhen-ying Cheng, Rui Jiang, Jing Lü et Hua-dong Fu. « Analysis and Comparison of Bayesian Methods for Measurement Uncertainty Evaluation ». Mathematical Problems in Engineering 2018 (4 juin 2018) : 1–10. http://dx.doi.org/10.1155/2018/7509046.

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Based on the Bayesian principle, the modern uncertainty evaluation methods can fully integrate prior and current sample information, determine the prior distribution according to historical information, and deduce the posterior distribution by integrating prior distribution and the current sample data with the Bayesian model. As such, it is possible to evaluate uncertainty, updating in real time the uncertainty of the measuring instrument according to regular measurement, and timely reflect the latest information on the accuracy of the measurement system. Based on the Bayesian information fusion and statistical inference principle, the model of uncertainty evaluation is established. The maximum entropy principle and the hill-climbing search optimization algorithm are introduced to determine the prior distribution probability density function and the sample information likelihood function. The probability density function of posterior distribution is obtained by the Bayesian formula to achieve the optimization estimation of uncertainty. Three methods of measurement uncertainty evaluation based on Bayesian analysis are introduced: the noninformative prior, the conjugate prior, and the maximum entropy prior distribution. The advantages and limitations of each method are discussed.

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SAITO, KENJI, HIROYUKI SHIOYA et TSUTOMU DA-TE. « A TREATMENT OF USEFULNESS OF KEYWORDS IN FUZZY REQUESTS FOR AN INFORMATION RETRIEVAL SYSTEM WITH BAYESIAN NETWORKS ». International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 07, n^o 04 (août 1999) : 399–406. http://dx.doi.org/10.1142/s0218488599000350.

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We improve a document retrieval method based on the so-called maximum entropy principle proposed by Cooper, and show how to implement this system on a Bayesian network. A Bayesian network is a probabilistic model for expressing probabilistic relations among random variables. We show advantages of a document retrieval system on a Bayesian network in comparison with Cooper's system. The original document retrieval system based on the maximum entropy principle has a drawback: a result of retrieval can not be obtained in some cases. In this paper, we resolve this drawback by fuzzification of user retrieval requests.

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Reyad, Hesham, Adil Younis et Amal Alkhedir. « Quasi-E-Bayesian criteria versus quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian methods for estimating the scale parameter of the Erlang distribution ». International Journal of Advanced Statistics and Probability 4, n^o 1 (10 mai 2016) : 62. http://dx.doi.org/10.14419/ijasp.v4i1.6095.

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This paper proposes a new modification for the E-Bayesian method of estimation to introduce a new technique namely Quasi E-Bayesian method (or briefly QE-Bayesian). The suggested criteria built in replacing the likelihood function by the quasi likelihood function in the E-Bayesian technique. This study is devoted to evaluate the performance of the new method versus the quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian approaches in estimating the scale parameter of the Erlang distribution. All estimators are obtained under symmetric loss function [squared error loss (SELF))] and four different asymmetric loss functions [Precautionary loss function (PLF), entropy loss function (ELF), Degroot loss function (DLF) and quadratic loss function (QLF)]. The properties of the QE-Bayesian estimates are introduced and the relations between the QE-Bayes and quasi-hierarchical Bayes estimates are discussed. Comparisons among all estimators are performed in terms of mean square error (MSE) via Monte Carlo simulation.

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Caticha, Ariel. « Entropy, Information, and the Updating of Probabilities ». Entropy 23, n^o 7 (14 juillet 2021) : 895. http://dx.doi.org/10.3390/e23070895.

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This paper is a review of a particular approach to the method of maximum entropy as a general framework for inference. The discussion emphasizes pragmatic elements in the derivation. An epistemic notion of information is defined in terms of its relation to the Bayesian beliefs of ideally rational agents. The method of updating from a prior to posterior probability distribution is designed through an eliminative induction process. The logarithmic relative entropy is singled out as a unique tool for updating (a) that is of universal applicability, (b) that recognizes the value of prior information, and (c) that recognizes the privileged role played by the notion of independence in science. The resulting framework—the ME method—can handle arbitrary priors and arbitrary constraints. It includes the MaxEnt and Bayes’ rules as special cases and, therefore, unifies entropic and Bayesian methods into a single general inference scheme. The ME method goes beyond the mere selection of a single posterior, and also addresses the question of how much less probable other distributions might be, which provides a direct bridge to the theories of fluctuations and large deviations.

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Hussain, I., J. Pilz et G. Spoeck. « Hierarchical Bayesian space-time interpolation versus spatio-temporal BME approach ». Advances in Geosciences 25 (30 mars 2010) : 97–102. http://dx.doi.org/10.5194/adgeo-25-97-2010.

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Abstract. The restrictions of the analysis of natural processes which are observed at any point in space or time to a purely spatial or purely temporal domain may cause loss of information and larger prediction errors. Moreover, the arbitrary combinations of purely spatial and purely temporal models may not yield valid models for the space-time domain. For such processes the variation can be characterized by sophisticated spatio-temporal modeling. In the present study the composite spatio-temporal Bayesian maximum entropy (BME) method and transformed hierarchical Bayesian space-time interpolation are used in order to predict precipitation in Pakistan during the monsoon period. Monthly average precipitation data whose time domain is the monsoon period for the years 1974–2000 and whose spatial domain are various regions in Pakistan are considered. The prediction of space-time precipitation is applicable in many sectors of industry and economy in Pakistan especially; the agricultural sector. Mean field maps and prediction error maps for both methods are estimated and compared. In this paper it is shown that the transformed hierarchical Bayesian model is providing more accuracy and lower prediction error compared to the spatio-temporal Bayesian maximum entropy method; additionally, the transformed hierarchical Bayesian model also provides predictive distributions.

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Wang, Jing-Qin, Zhi-Gang Zhang, Ching-Hsin Wang et Li Wang. « A Maximum Entropy Multisource Information Fusion Method to Evaluate the MTBF of Low-Voltage Switchgear ». Discrete Dynamics in Nature and Society 2018 (2018) : 1–7. http://dx.doi.org/10.1155/2018/2746871.

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When analyzing the reliability of low-voltage switchgear by Bayesian method, the maximum entropy multisource information fusion method was proposed to obtain the prior information of low-voltage switchgear and then evaluate the reliability. The historical data of low-voltage switchgear was collected and organized from a manufacturer. According to the expert experience and the data, the creditability analysis and the compatibility test were presented by the Smirnov test method. Based on the high creditability and compatibility, the result of the maximum entropy multisource information fusion method is the determination of prior information. Therefore, the distribution type of the prior information was confirmed by using the maximum entropy method, and the parameter of the prior information was received by bootstrap method with MATLAB. Then the posterior distribution was obtained to evaluate the MTBF of low-voltage switchgear. Finally, the historical data of years from 2007 to 2010 was taken as prior information to illustrate the maximum entropy multisource information fusion method and to get the MTBF of low-voltage switchgear. The evaluation result reduces the experimental period and test cost, which is an improvement for the reliability evaluation and management of low-voltage switchgear and also an improvement for other systems with simple sample data. Compared with traditional Bayesian networks, the proposed method can fuse experts experience and historical data and has advantages for the use of prior information effectively.

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Abe, Sumiyoshi. « Bayesian approach to extreme-value statistics based on conditional maximum-entropy method ». Journal of Physics : Conference Series 1113 (novembre 2018) : 012001. http://dx.doi.org/10.1088/1742-6596/1113/1/012001.

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Macaulay, V. A., et B. Buck. « The determination of nuclear charge distributions using a Bayesian maximum entropy method ». Nuclear Physics A 591, n^o 1 (août 1995) : 85–103. http://dx.doi.org/10.1016/0375-9474(95)00125-k.

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Šljivić, Nuša Mikuljan. « Cross-entropy method for estimation of posterior expectation in Bayesian VAR models ». Communications in Statistics - Theory and Methods 46, n^o 23 (29 août 2017) : 11933–47. http://dx.doi.org/10.1080/03610926.2017.1288252.

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Liu, Jianxiao, et Zonglin Tian. « Verification of Three-Phase Dependency Analysis Bayesian Network Learning Method for Maize Carotenoid Gene Mining ». BioMed Research International 2017 (2017) : 1–10. http://dx.doi.org/10.1155/2017/1813494.

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Background and Objective. Mining the genes related to maize carotenoid components is important to improve the carotenoid content and the quality of maize. Methods. On the basis of using the entropy estimation method with Gaussian kernel probability density estimator, we use the three-phase dependency analysis (TPDA) Bayesian network structure learning method to construct the network of maize gene and carotenoid components traits. Results. In the case of using two discretization methods and setting different discretization values, we compare the learning effect and efficiency of 10 kinds of Bayesian network structure learning methods. The method is verified and analyzed on the maize dataset of global germplasm collection with 527 elite inbred lines. Conclusions. The result confirmed the effectiveness of the TPDA method, which outperforms significantly another 9 kinds of Bayesian network learning methods. It is an efficient method of mining genes for maize carotenoid components traits. The parameters obtained by experiments will help carry out practical gene mining effectively in the future.

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Crehuet, Ramon, Pedro J. Buigues, Xavier Salvatella et Kresten Lindorff-Larsen. « Bayesian-Maximum-Entropy Reweighting of IDP Ensembles Based on NMR Chemical Shifts ». Entropy 21, n^o 9 (17 septembre 2019) : 898. http://dx.doi.org/10.3390/e21090898.

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Bayesian and Maximum Entropy approaches allow for a statistically sound and systematic fitting of experimental and computational data. Unfortunately, assessing the relative confidence in these two types of data remains difficult as several steps add unknown error. Here we propose the use of a validation-set method to determine the balance, and thus the amount of fitting. We apply the method to synthetic NMR chemical shift data of an intrinsically disordered protein. We show that the method gives consistent results even when other methods to assess the amount of fitting cannot be applied. Finally, we also describe how the errors in the chemical shift predictor can lead to an incorrect fitting and how using secondary chemical shifts could alleviate this problem.

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Bedouhene, Kahina, et Nabil Zougab. « A Bayesian procedure for bandwidth selection in circular kernel density estimation ». Monte Carlo Methods and Applications 26, n^o 1 (1 mars 2020) : 69–82. http://dx.doi.org/10.1515/mcma-2020-2056.

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AbstractA Bayesian procedure for bandwidth selection in kernel circular density estimation is investigated, when the Markov chain Monte Carlo (MCMC) sampling algorithm is utilized for Bayes estimates. Under the quadratic and entropy loss functions, the proposed method is evaluated through a simulation study and real data sets, which were already discussed in the literature. The proposed Bayesian approach is very competitive in comparison with the existing classical global methods, namely plug-in and cross-validation techniques.

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Lupu, Radu, Adrian Cantemir Călin, Cristina Georgiana Zeldea et Iulia Lupu. « A Bayesian Entropy Approach to Sectoral Systemic Risk Modeling ». Entropy 22, n^o 12 (4 décembre 2020) : 1371. http://dx.doi.org/10.3390/e22121371.

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We investigate the dynamics of systemic risk of European companies using an approach that merges paradigmatic risk measures such as Marginal Expected Shortfall, CoVaR, and Delta CoVaR, with a Bayesian entropy estimation method. Our purpose is to bring to light potential spillover effects of the entropy indicator for the systemic risk measures computed on the 24 sectors that compose the STOXX 600 index. Our results show that several sectors have a high proclivity for generating spillovers. In general, the largest influences are delivered by Capital Goods, Banks, Diversified Financials, Insurance, and Real Estate. We also bring detailed evidence on the sectors that are the most pregnable to spillovers and on those that represent the main contributors of spillovers.

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Fornalski, K. W., G. Parzych, M. Pylak, D. Satuła et L. Dobrzyński. « Application of Bayesian Reasoning and the Maximum Entropy Method to Some Reconstruction Problems ». Acta Physica Polonica A 117, n^o 6 (juin 2010) : 892–99. http://dx.doi.org/10.12693/aphyspola.117.892.

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Zeng, Xiankui, Jichun Wu, Dong Wang, Xiaobin Zhu et Yuqiao Long. « Assessing Bayesian model averaging uncertainty of groundwater modeling based on information entropy method ». Journal of Hydrology 538 (juillet 2016) : 689–704. http://dx.doi.org/10.1016/j.jhydrol.2016.04.038.

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Yu, Hwa-Lung, et Chih-Hsin Wang. « Spatiotemporal Estimation of PM2.5 by Land Use Regression and Bayesian Maximum Entropy Method ». Epidemiology 22 (janvier 2011) : S175—S176. http://dx.doi.org/10.1097/01.ede.0000392214.28391.b3.

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Baroň, Petr, et Jiří Kvita. « Extending the Fully Bayesian Unfolding with Regularization Using a Combined Sampling Method ». Symmetry 12, n^o 12 (17 décembre 2020) : 2100. http://dx.doi.org/10.3390/sym12122100.

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Regularization extensions to the Fully Bayesian Unfolding are implemented and studied with an algorithm of combined sampling to find, in a reasonable computational time, an optimal value of the regularization strength parameter in order to obtain an unfolded result of a desired property, like smoothness. Three regularization conditions using the curvature, entropy and derivatives are applied, as a model example, to several simulated spectra of top-pair quark pairs that are produced in high energy pp collisions. The existence of a minimum of a χ2 between the unfolded and particle-level spectra is discussed, with recommendations on the checks and validity of the usage of the regularization feature in Fully Bayesian Unfolding (FBU).

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Alduais, Fuad. « Comparison of classical and Bayesian estimators to estimate the parameters in Weibull distribution under weighted general entropy loss function ». International Journal of ADVANCED AND APPLIED SCIENCES 8, n^o 3 (mars 2021) : 57–62. http://dx.doi.org/10.21833/ijaas.2021.03.008.

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In this work, we have developed a General Entropy loss function (GE) to estimate parameters of Weibull distribution (WD) based on complete data when both shape and scale parameters are unknown. The development is done by merging weight into GE to produce a new loss function called the weighted General Entropy loss function (WGE). Then, we utilized WGE to derive the parameters of the WD. After, we compared the performance of the developed estimation in this work with the Bayesian estimator using the GE loss function. Bayesian estimator using square error (SE) loss function, Ordinary Least Squares Method (OLS), Weighted Least Squared Method (WLS), and maximum likelihood estimation (MLE). Based on the Monte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s). The results show that the performance of the Bayes estimator under developed method (WGE) loss function is the best for estimating shape parameters in all cases and has good performance for estimating scale parameter.

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Bayat, Bardia, Mohsen Nasseri et Gholamreza Naser. « Improving Bayesian maximum entropy and ordinary Kriging methods for estimating precipitations in a large watershed : a new cluster-based approach ». Canadian Journal of Earth Sciences 51, n^o 1 (janvier 2014) : 43–55. http://dx.doi.org/10.1139/cjes-2013-0062.

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The main purpose of this research is to investigate spatial variations of mean annual precipitation in a watershed. As a case study, the research focused on the Namak Lake watershed in Iran. Literature provides various techniques for studying spatial patterns of precipitation in a watershed. These techniques often require a large dataset. On the other hand, nonuniform data distribution in a watershed can reduce the accuracy and reliability of the predictions. To overcome these problems, this research applied the cluster method coupled with ordinary Kriging and Bayesian maximum entropy techniques. An estimated point was modified based on the distance from the point to the cluster center. The research considered elevation variations as a secondary variable. A cross-validation technique was used for evaluating the results of mean annual precipitations. The research compared the results of ordinary Kriging and Bayesian maximum entropy methods with and without the application of the clustering method. The research concluded that the cluster-based method can estimate the dynamics of long-term mean annual precipitation more reliably and accurately. The research also revealed more informative results for the cluster-based method.

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Hernández, Damián G., et Inés Samengo. « Estimating the Mutual Information between Two Discrete, Asymmetric Variables with Limited Samples ». Entropy 21, n^o 6 (25 juin 2019) : 623. http://dx.doi.org/10.3390/e21060623.

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Determining the strength of nonlinear, statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual information from limited samples is a challenging task. Since the mutual information is the difference of two entropies, the existing Bayesian estimators of entropy may be used to estimate information. This procedure, however, is still biased in the severely under-sampled regime. Here, we propose an alternative estimator that is applicable to those cases in which the marginal distribution of one of the two variables—the one with minimal entropy—is well sampled. The other variable, as well as the joint and conditional distributions, can be severely undersampled. We obtain a consistent estimator that presents very low bias, outperforming previous methods even when the sampled data contain few coincidences. As with other Bayesian estimators, our proposal focuses on the strength of the interaction between the two variables, without seeking to model the specific way in which they are related. A distinctive property of our method is that the main data statistics determining the amount of mutual information is the inhomogeneity of the conditional distribution of the low-entropy variable in those states in which the large-entropy variable registers coincidences.

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ISOZAKI, TAKASHI, NORIJI KATO et MAOMI UENO. « "DATA TEMPERATURE" IN MINIMUM FREE ENERGIES FOR PARAMETER LEARNING OF BAYESIAN NETWORKS ». International Journal on Artificial Intelligence Tools 18, n^o 05 (octobre 2009) : 653–71. http://dx.doi.org/10.1142/s0218213009000342.

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Maximum likelihood method for estimating parameters of Bayesian networks (BNs) is efficient and accurate for large samples. However, the method suffers from overfitting when the sample size is small. Bayesian methods, which are effective to avoid overfitting, present difficulties for determining optimal hyperparameters of prior distributions with good balance between theoretical and practical points of view when no prior knowledge is available. As described in this paper, we propose an alternative estimation method of the parameters on BNs. The method uses a principle, rooted in thermodynamics, of minimizing free energy (MFE). We define internal energies, entropies, and temperature, which constitute free energies. Especially for temperature, we propose a "data temperature" assumption and some explicit models. This approach can treat the maximum likelihood principle and the maximum entropy principle in a unified manner of the MFE principle. For assessments of classification accuracy, our method shows higher accuracy than that obtained using the Bayesian method with normally recommended hyperparameters. Moreover, our method exhibits robustness for the choice of introduced hyperparameters.

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Gzyl, Henryk, et Enrique Ter Horst. « Recovering Decay Rates from Noisy Measurements with Maximum Entropy in the Mean ». Journal of Probability and Statistics 2009 (2009) : 1–13. http://dx.doi.org/10.1155/2009/563281.

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We present a new method, based on the method of maximum entropy in the mean, which builds upon the standard method of maximum entropy, to improve the parametric estimation of a decay rate when the measurements are corrupted by large level of noise and, more importantly, when the number of measurements is small. The method is developed in the context on a concrete example: that of estimation of the parameter in an exponential distribution. We show how to obtain an estimator with the noise filtered out, and using simulated data, we compare the performance of our method with the Bayesian and maximum likelihood approaches.

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Pylak, Maciej, Krzysztof Wojciech Fornalski, Joanna Reszczyńska, Piotr Kukulski, Michael P. R. Waligórski et Ludwik Dobrzyński. « Analysis of Indoor Radon Data Using Bayesian, Random Binning, and Maximum Entropy Methods ». Dose-Response 19, n^o 2 (1 avril 2021) : 155932582110093. http://dx.doi.org/10.1177/15593258211009337.

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Three statistical methods: Bayesian, randomized data binning and Maximum Entropy Method (MEM) are described and applied in the analysis of US radon data taken from the US registry. Two confounding factors—elevation of inhabited dwellings, and UVB (ultra-violet B) radiation exposure—were considered to be most correlated with the frequency of lung cancer occurrence. MEM was found to be particularly useful in extracting meaningful results from epidemiology data containing such confounding factors. In model testing, MEM proved to be more effective than the least-squares method (even via Bayesian analysis) or multi-parameter analysis, routinely applied in epidemiology. Our analysis of the available residential radon epidemiology data consistently demonstrates that the relative number of lung cancers decreases with increasing radon concentrations up to about 200 Bq/m3, also decreasing with increasing altitude at which inhabitants live. Correlation between UVB intensity and lung cancer has also been demonstrated.

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Rothkopf, Alexander. « Bryan’s Maximum Entropy Method—Diagnosis of a Flawed Argument and Its Remedy ». Data 5, n^o 3 (17 septembre 2020) : 85. http://dx.doi.org/10.3390/data5030085.

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The Maximum Entropy Method (MEM) is a popular data analysis technique based on Bayesian inference, which has found various applications in the research literature. While the MEM itself is well-grounded in statistics, I argue that its state-of-the-art implementation, suggested originally by Bryan, artificially restricts its solution space. This restriction leads to a systematic error often unaccounted for in contemporary MEM studies. The goal of this paper is to carefully revisit Bryan’s train of thought, point out its flaw in applying linear algebra arguments to an inherently nonlinear problem, and suggest possible ways to overcome it.

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Rogers, David M. « Protein Conformational States—A First Principles Bayesian Method ». Entropy 22, n^o 11 (31 octobre 2020) : 1242. http://dx.doi.org/10.3390/e22111242.

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Automated identification of protein conformational states from simulation of an ensemble of structures is a hard problem because it requires teaching a computer to recognize shapes. We adapt the naïve Bayes classifier from the machine learning community for use on atom-to-atom pairwise contacts. The result is an unsupervised learning algorithm that samples a ‘distribution’ over potential classification schemes. We apply the classifier to a series of test structures and one real protein, showing that it identifies the conformational transition with >95% accuracy in most cases. A nontrivial feature of our adaptation is a new connection to information entropy that allows us to vary the level of structural detail without spoiling the categorization. This is confirmed by comparing results as the number of atoms and time-samples are varied over 1.5 orders of magnitude. Further, the method’s derivation from Bayesian analysis on the set of inter-atomic contacts makes it easy to understand and extend to more complex cases.

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Li, Aihua, Yanchen Bo, Yuxin Zhu, Peng Guo, Jian Bi et Yaqian He. « Blending multi-resolution satellite sea surface temperature (SST) products using Bayesian maximum entropy method ». Remote Sensing of Environment 135 (août 2013) : 52–63. http://dx.doi.org/10.1016/j.rse.2013.03.021.

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SHINKAWA, Takao, Natuko NAKAMURA, Hiroshi KATO, Kazuyoshi SHIBUYA et Munetaka NAKATA. « Applications of a Bayesian Based Maximum Entropy Method to Energy Dispersive X-ray Spectra ». Journal of the Spectroscopical Society of Japan 54, n^o 4 (2005) : 238–44. http://dx.doi.org/10.5111/bunkou.54.238.

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Zou, Bo, Jingsheng Zhai, Jian Xu, Zhaoxing Li et Sunpei Gao. « A Method for Estimating Dominant Acoustic Backscatter Mechanism of Water-Seabed Interface via Relative Entropy Estimation ». Mathematical Problems in Engineering 2018 (2 décembre 2018) : 1–10. http://dx.doi.org/10.1155/2018/4272436.

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It is important to distinguish the dominant mechanism of seabed acoustic scattering for the quantitative inversion of seabed parameters. An identification scheme is proposed based on Bayesian inversion with the relative entropy used to estimate dominant acoustic backscatter mechanism. DiffeRential Evolution Adaptive Metropolis is used to obtain samples from posterior probability density in Bayesian inversion. Three mechanisms for seabed scattering are considered: scattering from a rough water-seabed interface, scattering from volume heterogeneities, and mixed scattering from both interface roughness and volume heterogeneities. Roughness scattering and volume scattering are modelled based on Fluid Theories using Small-Slope Approximation and Small-Perturbation Fluid Approximation, respectively. The identification scheme is applied to three simulated observation data sets. The results indicate that the scheme is promising and appears capable of distinguishing sediment volume from interface roughness scattering and can correctly identify the dominant acoustic backscatter mechanism.

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Pérez-Sánchez, Belén, Martín González, Carmen Perea et Jose J. López-Espín. « A New Computational Method for Estimating Simultaneous Equations Models Using Entropy as a Parameter Criteria ». Mathematics 9, n^o 7 (24 mars 2021) : 700. http://dx.doi.org/10.3390/math9070700.

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Simultaneous Equations Models (SEM) is a statistical technique widely used in economic science to model the simultaneity relationship between variables. In the past years, this technique has also been used in other fields such as psychology or medicine. Thus, the development of new estimating methods is an important line of research. In fact, if we want to apply the SEM to medical problems with the main goal being to obtain the best approximation between the parameters of model and their estimations. This paper shows a computational study between different methods for estimating simultaneous equations models as well as a new method which allows the estimation of those parameters based on the optimization of the Bayesian Method of Moments and minimizing the Akaike Information Criteria. In addition, an entropy measure has been calculated as a parameter criteria to compare the estimation methods studied. The comparison between those methods is performed through an experimental study using randomly generated models. The experimental study compares the estimations obtained by the different methods as well as the efficiency when comparing solutions by Akaike Information Criteria and Entropy Measure. The study shows that the proposed estimation method offered better approximations and the entropy measured results more efficiently than the rest.

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Ortega, P. A., et D. A. Braun. « A Minimum Relative Entropy Principle for Learning and Acting ». Journal of Artificial Intelligence Research 38 (16 août 2010) : 475–511. http://dx.doi.org/10.1613/jair.3062.

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This paper proposes a method to construct an adaptive agent that is universal with respect to a given class of experts, where each expert is designed specifically for a particular environment. This adaptive control problem is formalized as the problem of minimizing the relative entropy of the adaptive agent from the expert that is most suitable for the unknown environment. If the agent is a passive observer, then the optimal solution is the well-known Bayesian predictor. However, if the agent is active, then its past actions need to be treated as causal interventions on the I/O stream rather than normal probability conditions. Here it is shown that the solution to this new variational problem is given by a stochastic controller called the Bayesian control rule, which implements adaptive behavior as a mixture of experts. Furthermore, it is shown that under mild assumptions, the Bayesian control rule converges to the control law of the most suitable expert.

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Liu, Shuhan, et Wenhao Gui. « Estimating the Parameters of the Two-Parameter Rayleigh Distribution Based on Adaptive Type II Progressive Hybrid Censored Data with Competing Risks ». Mathematics 8, n^o 10 (15 octobre 2020) : 1783. http://dx.doi.org/10.3390/math8101783.

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This paper attempts to estimate the parameters for the two-parameter Rayleigh distribution based on adaptive Type II progressive hybrid censored data with competing risks. Firstly, the maximum likelihood function and the maximum likelihood estimators are derived before the existence and uniqueness of the latter are proven. Further, Bayesian estimators are considered under symmetric and asymmetric loss functions, that is the squared error loss function, the LINEXloss function, and the general entropy loss function. As the Bayesian estimators cannot be obtained explicitly, the Lindley method is applied to compute the approximate Bayesian estimates. Finally, a simulation study is conducted, and a real dataset is analyzed for illustrative purposes.

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Schmidt, Mikkel N., Daniel Seddig, Eldad Davidov, Morten Mørup, Kristoffer Jon Albers, Jan Michael Bauer et Fumiko Kano Glückstad. « Latent profile analysis of human values : What is the optimal number of clusters ? » Methodology 17, n^o 2 (30 juin 2021) : 127–48. http://dx.doi.org/10.5964/meth.5479.

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Latent Profile Analysis (LPA) is a method to extract homogeneous clusters characterized by a common response profile. Previous works employing LPA to human value segmentation tend to select a small number of moderately homogeneous clusters based on model selection criteria such as Akaike information criterion, Bayesian information criterion and Entropy. The question is whether a small number of clusters is all that can be gleaned from the data. While some studies have carefully compared different statistical model selection criteria, there is currently no established criteria to assess if an increased number of clusters generates meaningful theoretical insights. This article examines the content and meaningfulness of the clusters extracted using two algorithms: Variational Bayesian LPA and Maximum Likelihood LPA. For both methods, our results point towards eight as the optimal number of clusters for characterizing distinctive Schwartz value typologies that generate meaningful insights and predict several external variables.

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Chang, Yan. « Efficient two-level image thresholding method based on Bayesian formulation and the maximum entropy principle ». Optical Engineering 41, n^o 10 (1 octobre 2002) : 2487. http://dx.doi.org/10.1117/1.1501094.

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Tang, Shaolei, Xiaofeng Yang, Di Dong et Ziwei Li. « Merging daily sea surface temperature data from multiple satellites using a Bayesian maximum entropy method ». Frontiers of Earth Science 9, n^o 4 (2 septembre 2015) : 722–31. http://dx.doi.org/10.1007/s11707-015-0538-z.

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Knobles, D. P., Preston S. Wilson, William S. Hodgkiss, Lin Wan et Mohsen Badiey. « Bayesian-Maximum Entropy method applied to seabed geoacoustic models using broadband and narrowband acoustic measurements ». Journal of the Acoustical Society of America 142, n^o 4 (octobre 2017) : 2557. http://dx.doi.org/10.1121/1.5014349.

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Tang, Qingxin, Yanchen Bo et Yuxin Zhu. « Spatiotemporal fusion of multiple‐satellite aerosol optical depth (AOD) products using Bayesian maximum entropy method ». Journal of Geophysical Research : Atmospheres 121, n^o 8 (21 avril 2016) : 4034–48. http://dx.doi.org/10.1002/2015jd024571.

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Bonomi, Massimiliano, Carlo Camilloni, Andrea Cavalli et Michele Vendruscolo. « Metainference : A Bayesian inference method for heterogeneous systems ». Science Advances 2, n^o 1 (janvier 2016) : e1501177. http://dx.doi.org/10.1126/sciadv.1501177.

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Modeling a complex system is almost invariably a challenging task. The incorporation of experimental observations can be used to improve the quality of a model and thus to obtain better predictions about the behavior of the corresponding system. This approach, however, is affected by a variety of different errors, especially when a system simultaneously populates an ensemble of different states and experimental data are measured as averages over such states. To address this problem, we present a Bayesian inference method, called “metainference,” that is able to deal with errors in experimental measurements and with experimental measurements averaged over multiple states. To achieve this goal, metainference models a finite sample of the distribution of models using a replica approach, in the spirit of the replica-averaging modeling based on the maximum entropy principle. To illustrate the method, we present its application to a heterogeneous model system and to the determination of an ensemble of structures corresponding to the thermal fluctuations of a protein molecule. Metainference thus provides an approach to modeling complex systems with heterogeneous components and interconverting between different states by taking into account all possible sources of errors.

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Thach, Tien Thanh, et Radim Bris. « Improved new modified Weibull distribution : A Bayes study using Hamiltonian Monte Carlo simulation ». Proceedings of the Institution of Mechanical Engineers, Part O : Journal of Risk and Reliability 234, n^o 3 (25 janvier 2020) : 496–511. http://dx.doi.org/10.1177/1748006x19896740.

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The newly modified Weibull distribution defined in the literature is a model based on combining the Weibull and modified Weibull distributions. It has been demonstrated as the best model for fitting to the bathtub-shaped failure rate data sets. However, another new model based on combining the modified Weibull and Gompertz distributions has been demonstrated later to be even better than the first model. In this article, we have shown how to improve the former model into a better model, and more importantly, we have provided a full Bayesian analysis of the improved model. The Hamiltonian Monte Carlo and cross-entropy methods have been exploited to empower the traditional methods of statistical estimation. Bayes estimators have been obtained using Hamiltonian Monte Carlo for posterior simulations. Bayesian model checking has also been provided in order to check the validation of the model when fitting to real data sets. We have also provided the maximum likelihood estimators of the model parameters using the cross-entropy method to optimize the log-likelihood function. The results derived from the analysis of two well-known data sets show that the improved model is much better than its original form.

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Li, Dawei, Xiaojian Hu, Cheng-jie Jin et Jun Zhou. « Learning to Detect Traffic Incidents from Data Based on Tree Augmented Naive Bayesian Classifiers ». Discrete Dynamics in Nature and Society 2017 (2017) : 1–9. http://dx.doi.org/10.1155/2017/8523495.

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This study develops a tree augmented naive Bayesian (TAN) classifier based incident detection algorithm. Compared with the Bayesian networks based detection algorithms developed in the previous studies, this algorithm has less dependency on experts’ knowledge. The structure of TAN classifier for incident detection is learned from data. The discretization of continuous attributes is processed using an entropy-based method automatically. A simulation dataset on the section of the Ayer Rajah Expressway (AYE) in Singapore is used to demonstrate the development of proposed algorithm, including wavelet denoising, normalization, entropy-based discretization, and structure learning. The performance of TAN based algorithm is evaluated compared with the previous developed Bayesian network (BN) based and multilayer feed forward (MLF) neural networks based algorithms with the same AYE data. The experiment results show that the TAN based algorithms perform better than the BN classifiers and have a similar performance to the MLF based algorithm. However, TAN based algorithm would have wider vista of applications because the theory of TAN classifiers is much less complicated than MLF. It should be found from the experiment that the TAN classifier based algorithm has a significant superiority over the speed of model training and calibration compared with MLF.

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