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hierarchical bayesian inference for Ill-posed problems via variational method

JOURNAL OF COMPUTATIONAL PHYSICS 2010年第19期229卷 7317-7343页

作者： Jin, Bangti Zou, Jun Univ Bremen Ctr Ind Math D-28334 Bremen Germany Chinese Univ Hong Kong Dept Math Shatin Hong Kong Peoples R China

This paper investigates a novel approximate bayesian inference procedure for numerically solving inverse problems. A hierarchical formulation which determines automatically the regularization parameter and the noise level together with the inverse solution is adopted. The framework is of variational type, and it can deliver the inverse solution and regularization parameter together with their uncertainties calibrated. It approximates the posteriori probability distribution by separable distributions based on Kullback-Leibler divergence. Two approximations are derived within the framework, and some theoretical properties, e.g. variance estimate and consistency, are also provided. Algorithms for their efficient numerical realization are described, and their convergence properties are also discussed. Extensions to nonquadratic regularization/nonlinear forward models are also briefly studied. Numerical results for linear and nonlinear Cauchy-type problems arising in heat conduction with both smooth and nonsmooth solutions are presented for the proposed method, and compared with that by Markov chain Monte Carlo. The results illustrate that the variational method can faithfully capture the posteriori distribution in a computationally efficient way. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Variational method hierarchical bayesian inference Inverse problem Uncertainty quantification Cauchy problem

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Comparison of lower limb joint moment and power during turning gait between young and old adults using hierarchical bayesian inference

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JOURNAL OF BIOMECHANICS 2020年 103卷 109702-000页

作者： Fukuda, Yuto Masani, Kei Yamaguchi, Takeshi Tohoku Univ Grad Sch Engn Aoba Ku 6-6-01 Aramaki Aza Aoba Sendai Miyagi 9808579 Japan Univ Toronto Inst Biomat & Biomed Engn Toronto ON Canada Univ Hlth Network KITE Res Inst Toronto Rehabil Inst Toronto ON Canada Tohoku Univ Grad Sch Biomed Engn Aoba Ku 6-6-01 Aramaki Aza Aoba Sendai Miyagi 9808579 Japan

Age-related differences in lower limb joint moment (JM), and joint power QP) during turning remain unclear. The present study investigated age-related differences in lower limb JM and JP during turning between young adults (YAs) and old adults (OAs). We introduced the hierarchical bayesian inference for comparing and identifying differences in JM, angular velocity(omega), and JP at each stance phase in the two age groups. This study included 16 healthy YAs and 16 healthy OAs (8 men and 8 women in each group). Participants performed 90 degrees step turns to the right at a self-selected natural speed. On comparing the age groups, during 90 degrees step turning, the OA group exhibited larger extention hip JM and JP to control (brake) the upper body in the sagittal plane, exhibited larger abductor moment in each lower limb joint for preventing the body from leaning in the frontal plane during the mid-stance phase, and exhibited larger hip JP and omega and smaller ankle JM in the transverse plane to rotate the body during the mid-stance phase. Our findings suggested that the overall reliance on the hip joint to control body motion in each anatomical plane during step turning is higher in the OA group than in the YA group. In addition, the hierarchical bayesian inference is useful for comparing the time courses of JM, omega, and JP. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Turn Aging Joint moment Joint power hierarchical bayesian inference

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Combining discrepancy models with hierarchical bayesian inference for parameter estimation of very ill posed thermal problems

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Journal of Physics: Conference Series 2008年第1期135卷 012013-012013页

作者： Bardot, D. Emery, F. Department of Mechanical Engineering University of Washington Seattle WA 98195-2600 United States

Parameter estimation assumes that the model is an accurate representation of the system being studied and that any deviations are caused by measurement noise. For real experimental data this is often not the case. Clearly, the model will constructed to the highest fidelity by the analyst but when it is deficient, the remedy is not always obvious. One approach is to include a discrepancy function which one hopes will resolve any differences. The paper describes the use of such a function for a very ill posed problem using bayesian inference effected by Markov Chain Monte Carlo sampling.

关键词： Discrepancy Model hierarchical bayesian inference Parameter Estimation

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A hierarchical bayesian model updating method for bridge structures by fusing multi-source information

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STRUCTURAL HEALTH MONITORING-AN INTERNATIONAL JOURNAL 2025年第2期24卷 1292-1310页

作者： Luo, Lanxin Song, Mingming Li, Yixian Sun, Limin Tongji Univ Dept Bridge Engn 1239 Siping Rd Shanghai 200092 Peoples R China Hong Kong Polytech Univ Dept Civil & Environm Engn Hong Kong Peoples R China Tongji Univ State Key Lab Disaster Reduct Civil Engn 1239 Siping Rd Shanghai 200092 Peoples R China Shanghai Qizhi Inst Shanghai Peoples R China

The expanding structural health monitoring (SHM) systems on bridge structures have provided an abundance of multi-source data for finite element model updating (FEMU). The SHM systems on bridges usually include surveillance cameras, vibration sensors (e.g., accelerometers, strain gauges, and displacement sensors), and sometimes a weight-in-motion (WIM) system. Currently, the majority of FEMU studies focus on identified modal parameters derived from vibration data, neglecting the incorporation of video and WIM data in the updating process, which impedes a thorough quantification of uncertainty associated with the structural parameters of interest. Therefore, this paper proposes a hierarchical bayesian FEMU framework to comprehensively integrate a variety of information sources, including videos, WIM, and vibration data. The data features comprise the static deflections of the bridge under traffic load and modal parameters identified from acceleration measurements. The measured static deflections are extracted from raw displacement data using the locally weighted regression and smoothing scatterplots method. Computer vision-based technology is employed to pinpoint the location of vehicle load on the bridge, which is then integrated into a FEM to predict vehicle-load-induced static deflection. A two-stage Markov Chain Monte Carlo sampling approach is proposed to evaluate the high-dimensional posterior distribution efficiently. The effectiveness of the proposed method is demonstrated on a laboratory three-span bridge model. The results show that the hierarchical bayesian FEMU can provide accurate estimation and uncertainty quantification on structural stiffness and mass parameters. The updated model accurately predicts both static deflection and modal parameters, exhibiting model-predicted variability in close alignment with the identified values for observed and unobserved responses. Remarkably, this holds true even for unseen loading conditions which are not included

关键词： finite element model updating hierarchical bayesian inference two-stage stochastic sampling static and dynamic measurements vehicle load identification

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Retain, reactivate or acquire: Can nonprofits reliably use community profiles as an alternative to past donation data?

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JOURNAL OF BUSINESS RESEARCH 2025年 186卷

作者： Sinha, Shameek Malik, Sumit Mahajan, Vijay ter Hofstede, Frenkel Univ Auckland Business Sch Mkt Dept 12 Grafton Rd Sir Owen G Glenn Bldg Auckland Central 1010 New Zealand Univ Liverpool Management Sch Mkt Dept Liverpool L69 3BX England Univ Texas Austin Red McCombs Sch Business John P Harbin Centennial Chair Business Mkt Dept CBA 3-228 B6700) Austin TX 78712 USA Univ Texas Austin Red McCombs Sch Business Mkt Dept Austin TX USA

Nonprofits face the challenge of low response rates to solicitations, leading to unachieved fundraising goals. They face difficulty in retaining active donors, reactivating lapsed donors, and acquiring prospective donors. The challenge often stems from the need for more reliable data for predicting the expected behavior of different groups of donors. Although nonprofits have reliable data relating to past donations from active donors, the data on lapsed donors is limited, and data on prospective donors is nonexistent. We propose that nonprofits can use community-clustered donor profiles to predict the expected donations. Our results validate that predictions based on "actual donation data" and "community donor profiles" are equivalent in accuracy. Drawing insights from the nonprofit marketing and social psychology literature, we suggest that nonprofits can reliably devise targeting strategies for active, lapsed, and prospective donors using community-clustered profiles. We test these predictions using a donation incidence model and conduct several robustness checks.

关键词： Nonprofit organizations Donor groups Community profiles Hazard model hierarchical bayesian inference Predictive analytics

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Mathematical modelling, selection and hierarchical inference to determine the minimal dose in IFNα therapy against myeloproliferative neoplasms

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MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2024年第2期41卷 110-134页

作者： Hermange, Gurvan Vainchenker, William Plo, Isabelle Cournede, Paul-Henry Univ Paris Saclay Lab Math & Informat MICS CentraleSupelec Gif Sur Yvette France Univ Paris Saclay INSERM U1287 INSERM Gustave Roussy Villejuif France Gustave Roussy Villejuif France Univ Paris Saclay Villejuif France

Myeloproliferative neoplasms (MPN) are blood cancers that appear after acquiring a driver mutation in a hematopoietic stem cell. These hematological malignancies result in the overproduction of mature blood cells and, if not treated, induce a risk of cardiovascular events and thrombosis. Pegylated IFN$\alpha $ is commonly used to treat MPN, but no clear guidelines exist concerning the dose prescribed to patients. We applied a model selection procedure and ran a hierarchical bayesian inference method to decipher how dose variations impact the response to the therapy. We inferred that IFN$\alpha $ acts on mutated stem cells by inducing their differentiation into progenitor cells;the higher the dose, the higher the effect. We found that the treatment can induce long-term remission when a sufficient (patient-dependent) dose is reached. We determined this minimal dose for individuals in a cohort of patients and estimated the most suitable starting dose to give to a new patient to increase the chances of being cured.

关键词： model selection hierarchical bayesian inference myeloproliferative neoplasms IFN alpha therapy

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A quadratic hierarchical bayesian dynamic prediction model for infrastructure maintenance

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NONLINEAR DYNAMICS 2014年第1期76卷 609-626页

作者： Cho, Taejun Kim, Seong-Soo Kim, Tae-Soo Daejin Univ Dept Civil Engn Pochon 487711 South Korea Hanbat Natl Univ Dept Architectural Engn Taejon 305719 South Korea

The main objective of this study is the development of a correlation model in dynamic bayesian belief networks (DBBNs) followed by an inverse economic analysis. This is based on a quadratic hierarchical bayesian inference prediction method using Markov chain Monte Carlo simulations. The developed model is implemented to predict the future degradation and maintenance budget for a suspension bridge system. bayesian inference is applied to find the posterior probability density function of the source parameters (damage indices and serviceability), given 10 years maintenance data. The simulated risk prediction under decreased serviceability conditions gives posterior distributions based on a prior distribution and likelihood data updated from annual maintenance tasks. Compared with a conventional linear prediction model, the proposed quadratic model provides highly improved convergence and closeness to the measured data. Finally, the developed inverse DBBN analysis method allows forecasts of future performance and the financial management of complex infrastructures by providing the sensitivity of serviceability and risky factors to the maintenance budgets of structural components and the overall system.

关键词： IDBBN hierarchical bayesian inference MCMC Infrastructure maintenance

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hierarchical bayesian LSTM for Head Trajectory Prediction on Omnidirectional Images

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2022年第11期44卷 7563-7580页

作者： Yang, Li Xu, Mai Guo, Yichen Deng, Xin Gao, Fangyuan Guan, Zhenyu Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China Beihang Univ Sch Cyber Sci & Technol Beijing 100191 Peoples R China

When viewing omnidirectional images (ODIs), viewers can access different viewports via head movement (HM), which sequentially forms head trajectories in spatial-temporal domain. Thus, head trajectories play a key role in modeling human attention on ODIs. In this paper, we establish a large-scale dataset collecting 21,600 head trajectories on 1,080 ODIs. By mining our dataset, we find two important factors influencing head trajectories, i.e., temporal dependency and subject-specific variance. Accordingly, we propose a novel approach integrating hierarchical bayesian inference into long short-term memory (LSTM) network for head trajectory prediction on ODIs, which is called HiBayes-LSTM. In HiBayes-LSTM, we develop a mechanism of Future Intention Estimation (FIE), which captures the temporal correlations from previous, current and estimated future information, for predicting viewport transition. Additionally, a training scheme called hierarchical bayesian inference (HBI) is developed for modeling inter-subject uncertainty in HiBayes-LSTM. For HBI, we introduce a joint Gaussian distribution in a hierarchy, to approximate the posterior distribution over network weights. By sampling subject-specific weights from the approximated posterior distribution, our HiBayes-LSTM approach can yield diverse viewport transition among different subjects and obtain multiple head trajectories. Extensive experiments validate that our HiBayes-LSTM approach significantly outperforms 9 state-of-the-art approaches for trajectory prediction on ODIs, and then it is successfully applied to predict saliency on ODIs.

关键词： Trajectory Head Magnetic heads Hidden Markov models Predictive models Bayes methods Computational modeling Omnidirectional images head trajectory hierarchical bayesian inference

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hierarchical bayesian LASSO for a negative binomial regression

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2016年第11期86卷 2182-2203页

作者： Fu, Shuai SUPSI Dalle Molle Inst Artificial Intelligence Manno Switzerland

Numerous researches have been carried out to explain the relationship between the count data y and numbers of covariates x through a generalized linear model (GLM). This paper proposes a hierarchical bayesian least absolute shrinkage and selection operator (LASSO) solution using six different prior models to the negative binomial regression. Latent variables Z have been introduced to simplify the GLM to a standard linear regression model. The proposed models regard two conjugate zero-mean Normal priors for the regression parameters and three independent priors for the variance: the Exponential, Inverse-Gamma and Scaled Inverse-chi(2) distributions. Different types of priors result in different amounts of shrinkage. A Metropolis-Hastings-within-Gibbs algorithm is used to compute the posterior distribution of the parameters of interest through a data augmentation process. Based on the posterior samples, an original double likelihood ratio test statistic have been proposed to choose the most relevant covariates and shrink the insignificant coefficients to zero. Numerical experiments on a real-life data set prove that bayesian LASSO methods achieved significantly better predictive accuracy and robustness than the classical maximum likelihood estimation and the standard bayesian inference.

关键词： hierarchical bayesian inference LASSO latent variable generalized linear regression negative binomial Markov chain Monte Carlo

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How higher goals are constructed and collapse under stress: A hierarchical bayesian control systems perspective

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NEUROSCIENCE AND BIOBEHAVIORAL REVIEWS 2021年 123卷 257-285页

作者： Goekoop, Rutger de Kleijn, Roy PsyQ Parnassia Grp Dept Anxiety Disorders Early Detect & Intervent Team EDIT Lijnbaan 4 NL-2512 VA The Hague Netherlands Leiden Univ Cognit Psychol Unit Leiden Netherlands

In this paper, we show that organisms can be modeled as hierarchical bayesian control systems with small world and information bottleneck (bow-tie) network structure. Such systems combine hierarchical perception with hierarchical goal setting and hierarchical action control. We argue that hierarchical bayesian control systems produce deep hierarchies of goal states, from which it follows that organisms must have some form of 'highest goals'. For all organisms, these involve internal (self) models, external (social) models and overarching (normative) models. We show that goal hierarchies tend to decompose in a top-down manner under severe and prolonged levels of stress. This produces behavior that favors short-term and self-referential goals over long term, social and/or normative goals. The collapse of goal hierarchies is universally accompanied by an increase in entropy (disorder) in control systems that can serve as an early warning sign for tipping points (disease or death of the organism). In humans, learning goal hierarchies corresponds to personality development (maturation). The failure of goal hierarchies to mature properly corresponds to personality deficits. A top-down collapse of such hierarchies under stress is identified as a common factor in all forms of episodic mental disorders (psychopathology). The paper concludes by discussing ways of testing these hypotheses empirically.

关键词： Organisms Human behavior hierarchical bayesian control systems Machine learning Biological networks Network theory Information bottleneck structure Bow-tie motif Variational auto-encoders hierarchical bayesian inference Free energy Active inference Entropy Goal-directed learning Goal hierarchy Higher goals Moral functioning Stress Personality Mental disorders Psychopathology

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