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approximate bayesian computation for a Dual-Failure-Modes Models and Its Application to Failure Times Data

IEEE ACCESS 2025年 13卷 50635-50651页

作者： Muhammad, Mustapha Abba, Badamasi Xiao, Jinsen Guangdong Univ Petrochem Technol Dept Math Maoming 525000 Peoples R China Cent South Univ Sch Math & Stat Changsha 410083 Peoples R China

In this study, comprehensive approximate bayesian computation (ABC) technique is explored, and develop for an innovative model. We practically demonstrate approximate bayesian computation (ABC)-Gibbs scheme using Kolmogorov-Smirnov as distance function;this method is a simulation-based scheme, which the explicit formulation of the likelihood function is not required, hence, suitable for a complex model or big data, where the "accept-reject" mechanism is required for the posterior computation. The proposed ABC-Gibbs algorithm presents a remarkable computational efficiency and accuracy in simulation studies and practice. Additionally, we utilize an adaptable Weibull related lifetime distribution for the purpose of testing the proposed algorithm. The model was designed for the analysis of complex systems exhibiting bathtub-shaped failure rate, and its termed as the two-parameter-modified-Weibull-Chen (TMWC). Some vital reliability characteristics of the TMWC are derived, applied and thoroughly discussed. The TMWC model show its significance within reliability frameworks, notably presenting a bathtub-shaped failure rate with an extended-flat-region, presenting a distinctive burn-in and wear-out periods. Extensive simulation studies were conducted to evaluate the performance of ABC-Gibbs on TMWC. Results showed that incorporating the KS distance metric lead to significant improvement;as we decreases the tolerance threshold, the ABC posterior converges more accurately to the true posterior, though with a lower acceptance rate. Finally, a practical study involving the modeling of two failure datasets with a bathtub failure rate is presented-namely, the failure times of thirty devices, and the failure times of dielectric insulation in a generator armature. This study confirms the practical efficiency of the TMWC model and the ABC-Gibbs methodology in reliability engineering.

关键词： approximate bayesian computation modified Weibull model failure analysis reliability statistics simulation mean residual life approximate bayesian computation modified Weibull model failure analysis reliability statistics simulation mean residual life

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Using approximate bayesian computation to Calibrate the Model Parameters Characterizing the Autoregulatory Behavior of Microvessels

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2025年第3期41卷 e70023页

作者： Daher, Ali Univ Oxford Inst Biomed Engn Dept Engn Sci Oxford England

This study aims to leverage available experimental data on the myogenic and endothelial responses of the microvessels to calibrate the parameters and refine the functional form of the compliance feedback model. The experimental data used in this study trace the changes in the vessel calibre of individual arteriolar vessels in response to changes in the intraluminal pressure and/or the pressure gradient, which correspond to the myogenic and endothelial mechanisms, respectively. The compliance feedback model was previously developed to characterize the elastic and autoregulatory behavior of microvessels. We devise and employ a two-stage sequential Monte Carlo (MC) approximate bayesian computation (ABC) scheme to obtain the posterior distribution of the model's parameters, such that the final parameter space distribution integrates information from any prior knowledge of the parameters, the model dynamics, and the available experimental data. Furthermore, the calibration scheme provides key insights into the underlying mechanistic features of the dynamical system;namely, the ABC scheme reveals that there is a marked difference in the time constants between the myogenic-induced dilation and constriction. Overall, upon parameter calibration, the computationally low-cost compliance feedback model achieves very good agreement with the experimental measurements, despite limited data availability, demonstrating that the model provides a simple, compact, yet robust and physiologically grounded characterization of the autoregulatory response, all of which are essential attributes to increase the translatability of hemodynamic models into the clinical environment for future clinical applications.

关键词： approximate bayesian computation autoregulation compliance feedback model microvessels parameter calibration

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Stochastic Calibration of Automated Vehicle Car-Following Control: An approximate bayesian computation Approach

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2025年第3期26卷 3115-3127页

作者： Jiang, Jiwan Zhou, Yang Jafarsalehi, Ghazaleh Wang, Xin Ahn, Soyoung Lee, John D. Univ Wisconsin Madison Dept Civil & Environm Engn Madison WI 53706 USA Texas A&M Univ Zachry Dept Civil & Environm Engn College Stn TX 77840 USA Univ Calif Davis Civil & Environm Engn Davis CA 95616 USA Univ Wisconsin Madison Dept Ind & Syst Engn Madison WI 53706 USA

This paper presents a stochastic calibration method based on approximate bayesian computation (ABC). This method is applied to calibrate two car-following control models: linear control and model predictive control (MPC). The method is likelihood-function-free, where the likelihood function is replaced by simulation to approximate the posterior distribution of model parameters. This structure affords flexibility to calibrate posterior joint distributions of complex models, even those without analytical closed forms such as MPC. Two experiments were conducted to evaluate how well the proposed method reproduces: (i) marginal and joint distributions of model parameters, using synthetic data and (ii) vehicle trajectories (acceleration, speed, and position), using field data involving two commercial adaptive cruise control (ACC) systems. The results showed that the ABC method can reproduce marginal and joint distributions reasonably well for the linear controller as well as the non-analytical MPC-based controller, which was previously infeasible. The method can also robustly characterize the commercial ACC behavior at the trajectory level, which suggests that the simple linear controller better describes their behavior.

关键词： Calibration Stochastic processes Modeling Bayes methods Analytical models Trajectory Correlation Roads Predictive models Predictive control Automated vehicles adaptive cruise control stochastic calibration approximate bayesian computation likelihood-free parametric joint distribution

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Inferences for Skew-Wiener Degradation Model: approximate bayesian computation via Gibbs-Step and Model Selection

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IEEE ACCESS 2025年 13卷 32511-32528页

作者： Muhammad, Isyaku Muhammad, Mustapha Ren, Aihua Zhang, Aiqiang Hubei Univ Automot Technol Coll Mech Engn Shiyan 442002 Peoples R China Guangdong Univ Petrochem Technol Dept Math Maoming 525000 Peoples R China

The Skew-Wiener Degradation (SKWD) model presents a novel approach for addressing unit-to-unit variability in degradation processes by integrating the skew-normal distribution into the Wiener process. This study introduces a robust parameter estimation method for the Skew-Wiener model using approximate bayesian computation with Gibbs sampling (ABC-Gibbs), providing an alternative to the Expectation-Maximization (EM) algorithm. ABC-Gibbs offers a computationally efficient, likelihood-free inference approach, particularly well-suited for high-dimensional parameter spaces where direct likelihood calculations are computationally expensive. Through extensive simulations and real-world applications, including laser and LED degradation datasets, the efficiency and practical utility of the proposed method were validated. Additionally, an ABC model choice (ABC-MC) procedure is implemented to compare linear and nonlinear SKWD models, identifying the most suitable model for specific degradation datasets. The findings demonstrate that ABC significantly enhances parameter estimation accuracy, and ABC-MC effectively distinguishes between competing models, making the approach highly valuable for reliability analysis.

关键词： Skew-wiener degradation model approximate bayesian computation drift variables Gibbs sampling model selection Skew-wiener degradation model approximate bayesian computation drift variables Gibbs sampling model selection

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Accounting for contact network uncertainty in epidemic inferences with approximate bayesian computation

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APPLIED NETWORK SCIENCE 2025年第1期10卷 1-25页

作者： Wang, Maxwell H. Onnela, Jukka-Pekka Harvard Univ Dept Biostat 677 Huntington Ave Boston MA 02115 USA

In models of infectious disease dynamics, the incorporation of contact network information allows for the capture of the non-randomness and heterogeneity of realistic contact patterns. Oftentimes, it is assumed that this underlying network is known with perfect certainty. However, in realistic settings, the observed data usually serves as an imperfect proxy of the actual contact patterns in the population. Furthermore, event times in observed epidemics are not perfectly recorded;individual infection and recovery times are often missing. In order to conduct accurate inferences on parameters of contagion spread, it is crucial to incorporate these sources of uncertainty. In this paper, we propose the use of Network-augmented Mixture Density Network-compressed ABC (NA-MDN-ABC) to learn informative summary statistics for the available data. This method will allow for bayesian inference on the parameters of a contagious process, while accounting for imperfect observations on the epidemic and the contact network. We will demonstrate the use of this method on simulated epidemics and networks, and extend this framework to analyze the spread of Tattoo Skin Disease (TSD) among bottlenose dolphins in Shark Bay, Australia.

关键词： Networks approximate bayesian computation SIR model

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Stratified distance space improves the efficiency of sequential samplers for approximate bayesian computation

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computationAL STATISTICS & DATA ANALYSIS 2025年 207卷

作者： Pesonen, Henri Corander, Jukka Oslo Univ Hosp Oslo Ctr Biostat & Epidemiol POB 4950 N-0424 Oslo Norway Univ Oslo Dept Biostat Oslo Norway Wellcome Sanger Inst Parasites & Microbes Hinxton Cambridgeshire England Univ Helsinki Helsinki Inst Informat Technol HIIT Dept Math & Stat Helsinki Finland

approximate bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic rejection sampling ABC algorithm is to use sequential Monte Carlo (ABC SMC) to produce a sequence of proposal distributions adapting towards the posterior, instead of generating values from the prior distribution of the model parameters. Proposal distribution for the subsequent iteration is typically obtained from a weighted set of samples, often called particles, of the current iteration of this sequence. Current methods for constructing these proposal distributions treat all the particles equivalently, regardless of the corresponding value generated by the sampler, which may lead to inefficiency when propagating the information across iterations of the algorithm. To improve sampler efficiency, a modified approach called stratified distance ABC SMC is introduced. The algorithm stratifies particles based on their distance between the corresponding synthetic and observed data, and then constructs distinct proposal distributions for all the strata. Taking into account the distribution of distances across the particle space leads to substantially improved acceptance rate of the rejection sampling. It is shown that further efficiency could be gained by using a newly proposed stopping rule for the sequential process based on the stratified posterior samples and these advances are demonstrated by several examples.

关键词： approximate bayesian computation Importance sampling Likelihood-free inference Sequential Monte Carlo

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approximate bayesian computation methods for daily spatiotemporal precipitation occurrence simulation

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WATER RESOURCES RESEARCH 2017年第4期53卷 3352-3372页

作者： Olson, Branden Kleiber, William Univ Washington Dept Stat Seattle WA 98195 USA Univ Colorado Dept Appl Math Boulder CO 80309 USA

Stochastic precipitation generators (SPGs) produce synthetic precipitation data and are frequently used to generate inputs for physical models throughout many scientific disciplines. Especially for large data sets, statistical parameter estimation is difficult due to the high dimensionality of the likelihood function. We propose techniques to estimate SPG parameters for spatiotemporal precipitation occurrence based on an emerging set of methods called approximate bayesian computation (ABC), which bypass the evaluation of a likelihood function. Our statistical model employs a thresholded Gaussian process that reduces to a probit regression at single sites. We identify appropriate ABC penalization metrics for our model parameters to produce simulations whose statistical characteristics closely resemble those of the observations. Spell length metrics are appropriate for single sites, while a variogram-based metric is proposed for spatial simulations. We present numerical case studies at sites in Colorado and Iowa where the estimated statistical model adequately reproduces local and domain statistics. Plain Language Summary Statistical simulations of precipitation and other weather quantities are commonly used in many sciences. Modern datasets are extremely high dimensional, which challenge traditional model estimation paradigms. We propose a novel technique specially adapted for estimation using approximate bayesian computation (ABC), and show how important characteristics such as dry and wet spells can be used to quantify uncertain model parameters. The proposed method offers promising future directions for further research.

关键词： stochastic weather generators approximate bayesian computation bayesian inference precipitation simulation Gaussian processes uncertainty quantification

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approximate bayesian computation using Markov Chain Monte Carlo simulation: DREAM_(ABC)

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WATER RESOURCES RESEARCH 2014年第8期50卷 6767-6787页

作者： Sadegh, Mojtaba Vrugt, Jasper A. Univ Calif Irvine Dept Civil & Environm Engn Irvine CA 92697 USA Univ Calif Irvine Dept Earth Syst Sci Irvine CA USA Forschungszentrum Julich IBG Agrosphere 3 D-52425 Julich Germany

The quest for a more powerful method for model evaluation has inspired Vrugt and Sadegh (2013) to introduce likelihood-free inference as vehicle for diagnostic model evaluation. This class of methods is also referred to as approximate bayesian computation (ABC) and relaxes the need for a residual-based likelihood function in favor of one or multiple different summary statistics that exhibit superior diagnostic power. Here we propose several methodological improvements over commonly used ABC sampling methods to permit inference of complex system models. Our methodology entitled DREAM((ABC)) uses the DiffeRential Evolution Adaptive Metropolis algorithm as its main building block and takes advantage of a continuous fitness function to efficiently explore the behavioral model space. Three case studies demonstrate that DREAM((ABC)) is at least an order of magnitude more efficient than commonly used ABC sampling methods for more complex models. DREAM((ABC)) is also more amenable to distributed, multi-processor, implementation, a prerequisite to diagnostic inference of CPU-intensive system models.

关键词： approximate bayesian computation Markov chain Monte Carlo Population Monte Carlo hydrologic modeling

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approximate bayesian computation (ABC) method for estimating parameters of the gamma process using noisy data

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2020年 198卷

作者： Hazra, Indranil Pandey, Mahesh D. Manzana, Noldainerick Univ Waterloo Dept Civil & Environm Engn 200 Univ Ave West Waterloo ON N2L 3G1 Canada

The stochastic gamma process (GP) has emerged as a versatile model of degradation processes affecting the performance of engineering structures and components. The GP model captures the temporal uncertainty in the degradation process, whereas the bayesian approach is used to account for uncertainty in the model parameters. Although the conceptual approach to GP parameter estimation is straightforward, its practical implementation is quite challenging. The reason is that degradation data required for parameter estimation are invariably contaminated by measurement noise, which turns the likelihood function into a high-dimensional multivariate integral. To circumvent this difficulty, the paper presents a novel and practical approach based on the approximate bayesian computation (ABC) technique. The ABC method is a simulation-based approach that does not require an explicit formulation of the likelihood function. Instead, ABC uses an "accept-reject" mechanism to perform the posterior computation. To reduce the rejection rate, the Markov chain Monte Carlo (MCMC) approach is used within the ABC algorithm. The proposed ABC-MCMC algorithm is shown to be computationally more efficient than the traditional likelihood-based method without compromising the numerical accuracy. A case study involving the modelling of corrosion in nuclear piping systems is presented, which confirms the practical usefulness of the proposed method.

关键词： Stochastic degradation modelling Gamma process bayesian inference Parameter estimation Likelihood-free inference approximate bayesian computation Markov chain Monte Carlo Metropolis-Hastings algorithm

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approximate bayesian computation schemes for parameter inference of discrete stochastic models using simulated likelihood density

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BMC BIOINFORMATICS 2014年第12期15卷 1-10页

作者： Wu, Qianqian Smith-Miles, Kate Tian, Tianhai Monash Univ Sch Math Sci Melbourne Vic 3004 Australia

Background: Mathematical modeling is an important tool in systems biology to study the dynamic property of complex biological systems. However, one of the major challenges in systems biology is how to infer unknown parameters in mathematical models based on the experimental data sets, in particular, when the data are sparse and the regulatory network is stochastic. Results: To address this issue, this work proposed a new algorithm to estimate parameters in stochastic models using simulated likelihood density in the framework of approximate bayesian computation. Two stochastic models were used to demonstrate the efficiency and effectiveness of the proposed method. In addition, we designed another algorithm based on a novel objective function to measure the accuracy of stochastic simulations. Conclusions: Simulation results suggest that the usage of simulated likelihood density improves the accuracy of estimates substantially. When the error is measured at each observation time point individually, the estimated parameters have better accuracy than those obtained by a published method in which the error is measured using simulations over the entire observation time period.

关键词： approximate bayesian computation Discrepancy Tolerance Sequential Monte Carlo Stochastic Simulation Algorithm bayesian Inference Method

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