Metropolis-Hastings Research Articles

Bayesian model updating of super high‐rise building for construction simulation

SummaryA finite element model was established using SAP2000 software for the C1 tower, a super high‐rise building in the second phase of the Nanjing Financial City project, and the construction process of the tower was simulated. The C1 tower adopts a frame core tube extension arm and ring truss structure system, with 87 floors above ground and five floors underground. The roof structure has an elevation of 416.6 m. Precise measurements of inter‐story compression deformation were conducted using advanced surveying equipment. Sensitivity analysis, based on the finite difference method, identified the shear wall elastic modulus, frame column elastic modulus, steel beam elastic modulus, and shear wall unit weight as four highly influential parameters. Employing the Bayesian principle, the Markov Chain Monte Carlo (MCMC) method was applied to determine the posterior density probability function of the parameters targeted for modification. Subsequently, the Metropolis–Hastings (MH) sampling algorithm was employed to refine the C1 Tower model. This refinement significantly reduced the root mean square error between the measured and simulated vertical displacements, achieving an error reduction of approximately 10% from 6.082 to around 2.160. The modified material parameters, for the most part, adhered to a normal distribution assumption and exhibited mean values in the posterior probability density functions for the elastic modulus of Q345 steel beams, C70 frame columns, and C60 shear walls. Compared to the initial finite element parameters, the variation range was approximately 13% to 17%. These results serve as a validation of the effectiveness of the proposed method.

Numerical analyses of M31 dark matter profiles

In this paper, we reproduce the rotation curve of the Andromeda galaxy (M31) by taking into account its bulge, disk and halo components, considering the last one to contain the major part of dark matter mass. Hence, our prescription is to split the galactic bulge into two components, namely, the inner and main bulges, respectively. Both bulges are thus modeled by exponential density profiles since we underline that the widely accepted de Vaucouleurs law fails to reproduce the whole galactic bulge rotation curve. In addition, we adopt various well-known phenomenological dark matter profiles to estimate the dark matter mass in the halo region. Moreover, we apply the least-squares fitting method to determine from the rotation curve the model free parameters, namely, the characteristic (central) density, scale radius and consequently the total mass. To do so, we perform Markov chain Monte Carlo statistical analyses based on the Metropolis algorithm, maximizing our likelihoods adopting velocity and radii data points of the rotation curves. We do not fit separately the components for bulges, disk and halo, but we perform an overall fit including all the components and employing all the data points. Thus, we critically analyze our corresponding findings and, in particular, we employ the Bayesian information criterion to assess the most accredited model to describe M31 dark matter dynamics.

An improved sequential insertion algorithm and tabu search to vehicle routing problem with time windows

The vehicle routing problem (VRP) is a well-researched problem in the operations re- search literature. This paper studies a vehicle routing problem with time windows. Based on Solomon’s research, an improved sequential initialization algorithm, Solomon i1 with DTWC (Solomon i1 with Dynamic Time Windows Compatibility), is proposed in this paper to construct feasible initial solutions with higher quality in less calculation time. A tabu search with VNS (Variable Neighborhood Search) and the Metropolis criterion is used to further optimize the solutions that the proposed initialization algorithm provides. We run computational experiments on cases of well-known problems. Results show that compared to the initialization method before the change, our improved initialization approach performs well in terms of providing a better feasible initialization solution in less time, with an average 10% improvement in solution quality and an average 34% computational time savings. The proposed initialization algorithm’s superiority is also demonstrated by the tabu search’s better performance on the initial solutions it produces.

COMPARISON OF APARCH-TYPE MODELS: DOES THE CONTINUOUS AND JUMP COMPONENTS OF REALIZED VOLATILITY IMPROVE THE FITTING?

This study aims to extend an APARCH-X(1,1) model to the APARCH-CJ(1,1) by separating the exogenous variable X into two components: continuous and discontinuous (jump). The study was based on the application of models to 1-min intraday high-frequency data from the Tokyo Stock Price Index from 2004 to 2011, where its dependent variable is daily return and its exogenous variability is Realized Volatility. As a basic framework, the return errors follow a Normal distribution. An Adaptive Random Walk Metropolis (ARWM) method was constructed in the Markov Chain Monte Carlo algorithm to estimate model parameters so that the model fits the observed return time series. By visual inspection, the parameter trace plots showed good convergence of the Markov chains, indicating that the ARWM method is efficient in estimating the studied models. Based on the results of the Akaike Information Criterion for model fitting to data, this study found that APARCH-CJ(1,1) is inferior to APARCH(1,1).

Prediction of bridge structure deformation and strain based on dynamic testing and intelligent algorithms

The field load test is a direct and effective method for evaluating the performance of bridge structures. However, existing bridge field static load tests are costly and inefficient; moreover, they obstruct traffic and cause unavoidable damage to the bridge structure. As an alternative the the static load test, a random model update method based on bridge dynamic load tests and the Bayesian inference is proposed in this paper. The bridge static load test results were predicted with a high accuracy. To speed up the Bayesian method to infer the posterior probability density of the updated parameters, the Gaussian process was used in place of the finite element model, and the Bayesian inference used the Markov chain Monte Carlo method based on the delayed rejection adaptive Metropolis algorithm. First, the parameters to be modified for the bridge structure analysis model were determined based on the global sensitivity analysis method. Second, a uniform design sampling method was used to establish the Gaussian process optimization model to update the random model of the bridge structure. Finally, a reinforced concrete truss arch bridge was used to verify the correctness of the static load results of the bridge predicted by the random model update method based on dynamic load testing and Bayesian inference. The research results reveal that the prediction results of the bridge static load test based on the dynamic load test and Bayesian inference method agree with the actual test results.

Critical dynamics of cluster algorithms in the random-bond Ising model.

In the present work, we present an extensive Monte Carlo simulation study on the dynamical properties of the two-dimensional random-bond Ising model. The correlation time τ of the Swendsen-Wang and Wolff cluster algorithms is calculated at the critical point. The dynamic critical exponent z of both algorithms is also measured by using the numerical data for several lattice sizes up to L=512. It is found for both algorithms that the autocorrelation time decreases considerably and the critical slowing-down effect reduces upon the introduction of bond disorder. Additionally, simulations with the Metropolis algorithm are performed, and the critical slowing-down effect is observed to be more pronounced in the presence of disorder, confirming the previous findings in the literature. Moreover, the existence of the non-self-averaging property of the model is demonstrated by calculating the scaled form of the standard deviation of autocorrelation times. Finally, the critical exponent ratio of the magnetic susceptibility is estimated by using the average cluster size of the Wolff algorithm.

A new factor analysis model for factors obeying a Gamma distribution

The traditional factor analysis model assumes that the factors obey a normal distribution, which is not appropriate in fields whose data are nonnegative. For this kind of problem, we construct a more practical factor model, assuming that the factors obey a Gamma distribution. We develop a new factor analysis model and discuss its true loading matrix. Then we study its parameter estimation with the maximum likelihood estimation (MLE) method based on an Expectation-Maximization (EM) algorithm, where step E is realized by the Metropolis-Hastings (M-H) algorithm in the Markov Chain Monte Carlo (MCMC) method. We use the new model to empirically study real data, and evaluate its information extraction ability, using the defined true loading matrix to calculate the true loading of the factor. We compare the new model and traditional factor analysis models on simulated and real data, respectively, whose results show that the new model has better information extraction ability for nonnegative data when the number of factors is the same.

On the reliable estimation of sequential Monod kinetic parameters

While dozens of studies have attempted to estimate the Monod kinetic parameters of microbial reductive dechlorination, published values in the literature vary by 2–6 orders of magnitude. This lack of consensus can be attributed in part to limitations of both experimental design and parameter estimation techniques. To address these issues, Hamiltonian Monte Carlo was used to produce more than one million sets of realistic simulated microcosm data under a variety of experimental conditions. These data were then employed in model fitting experiments using a number of parameter estimation algorithms for determining Monod kinetic parameters. Analysis of data from conventional triplicate microcosms yielded parameter estimates characterized by high collinearity, resulting in poor estimation accuracy and precision. Additionally, confidence intervals computed by commonly used classical regression analysis techniques contained true parameter values much less frequently than their nominal confidence levels. Use of an alternative experimental design, requiring the same number of analyses as conventional experiments but comprised of microcosms with varying initial chlorinated ethene concentrations, is shown to result in order-of-magnitude decreases in parameter uncertainty. A Metropolis algorithm which can be run on a typical personal computer is demonstrated to return more reliable parameter interval estimates.

Evaluation and optimisation of the soil carbon turnover routine in the MONICA model (version 3.3.1)

Abstract. Simulation models are tools commonly used to predict changes in soil carbon stocks. Prior validation is essential, however, for determining the reliability and applicability of model results. In this study, the process-based biogeochemical model MONICA (Model of Nitrogen and Carbon dynamics on Agro-ecosystems) was evaluated with respect to soil organic carbon (SOC), using long-term monitoring data from 46 German agricultural sites. A revision and parameterisation of equations, encompassing crop- and fertiliser-specific C contents and the abiotic factors of soil temperature, soil water and clay content, were undertaken and included in the model. The modified version was also used for a Morris elementary effects screening method, which confirmed the importance of environmental and management factors to the model's performance. The model was then calibrated by means of Bayesian inference, using the Metropolis–Hastings algorithm. The performance of the MONICA model was compared with that of five established carbon turnover models (CCB, CENTURY, C-TOOL, ICBM and RothC). The original MONICA model systematically overestimated SOC decomposition rates and produced on average a ∼17 % greater mean absolute error (MAE) than the other models. The modification and calibration significantly improved its performance, reducing the MAE by ∼30 %. Consequently, MONICA outperformed CENTURY, CCB and C-TOOL, and produced results comparable with ICBM and RothC. Use of the modified model allowed mostly adequate reproduction of site-specific SOC stocks, while the availability of a nitrogen, plant growth and water submodel enhanced its applicability when compared with models that only describe carbon dynamics.

Critical behavior, structural, electronic, and magnetic properties of the Heusler alloy: CoFeCrP

In this work, we study the equiatomic quaternary Heusler alloy (EQHA) CoFeCrP using two methods: density functional theory (DFT) and Monte Carlo simulations. The DFT method allowed us to illustrate the structural, electronic, and magnetic properties of this alloy. The ground state phase diagrams have been presented to show the stable configurations in different physical parameter planes. On the other hand, the Monte Carlo simulations, performed under the Metropolis algorithm, permitted to deduce the critical the behavior of the EQHA CoFeCrP. The structural properties results show that the phase of type I, of this alloy is the most stable configuration. In addition, the band structures and density of states calculations results show that this compound exhibits a half-metallic character with a 100% of spin polarization (SP) at the Fermi-level. The total magnetic moment of the Heusler compound is found to be 4.00 µB. Moreover, it is found that the Slater-Pauling is well described for this alloy. Our results show that this material is a potential candidate for the spintronic applications. This is due to its half-metallicity, its high spin moments, its complete SP polarization, and its high Curie temperature.

Impact of conditional modelling for a universal autoregressive quantum state

We present a generalized framework to adapt universal quantum state approximators, enabling them to satisfy rigorous normalization and autoregressive properties. We also introduce filters as analogues to convolutional layers in neural networks to incorporate translationally symmetrized correlations in arbitrary quantum states. By applying this framework to the Gaussian process state, we enforce autoregressive and/or filter properties, analyzing the impact of the resulting inductive biases on variational flexibility, symmetries, and conserved quantities. In doing so we bring together different autoregressive states under a unified framework for machine learning-inspired ansätze. Our results provide insights into how the autoregressive construction influences the ability of a variational model to describe correlations in spin and fermionic lattice models, as well as ab initio electronic structure problems where the choice of representation affects accuracy. We conclude that, while enabling efficient and direct sampling, thus avoiding autocorrelation and loss of ergodicity issues in Metropolis sampling, the autoregressive construction materially constrains the expressivity of the model in many systems.

Adaptive population-based simulated annealing for resource constrained job scheduling with uncertainty

Transporting ore from mines to ports is of significant interest in mining supply chains. These operations are commonly associated with growing costs and a lack of resources. Large mining companies are interested in optimally allocating resources to reduce operational costs. This problem has been previously investigated as resource constrained job scheduling (RCJS). While a number of optimisation methods have been proposed to tackle the deterministic problem, the uncertainty associated with resource availability, an inevitable challenge in mining operations, has received less attention. RCJS with uncertainty is a hard combinatorial optimisation problem that is challenging for existing optimisation methods. We propose an adaptive population-based simulated annealing algorithm that can overcome existing limitations of methods for RCJS with uncertainty, including pre-mature convergence, excessive number of hyper-parameters, and the inefficiency in coping with different uncertainty levels. This new algorithm effectively balances exploration and exploitation, by using a population, modifying the cooling schedule in the Metropolis-Hastings algorithm, and using an adaptive mechanism to select perturbation operators. The results show that the proposed algorithm outperforms existing methods on a benchmark RCJS dataset considering different uncertainty levels. Moreover, new best known solutions are discovered for all but one problem instance across all uncertainty levels.

A DiffeRential Evolution Adaptive Metropolis (DREAM)-based inverse model for continuous release source identification in river pollution incidents: Quantitative evaluation and sensitivity analysis

The identification of continuous pollution sources for rivers is of great concern for emergency response. Most studies focused on instantaneous river pollution sources and associated incidents. There is a dire need to address continuous pollution sources, as pollutant discharge may impose a major impact on the water ecosystem. Therefore, in this study, a novel inverse model is proposed to identify the continuous point sources in river pollution incidents that would estimate the source strength, location, release time, and spill time. The proposed inverse model combines the advanced DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm and the forward transport advection-dispersion equation to infer the posterior probability distribution of source parameters for quantifying uncertainties. In addition, the performance of the DREAM-based model is compared with those of the Metropolis-Hastings (MH)-based and genetic algorithm (GA)-based models. The results show that the DREAM-based model performs accurately for both the hypothetical and the field tracer cases. The comparative analysis shows that the DREAM-based model performs better in saving computation time, improving the accuracy of results, and reconstructing pollutant concentrations. Observation errors significantly influence the accuracy of the identification results from the DREAM-based model. In addition, a comprehensive sensitivity analysis of the DREAM-based model is conducted. The identification results from the DREAM-based model are sensitive to the dispersion coefficient and river velocity. The accuracy of the inverse model could be improved by increasing the monitoring number and by monitoring locations closer to the spill site. The findings of this study can improve decision-making during emergency responses to sudden river pollution incidents.

Statistical inference of inverted Nadarajah–Haghighi distribution under type-II generalized hybrid censoring competing risks data

Tahir et al. (J Stat Comput Simul 88(14):2775–2798, 2018) introduced the inverse Nadarajah–Haghighi distribution (INHD) and demonstrated its ability to model positive real data sets with decreasing and upside-down bathtub hazard rate shapes. This article focuses on the inference of unknown parameters using a generalized Type-II hybrid censoring scheme (GT-II HCS) for the INHD in the presence of competing risks. The maximum likelihood (ML) and Bayes approaches are used to estimate the model parameters. Based on the squared error loss function, we compute Bayes estimates using Markov Chain Monte Carlo (MCMC) by applying Metropolis-Hasting (M-H) algorithm. Furthermore, the asymptotic confidence intervals, bootstrap confidence intervals (BCIs) and the highest posterior density (HPD) credible intervals are constructed. Using real data sets and simulation studies, we examined the introduced methods of inference with different sample sizes.

On bias reduction in parametric estimation in stage structured development models

Abstract Multi-stage models for cohort data are popular statistical models in several fields such as disease progressions, biological development of plants and animals, and laboratory studies of life cycle development. A Bayesian approach on adopting deterministic transformations in the Metropolis–Hastings (MH) algorithm was used to estimate parameters for these stage structured models. However, the biases in later stages are limitations of this methodology, especially the accuracy of estimates for the models having more than three stages. The main aim of this paper is to reduce these biases in parameter estimation. In particular, we conjoin insignificant previous stages or negligible later stages to estimate parameters of a desired stage, while an adjusted MH algorithm based on deterministic transformations is applied for the non-hazard rate models. This means that current stage parameters are estimated separately from the information of its later stages. This proposed method is validated in simulation studies and applied for a case study of the incubation period of COVID-19. The results show that the proposed methods could reduce the biases in later stages for estimates in stage structured models, and the results of the case study can be regarded as a valuable continuation of pandemic prevention.

Emergent communication of multimodal deep generative models based on Metropolis-Hastings naming game.

Deep generative models (DGM) are increasingly employed in emergent communication systems. However, their application in multimodal data contexts is limited. This study proposes a novel model that combines multimodal DGM with the Metropolis-Hastings (MH) naming game, enabling two agents to focus jointly on a shared subject and develop common vocabularies. The model proves that it can handle multimodal data, even in cases of missing modalities. Integrating the MH naming game with multimodal variational autoencoders (VAE) allows agents to form perceptual categories and exchange signs within multimodal contexts. Moreover, fine-tuning the weight ratio to favor a modality that the model could learn and categorize more readily improved communication. Our evaluation of three multimodal approaches - mixture-of-experts (MoE), product-of-experts (PoE), and mixture-of-product-of-experts (MoPoE)-suggests an impact on the creation of latent spaces, the internal representations of agents. Our results from experiments with the MNIST + SVHN and Multimodal165 datasets indicate that combining the Gaussian mixture model (GMM), PoE multimodal VAE, and MH naming game substantially improved information sharing, knowledge formation, and data reconstruction.

A method for constructing directional surface wave spectra from ICESat-2 altimetry

Abstract. Sea ice is important for Earth's energy budget as it influences surface albedo and air–sea fluxes in polar regions. On its margins, waves heavily impact sea ice. Routine and repeat observations of waves in sea ice are currently lacking, and therefore a comprehensive understanding of how waves interact with sea ice and are attenuated by it is elusive. In this paper, we develop methods to separate the two-dimensional (2D) surface wave spectra from sea-ice height observations made by the ICESat-2 (IS2) laser altimeter, a polar-orbiting satellite. A combination of a linear inverse method, called generalized Fourier transform (GFT), to estimate the wave spectra along each beam and a Metropolis–Hastings (MH) algorithm to estimate the dominant wave's incident angle was developed. It allows us to estimate the 2D wave signal and its uncertainty from the high-density, unstructured ATL03 ICESat-2 photon retrievals. The GFT is applied to re-binned photon retrievals on 25 km segments for all six beams and outperforms a discrete Fourier transform (DFT) in accuracy while having fewer constraints on the data structure. The MH algorithm infers wave direction from beam pairs every 25 km using coherent crests of the most energetic waves. Assuming a dominant incident angle, both methods together allow a decomposition into 2D surface wave spectra with the advantage that the residual surface heights can potentially be attributed to other sea-ice properties. The combined GFT–MH method shows promise in routinely isolating waves propagating through sea ice in ICESat-2 data. We demonstrate its ability on a set of example ICESat-2 tracks, suggesting a detailed comparison against in situ data is necessary to understand the quality of retrieved spectra.

Inference of reliability model with burr type XII distribution under two sample balanced progressive censored samples

Abstract The balanced joint progressive censoring scheme gives guidelines for researchers in reducing the expense and period of the experiment with modified efficiency. In this paper, the stress-strength reliability model are considered and investigated, in which two independent samples are generated from Burr Type XII distributions under balanced joint progressive censoring scheme. In the classical analysis, the maximum likelihood estimate of the reliability parameter is derived, then the relevant confidence interval is provided based on the Fisher matrix. Under the Bayesian framework, the Lindley’s technique and hybrid Gibbs within Metropolis-Hastings algorithm are applied to acquire the estimates of the parameters, and the corresponding highest posterior density credible interval of the reliability model is also constructed. The reliability inference is realized by numerical simulation, and the validity of the inference method is analyzed based on the splashing data of silicone oil droplets impact (SSODI) under two surfaces wettability conditions.

Efficient Bayesian inference for a defect rate based on completely censored data

This paper discusses the challenging issues that reliability practitioners face in conducting destructive tests that lead to completely censored lifetimes, especially in estimating the defect rate of products. Manufacturers need to measure the defect rate for quality control purposes, but obtaining enough defective devices for accurate estimation is not easy when the defect rate is relatively low. To address the issues, a Bayesian approach for estimating the defect rate is proposed in this paper. The proposed method is devised to make up for the heavy computational burdens of the Metropolis-Hastings algorithm. To quantify the uncertainty in the Bayesian estimation, a nonparametric bootstrap technique is employed to construct a credible interval for the defect rate. The performance of the proposed method is evaluated through a variety of Monte Carlo simulation studies. The efficiency of the proposed Bayesian estimation procedure is validated using a real-world dataset of return-springs in DC motor systems under an accelerated destructive degradation test.

Nonlinear characteristics identification of an impact oscillator with a one-sided elastic constraint

Impacting systems are widely used in many engineering applications, such as self-propelled robots, energy harvesting and percussive drilling, which exhibit rich and complex nonlinear phenomena. Among these applications, predicting nonlinearities and estimating system parameters are of great interest of nonlinear dynamics research community. Backbone curve is an analytical tool that captures the frequency–amplitude dependence of nonlinear systems. In this paper, we estimate the impacting stiffness of a single-degree-of-freedom non-smooth dynamical system qualitatively by using the backbone curve. It was found that an increase of the impacting stiffness may lead to lowering the backbone curve. An adaptive differential evolution algorithm with the Metropolis criterion is proposed to identify the parameters of the impacting system quantitatively using experimental data, which are consistent with our theoretical predictions. Finally, the identified parameters are verified, and the limitations of the backbone curve are drawn. The nonlinear characteristics identification method studied in this paper can be extended to other vibro-impact systems and is potentially applicable to structural health monitoring and robotic sensing.