Adaptive Metropolis Algorithm Research Articles

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.

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.

Stochastic inversion for equivalent hydraulic fracture characterization using low-frequency distributed acoustic sensing data

Distributed fiber-optic sensing, a game-changing technology, has been successfully applied in monitoring hydraulic fracturing treatments. The cross-well fiber-optic strain/strain-rate responses are directly related to the fracture-propagation process and dynamic fracture geometry. Extracting the insightful information regarding hydraulic fractures requires robust interpretation workflows. In this paper, we aim to develop a stochastic inversion approach to characterize the dynamic equivalent fracture geometry and quantify the associated uncertainties using cross-well low-frequency distributed acoustic sensing (LF-DAS) measurements. A fast analytical forward solver based on the 3D displacement discontinuity method is developed to model the strain. The objective function is the sum-of-squares error between the modeled strain and the measured strain. We focus on an equivalent fracture geometry with a predefined length centered around the monitoring well, which is a reasonable assumption considering the spatial sensitivity of LF-DAS. Therefore, the model parameters reduce to fracture width and height of the equivalent fracture. We adopted the delayed rejection adaptive metropolis (DRAM) algorithm, an efficient Markov-chain Monte Carlo (MCMC)-based method, to perform the optimization. The efficiency and accuracy of the algorithm are tested using a synthetic case that has three monitoring wells at different locations. The mean values of fracture width and height are both close to the true values with negligible standard deviations for all the three monitoring wells. The algorithm performance is not sensitive to the initial guess and the predefined length needs to be large enough. Then, a field case with a single cluster from the HFTS-2 project is presented. The fracture width increases from about 0.5 mm to about 0.9 mm during the pumping stage and gradually decreases during the shut-in period. The fracture height changes during the pumping stage and stabilizes at about 150 m during the shut-in period, the trend of which is consistent with the LF-DAS signals from the offset vertical monitoring well. To the best of our knowledge, this is the first algorithm that can efficiently quantify the fracture width and height simultaneously. The results could provide novel insights on the characteristics of fracture geometry and significantly improve the understanding of complex fracture propagation processes in subsurface reservoirs.

Bayesian inference for parameter identification in mechanistic models, exemplified using a cow lifetime performance model

Mechanistic models are valuable tools for studying the underlying mechanisms of complex biological phenomena. For example, cow lifespan models can be used to identify differences in resource acquisition and allocation strategies between individuals, which is relevant for decision-making in breeding programs. In such models, differences in simulated traits between individuals are consequences of the parameter set that represents the genetic potential of each animal and its interaction with the environment. This indicates that the identification of these differences is essentially a search for individual parameters. In mechanistic models, this search is generally a non-convex problem that has different local minima because the parameters interact within these models. Due to this and to the simulation time length (e.g. years), there is uncertainty associated with the inference of the parameter values for each individual. This uncertainty can be quantified using Bayesian inference since this approach treats the model parameters as random variables with an underlying probability distribution that describes them. The objective of this work was to employ the Delayed Rejection Adaptive Metropolis (DRAM) algorithm to identify the parameters of a cows’ lifespan model using two datasets of Holstein cows. The datasets contain periodic measurements of Milk Yield (MY), BW, and Body Condition Score (BCS). Additionally, one of the two datasets has information of BW from birth to first calving. The average Mean Absolute Percentage Error (MAPE) minimisation between the simulated and experimental data (MY, BW and BCS) was used as the objective function for parameter search. The Bayesian inference performance was compared with four optimisation metaheuristic approaches: Differential Evolution, Genetic Algorithm, Particle Swarm Optimisation, and Simulated Annealing. Although the results show that all methods are efficient in finding parameter values that reduce the distance between the simulated and experimental data (MAPE < 10%), the DRAM method is more efficient in terms of computational cost, and the parameter distributions obtained with this method offer more information about the statistical properties of each parameter (e.g. median).

Static Behavior Prediction of Concrete Truss Arch Bridge Based on Dynamic Test Data and Bayesian Inference

The field load test is a direct and effective method for evaluating the performance of bridge structures. However, the existing bridge static load tests on site are costly, inefficient, and obstruct traffic; moreover, improper loading may also cause some damage to the bridge structure. This paper proposes a random model update method based on bridge dynamic load tests and the Bayesian inference as an alternative to the static load test. The Gaussian process model was used instead of the finite element model to reduce the cost of model calculation. Furthermore, choose the Markov Chain Monte Carlo (MCMC) method based on delay rejection adaptive Metropolis algorithm for Bayesian inference to improve the speed of the Bayesian method inferring the posterior probability density of updated parameters. First, the parameters to be updated 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 results show that the predicted results of the bridge static load test based on the dynamic load test and Bayesian reasoning method have an excellent agreement with the measured results, and this method can effectively overcome the adverse effects of the existing bridge static load test.

Bayesian Model Updating for Structural Dynamic Applications Combing Differential Evolution Adaptive Metropolis and Kriging Model

The Bayesian model updating approach has attracted much attention by providing the most probable values (MPVs) of physical parameters and their uncertainties. However, the Bayesian approach has challenges in high-dimensional problems and requires high computational costs in large-scale engineering structures dealing with structural dynamics. This study proposes a new Bayesian updating framework using the Differential Evolution Adaptive Metropolis (DREAM) algorithm to enhance the Bayesian approach’s performance and computational efficiency. In addition, two time-saving strategies are proposed. Firstly, variance-based global sensitivity analysis is used to eliminate insignificant parameters to model responses and reduce model dimensionality. Secondly, a fast-running kriging model is employed as a surrogate of the time-consuming finite-element (FE) model to alleviate the computational burden. DREAM essentially is a multichain sampling method that runs different paths to seek all possible solutions and accurately approximate the posterior probability distribution function in the Bayesian approach. The proposed updating framework was demonstrated using one numerical example and a real-world cable-stayed pedestrian bridge. The results showed that the proposed method enables rationally identifying structural parameters and recovering dynamic responses. Compared with the traditional Bayesian approach without a surrogate model, the computational cost is orders of magnitude lower.

Bayesian kinetic modeling for tracer-based metabolomic data

BackgroundStable Isotope Resolved Metabolomics (SIRM) is a new biological approach that uses stable isotope tracers such as uniformly 13C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{13}C$$\\end{document}-enriched glucose (13C6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{13}C_6$$\\end{document}-Glc) to trace metabolic pathways or networks at the atomic level in complex biological systems. Non-steady-state kinetic modeling based on SIRM data uses sets of simultaneous ordinary differential equations (ODEs) to quantitatively characterize the dynamic behavior of metabolic networks. It has been increasingly used to understand the regulation of normal metabolism and dysregulation in the development of diseases. However, fitting a kinetic model is challenging because there are usually multiple sets of parameter values that fit the data equally well, especially for large-scale kinetic models. In addition, there is a lack of statistically rigorous methods to compare kinetic model parameters between different experimental groups.ResultsWe propose a new Bayesian statistical framework to enhance parameter estimation and hypothesis testing for non-steady-state kinetic modeling of SIRM data. For estimating kinetic model parameters, we leverage the prior distribution not only to allow incorporation of experts’ knowledge but also to provide robust parameter estimation. We also introduce a shrinkage approach for borrowing information across the ensemble of metabolites to stably estimate the variance of an individual isotopomer. In addition, we use a component-wise adaptive Metropolis algorithm with delayed rejection to perform efficient Monte Carlo sampling of the posterior distribution over high-dimensional parameter space. For comparing kinetic model parameters between experimental groups, we propose a new reparameterization method that converts the complex hypothesis testing problem into a more tractable parameter estimation problem. We also propose an inference procedure based on credible interval and credible value. Our method is freely available for academic use at https://github.com/xuzhang0131/MCMCFlux.ConclusionsOur new Bayesian framework provides robust estimation of kinetic model parameters and enables rigorous comparison of model parameters between experimental groups. Simulation studies and application to a lung cancer study demonstrate that our framework performs well for non-steady-state kinetic modeling of SIRM data.

A two-stage adaptive Metropolis algorithm

We propose a sampling algorithm combining two quite powerful ideas in the Markov chain Monte Carlo literature – the adaptive Metropolis sampler and the two-stage Metropolis-Hastings sampler. The proposed sampling method will be particularly very useful for high-dimensional posterior sampling in Bayesian models with expensive likelihoods. In the first stage of the proposed algorithm, an adaptive proposal is used based on the previously sampled states and the corresponding acceptance probability is computed based on an approximated inexpensive target density. The true expensive target density is evaluated while computing the second stage acceptance probability only if the proposal is accepted in the first stage. The adaptive nature of the algorithm guarantees faster convergence of the chain and very good mixing properties. On the other hand, the two-stage approach helps in rejecting the bad proposals in the inexpensive first stage, making the algorithm computationally efficient. As the proposals are dependent on the previous states the chain loses its Markov property, but we prove that it retains the desired ergodicity property. The performance of the proposed algorithm is compared with the existing algorithms in two simulated and two real data examples.

Probabilistic Predictions of Ecologically Relevant Hydrologic Indices Using a Hydrological Model

AbstractThis study evaluated the effects of prior knowledge obtained from multi‐objective optimization on the uncertainty quantification of simulated ecologically relevant hydrologic indices (ERHIs) using a hydrological model. Two experiments were formulated considering contrasting conditions in prior knowledge when implementing Bayesian parameter estimation. In the first experiment, we reproduced a common modeling practice in the absence of previous information where uniform priors are considered when calibrating hydrological and error model parameters. In the second experiment, near‐optimal Pareto solutions from multi‐objective calibration were used to build a multivariate prior distribution for estimating hydrological and error model parameters using Bayesian calibration. In both experiments, a likelihood function considering heteroscedasticity and autocorrelation effects was employed. The Unified Non‐dominated Sorting Algorithm III was used for multi‐objective calibration, whereas the multiple‐try differential evolution adaptive metropolis algorithm was used for Markov Chain Monte Carlo sampling. The experiments were tested using a hydrologic model. We selected a subset of ERHIs comprised of 32 central tendency Indicators of Hydrologic Alteration and seven additional indices describing basic streamflow statistical properties. In general, using near‐optimal Pareto parameter distributions as prior knowledge in Bayesian calibration reduced both the bias and variability ranges in ERHIs prediction. Furthermore, there was no significant loss in the reliability of streamflow predictions (from 2% to 6%, p = 0.07) when targeting the selected ERHIs, while improving precision (from 66% to 58%, p &lt; 0.05) and reducing the bias (from 6% to 4%, p &lt; 0.05). Moreover, parametric uncertainty substantially shrank by 72% when linking multi‐objective calibration and Bayesian parameter estimation.

Probabilistic damage detection and identification of coupled structural parameters using Bayesian model updating with added mass

Damage detection inevitably involves uncertainties originated from measurement noise and modeling error. It may cause incorrect damage detection results if not appropriately treating uncertainties. To this end, vibration-based Bayesian model updating (VBMU) is developed to utilize vibration responses or modal parameters to estimate structural parameters and the associated uncertainties of those estimates. However, traditional VBMU often assumes that mass is well known and invariant because simultaneous identification of mass and stiffness may yield an unidentifiable problem due to the coupling effect of the mass and stiffness. In addition, the posterior PDF in VBMU is usually approximated by single Markov Chain Monte Carlo (MCMC), leading to a low acceptance rate and limited capability for complex structures. This paper proposed a novel VBMU to address the coupling effect and identify mass and stiffness by adding known mass. Two vibration data sets are acquired from original and modified systems with added mass, giving the new characteristic equations. Then, the posterior PDF is reformulated by measured data and predicted counterparts from new characteristic equations. For efficiently approximating the posterior PDF, Differential Evolutionary Adaptive Metropolis (DREAM) algorithm is adopted to draw samples by running multiple Markov chains parallelly to enhance acceptance rate and sufficiently explore possible solutions. Finally, a numerical example with a ten-story shear building and a laboratory-scale three-story frame structure are utilized to demonstrate the efficacy of the proposed VBMU framework. The results show that the proposed method can successfully identify both mass and stiffness, and their uncertainties. Reliable probabilistic damage detection can also be achieved.

An adaptive multiple-try Metropolis algorithm

Markov chain Monte Carlo (MCMC) methods, specifically samplers based on random walks, often have difficulty handling target distributions with complex geometry such as multi-modality. We propose an adaptive multiple-try Metropolis algorithm designed to tackle such problems by combining the flexibility of multiple-proposal samplers with the user-friendliness and optimality of adaptive algorithms. We prove the ergodicity of the resulting Markov chain with respect to the target distribution using common techniques in the adaptive MCMC literature. In a Bayesian model for loss of heterozygosity in cancer cells, we find that our method outperforms traditional adaptive samplers, non-adaptive multiple-try Metropolis samplers, and various more sophisticated competing methods.

Bayesian uncertainty quantification of local volatility model

Local volatility is an important quantity in option pricing, portfolio hedging, and risk management. It is not directly observable from the market; hence calibrations of local volatility models are necessary using observed market data. Unlike most existing point-estimate methods, we cast the large-scale nonlinear inverse problem into the Bayesian framework, yielding a posterior distribution of the local volatility, which naturally quantifies its uncertainty. This extra uncertainty information enables traders and risk managers to make better decisions. To alleviate the computational cost, we apply Karhunen–Lòeve expansion to reduce the dimensionality of the Gaussian Process prior for local volatility. A modified two-stage adaptive Metropolis algorithm is applied to sample the posterior probability distribution, which further reduces computational burdens caused by repetitive numerical forward option pricing model solver and time of heuristic tuning. We demonstrate our methodology with both synthetic and market data.

A time-domain multisource Bayesian/Markov chain Monte Carlo formulation of time-lapse seismic waveform inversion

Seismic waveform inversion has been shown to be well-suited for identification and characterization of time-lapse changes in a reservoir. However, the subtle medium variations associated with enhanced oil recovery and/or [Formula: see text] storage problems give uncertainty quantification within such inverse approaches a heightened importance. To analyze both of these features of the time-lapse inverse problem, we formulate a Bayesian full-waveform inversion (FWI) procedure, based on a Markov chain Monte Carlo (MCMC) algorithm. The formulation uses several existing strategies, such as the use of a double-difference time-lapse FWI (DDFWI), incorporation of time-domain multisource data, and application of a local-updating target-oriented inversion. However, it incorporates these within a stochastic framework, involving computation of model covariance with an adaptive Metropolis algorithm, and a method to estimate data error statistics based on the features of time-lapse difference data that is incorporated. A random walk Metropolis-Hastings MCMC is adopted for optimization. In conventional, i.e., deterministic, DDFWI, inversions are carried out for the baseline and monitoring models; in the MCMC approach, a deterministic FWI procedure is carried out for the baseline model, and the MCMC algorithm is applied in the monitoring inversion stage; and the final time-lapse model is the difference between these. A feasibility study is carried out using synthetic 2D acoustic models and data, including time-lapse model estimation and uncertainty quantification. We compare the MCMC approach with conventional deterministic optimization DDFWI and remark on benefits derived, which appear to justify the expanded complexity and cost of a global approach. In addition to the availability of posterior distributions, which are critical for the assessment of the estimations, we observe that the MCMC approach tends to produce monitoring images with clearer edges and fewer coherent errors.

A Methodology for the Efficient Quantification of Parameter and Model Uncertainty

Abstract Complex structural systems often entail computationally intensive models that require efficient methods for statistical model calibration due to the high number of required model evaluations. In this paper, we present a Bayesian inference-based methodology for efficient statistical model calibration that builds upon the combination of the speed in the computation of a low-fidelity model with the accuracy of the computationally intensive high-fidelity model. The proposed two-stage method incorporates the adaptive Metropolis algorithm and a Gaussian process (GP)-based adaptive surrogate model as a low-fidelity model. In order to account for model uncertainty, we incorporate a GP-based discrepancy function into the model calibration. By calibrating the hyperparameters of the discrepancy function alongside the model parameters, we prevent the results of the model calibration to be biased. The methodology is illustrated by the statistical model calibration of a damping parameter in the modular active spring-damper system, a structural system developed within the collaborative research center SFB 805 at the Technical University of Darmstadt. The reduction of parameter and model uncertainty achieved by the application of our methodology is quantified and illustrated by assessing the predictive capability of the mathematical model of the modular active spring-damper system.

A generalized whole-cell model for wastewater-fed microbial fuel cells

A comprehensive mathematical modeling of wastewater-fed microbial fuel cells (MFC) demands an in-depth process understanding of the main electrical and bioelectrochemical interactions at both electrodes. In this study, a novel holistic simulation approach using a low-parameterized model was applied to predict pollutant transport, conversion, and electrical processes of mixed-culture single-chamber MFCs. The proposed whole-cell model couples the combined bioelectrochemical-electrical model with the well-established Activated Sludge Model No.1 (ASM1) and specific equations from ASM2. The cathodic gas–liquid mass transfer of oxygen and free ammonia nitrogen was described in terms of a diffusion film model, while the diminishing diffusivity due to salt deposits was considered via a fouling decline kinetic model. The predictive capacity of the model was validated using experimental data of three continuous-flow single-chamber MFCs operated with municipal wastewater for 150 days. Electrochemical parameters were estimated in real-time by pulse-width modulated connection of the external electrical load resistance. Following a sensitivity analysis, the most relevant model parameters were optimized through the Monte-Carlo Markov-Chain method using the adaptive Metropolis algorithm. All other parameters were adopted from benchmark simulation studies. The simulated relative contributions of aerobic carbon oxidation, denitrification, electrogenesis, and methanogenesis to the total COD removal rate were 21–22%, 44–45%, 21–25%, and 9–14%. Overall, the presented whole-cell model is able to successfully predict the evolution of electricity generation, methane production, and effluent concentrations (soluble COD and total ammonia nitrogen) under different hydraulic conditions and organic loading rates.

A Bayesian framework to assess and create risk maps of groundwater flooding

Groundwater flooding can cause severe damages to homes, utilities, and infrastructure and yield significant economic and social costs. Numerical models are used to understand these events and are the basis to produce imagery products for risk management and communication. However, such maps are generally produced using forward model simulations, and most of the mapping products are still deterministic. In contrast to pluvial and fluvial floods, an open issue in the analysis of susceptibility to groundwater flooding is the lack of probabilistic assessment and mapping products recognizing parametric uncertainty. Hence, we propose a Bayesian-based framework to create probabilistic risk maps and to identify the susceptibility to groundwater flood events. We aim to assess the spatial distribution and temporal variability of groundwater flooding by decomposing the uncertainty and the sensitivity of distributed groundwater numerical models. The scheme involves the use of the elementary effects method, the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm, and the exploration of the predictive posterior distributions of the groundwater heads to evaluate the susceptibility according to exceedance levels. We use the proposed Bayesian framework with a numerical model that simulates the groundwater flood event that occurred in the valley of the Alz River in 2013. This study developed two types of susceptibility maps based on the exceedance probability of certain groundwater levels and specific cellar depths. The Bayesian inference supports the parameter estimation and thereby increases the spatial confidence of the areas susceptible to inundation. This study shows that maps of susceptibility to groundwater flooding can be built over one single event models and acknowledge the inherent spatial and temporal uncertainty of such events.

Model Updating of a Prestressed Concrete Rigid Frame Bridge Using Multiple Markov Chain Monte Carlo Method and Differential Evolution

Model updating is a widely adopted method to minimize the error between test results from the real structure and outcomes from the finite element (FE) model for obtaining an accurate and reliable FE model of the target structure. However, uncertainties from the environment, excitation and measurement variability can reduce the accuracy of predictions of the updated FE model. The Bayesian model updating method using multiple Markov chains based on differential evolution adaptive metropolis (DREAM) algorithm is explored, which runs multiple chains simultaneously for a global exploration, and it automatically tunes the scale and orientation of the proposal distribution during the evolution of the posterior distribution. The performance of the proposed method is illustrated numerically with a beam model and a three-span rigid frame bridge. Results show that the DREAM algorithm is capable for updating the FE model in civil engineering. It extends the Bayesian model updating method to multiple Markov chains scenario, which provides higher accuracy than single chain algorithm such as the delayed rejection adaptive metropolis-hastings (DRAM) method. Moreover, results from both examples indicate that the proposed method is insensitive to values of initial parameters, which avoid errors resulting from inappropriate prior knowledge of parameters in the FE model updating.

Quantification of Precipitation and Evapotranspiration Uncertainty in Rainfall-Runoff Modeling

Mountainous watersheds have always been a challenge for modelers due to large variability and insufficient ground observations, which cause forcing data, model structure, and parameter uncertainty. This study employed Differential Evolution Adaptive Metropolis (DREAM) algorithm which utilizes Markov Chain Monte Carlo (MCMC) approach to account for forcing data uncertainty. A conceptual degree day snowmelt model, MIKE 11 NAM (Nedbor Afstromnings Model), was used to simulate snowmelt runoff from Ilgaz basin, with an area of 28.4 km2 area, located in the northern part of Turkey. The mean elevation is around 1700 m and the basin is covered with broadleaf forest and has mainly brown soil with a high water holding capacity. Precipitation and evapotranspiration (ET) values were optimized in combination with model parameters conditioned on observed discharges and corrected values of input data were utilized for calibration and validation. Results showed that the observed precipitation was over-estimated by almost 10%, while evapotranspiration calculated by Penman–Monteith method was underestimated. The mean values of storm and ET multipliers were obtained as 1.14 and 0.84, respectively. When only parameter uncertainty was considered, calibration did not yield Nash–Sutcliffe Efficiency (NSE) greater than 0.64. However, when forcing data uncertainty was incorporated in the DREAM approach, an improved value of NSE (0.84) was obtained. After calibration and treatment of forcing data errors, the model yielded reasonable prediction uncertainty bounds and well-defined posterior distributions of NAM model parameters. Main objectives of the study are to assess the applicability of MIKE 11 NAM model to the selected catchment. In addition, the importance of errors in the input forcing variables to the model is demonstrated.

Estimating tuberculosis drug resistance amplification rates in high-burden settings

BackgroundAntimicrobial resistance develops following the accrual of mutations in the bacterial genome, and may variably impact organism fitness and hence, transmission risk. Classical representation of tuberculosis (TB) dynamics using a single or two strain (DS/MDR-TB) model typically does not capture elements of this important aspect of TB epidemiology. To understand and estimate the likelihood of resistance spreading in high drug-resistant TB incidence settings, we used epidemiological data to develop a mathematical model of Mycobacterium tuberculosis (Mtb) transmission.MethodsA four-strain (drug-susceptible (DS), isoniazid mono-resistant (INH-R), rifampicin mono-resistant (RIF-R) and multidrug-resistant (MDR)) compartmental deterministic Mtb transmission model was developed to explore the progression from DS- to MDR-TB in The Philippines and Viet Nam. The models were calibrated using data from national tuberculosis prevalence (NTP) surveys and drug resistance surveys (DRS). An adaptive Metropolis algorithm was used to estimate the risks of drug resistance amplification among unsuccessfully treated individuals.ResultsThe estimated proportion of INH-R amplification among failing treatments was 0.84 (95% CI 0.79–0.89) for The Philippines and 0.77 (95% CI 0.71–0.84) for Viet Nam. The proportion of RIF-R amplification among failing treatments was 0.05 (95% CI 0.04–0.07) for The Philippines and 0.011 (95% CI 0.010–0.012) for Viet Nam.ConclusionThe risk of resistance amplification due to treatment failure for INH was dramatically higher than RIF. We observed RIF-R strains were more likely to be transmitted than acquired through amplification, while both mechanisms of acquisition were important contributors in the case of INH-R. These findings highlight the complexity of drug resistance dynamics in high-incidence settings, and emphasize the importance of prioritizing testing algorithms which allow for early detection of INH-R.

Model learning of the tire–road friction slip dependency under standard driving conditions

The maximum tire–road friction coefficient is a quantity allowing to increase significantly the performance of the driver-assistance systems. Unfortunately, this value is particularly difficult to estimate under standard driving conditions. Therefore, this paper focuses on a parametric method based on Monte-Carlo Markov Chain techniques to determine it accurately. Our solution combines the advantages of both a maximum likelihood method and an adaptive Metropolis algorithm to determine the tire–road friction coefficient. This approach requires friction measurements and a tire model representing the friction as a function of the slip ratio. After describing the theoretical aspects of the method, this paper focuses on its practical implementation. Several results obtained from both simulated data and real data are given to demonstrate the efficiency of the approach.