Markov Chain Monte Carlo Simulation Research Articles

Impact of Non-pharmaceutical Interventions on the Control of COVID-19 in Iran: A Mathematical Modeling Study.

During the first months of the coronavirus disease 2019 (COVID-19) pandemic, Iran reported high numbers of infections and deaths. In the following months, the burden of this infection decreased significantly, possibly due to the impact of a package of interventions. We modeled the dynamics of COVID-19 infection in Iran to quantify the impacts of these interventions. We used a modified susceptible-exposed-infected-recovered (SEIR) model to model the COVID-19 epidemic in Iran, from January 21, 2020 to September 21, 2020. We estimated the 95% uncertainty intervals (UIs) using Markov chain Monte Carlo simulation. Under different scenarios, we assessed the effectiveness of non-pharmaceutical interventions (NPIs) including physical distancing measures and self-isolation. We also estimated the time-varying reproduction number (Rt ), using our mathematical model and epidemiologic data. If no NPIs were applied, there could have been a cumulative number of 51 800 000 (95% UI: 1 910 000- 77 600 000) COVID-19 infections and 266 000 (95% UI: 119 000-476 000) deaths by September 21, 2020. If physical distancing interventions, such as school/border closures and self-isolation interventions had been introduced a week earlier than they were actually launched, 30.8% and 35.2% reduction in the number of deaths and infections respectively could have been achieved by September 21, 2020. The observed daily number of deaths showed that the Rt was one or more than one almost every day during the analysis period. Our models suggest that the NPIs implemented in Iran between January 21, 2020 and September 21, 2020 had significant effects on the spread of the COVID-19 epidemic. Our study also showed that the timely implementation of NPIs showed a profound effect on further reductions in the numbers of infections and deaths. This highlights the importance of forecasting and early detection of future waves of infection and of the need for effective preparedness and response capabilities.

A Bayesian Spatio-Temporal Analysis of Malaria in the Greater Accra Region of Ghana from 2015 to 2019.

The Greater Accra Region is the smallest of the 16 administrative regions in Ghana. It is highly populated and characterized by tropical climatic conditions. Although efforts towards malaria control in Ghana have had positive impacts, malaria remains in the top five diseases reported at healthcare facilities within the Greater Accra Region. To further accelerate progress, analysis of regionally generated data is needed to inform control and management measures at this level. This study aimed to examine the climatic drivers of malaria transmission in the Greater Accra Region and identify inter-district variation in malaria burden. Monthly malaria cases for the Greater Accra Region were obtained from the Ghanaian District Health Information and Management System. Malaria cases were decomposed using seasonal-trend decomposition, based on locally weighted regression to analyze seasonality. A negative binomial regression model with a conditional autoregressive prior structure was used to quantify associations between climatic variables and malaria risk and spatial dependence. Posterior parameters were estimated using Bayesian Markov chain Monte Carlo simulation with Gibbs sampling. A total of 1,105,370 malaria cases were recorded in the region from 2015 to 2019. The overall malaria incidence for the region was approximately 47 per 1000 population. Malaria transmission was highly seasonal with an irregular inter-annual pattern. Monthly malaria case incidence was found to decrease by 2.3% (95% credible interval: 0.7–4.2%) for each 1 °C increase in monthly minimum temperature. Only five districts located in the south-central part of the region had a malaria incidence rate lower than the regional average at >95% probability level. The distribution of malaria cases was heterogeneous, seasonal, and significantly associated with climatic variables. Targeted malaria control and prevention in high-risk districts at the appropriate time points could result in a significant reduction in malaria transmission in the Greater Accra Region.

Quantile Regression Neural Networks: A Bayesian Approach

This article introduces a Bayesian neural network estimation method for quantile regression assuming an asymmetric Laplace distribution (ALD) for the response variable. It is shown that the posterior distribution for feedforward neural network quantile regression is asymptotically consistent under a misspecified ALD model. This consistency proof embeds the problem from density estimation domain and uses bounds on the bracketing entropy to derive the posterior consistency over Hellinger neighborhoods. This consistency result is shown in the setting where the number of hidden nodes grow with the sample size. The Bayesian implementation utilizes the normal-exponential mixture representation of the ALD density. The algorithm uses Markov chain Monte Carlo (MCMC) simulation technique - Gibbs sampling coupled with Metropolis-Hastings algorithm. We have addressed the issue of complexity associated with the afore-mentioned MCMC implementation in the context of chain convergence, choice of starting values, and step sizes. We have illustrated the proposed method with simulation studies and real data examples.

PNS93 Analysis of SF-6D Health State Utility Scores: Is Beta Regression Appropriate?

Typically, modeling of health related quality of life data is often a troublesome since its distribution is positively or negatively skewed, spikes at zero or one, bounded and heteroscedasticity. In the present paper we aim to investigate whether Bayesian beta regression is appropriate for analysing the SF-6D health state utility scores and respondent characteristics. A sample of 126 Lebanese members from the American University of Beirut valued 49 health states defined by the SF-6D using the standard gamble technique. Three different models were fitted for SF-6D via Bayesian Markov chain Monte Carlo (MCMC) simulation methods. These comprised a beta regression, random effects and random effects with covariates. Results from applying the three Bayesian beta regression models were reported and compared based on their predictive ability to previously used linear regression models, using mean prediction error (MPE), root mean squared error (RMSE) and deviance information criterion (DIC). For the three different approaches, the beta regression model was found to perform better than the normal regression model under all criterions used. The beta regression with random effects model performs best, with MPE (0.084), RMSE (0.058) and DIC (1621). Compared to the traditionally linear regression model, the beta regression provided better predictions of observed values in the entire learning sample and in an out-of-sample validation. Beta regression provides flexible approach to modeling health state values. It also accounted for the boundedness and heteroscedasticity of the SF-6D index scores. Further research is encouraged.

Adaptive prediction of wall movement during excavation using Bayesian inference

In underground construction works, uncertainties and insufficient information about the underground environment lead to inaccurate predictions of soil-structure interactions. Supported excavations are often over-designed, which underscores a significant potential for cost optimization. However, the uncertainties exist, and the traditional design process does not allow for leaner designs at the start of the project. The emergence of advanced analysis tools enables the development of an Observational Method based approach for a decision-making process in which data can be best utilized to deliver real value, confidence, and control.An automated back analysis approach based on Bayesian inference is developed in this paper and validated with a synthetic case study. Probabilistic modeling and Markov Chain Monte Carlo simulation are used to deliver estimates of soil parameters for a given a geotechnical model, update the prediction of future excavation stages, and fully quantify uncertainties from the constructed model and measurements. Sensitivity analysis is used for model selection to achieve modeling robustness. The impact of prior engineering knowledge about the soil properties on the precision of the predictions is also examined. This approach significantly improves the efficiency of back analysis in current practice and provides a tool for data-driven decision making of design optimization during construction.

Effect of the spatial variability of soil parameters on the deformation behavior of excavated slopes

The prediction of slope stability is difficult due to the spatial variability of soil parameters and measurement errors from core samples. This study proposed a Bayesian updating framework that based on the random finite element model (RFEM) method. The proposed approach was applied in a field excavation slope project. The field data of a soil slope with anti-slide bored piles under four-stage excavations were compared to elucidate the spatial variability of the cohesion, friction angle and stiffness in different soil layers. Then, a Bayesian updating model with random finite element analysis was developed by considering the COV and SOF of the soil parameters. The proposed analysis approach utilized the prior information from the site investigation and field measurement results. The posterior statistical characteristic values of the soil parameters were obtained from equivalent samples calculated by Markov Chain Monte Carlo simulations. The results indicated that the proposed method can reduce the effect of uncertainty related to the soil properties. Finally, the effects of soil parameters and excavation conditions on the slope stability were established, enabling an evaluation of safety based on field measurement results.

Quantitative Characterization of Population-Wide Tissue- and Metabolite-Specific Variability in Perchloroethylene Toxicokinetics in Male Mice.

Quantification of interindividual variability is a continuing challenge in risk assessment, particularly for compounds with complex metabolism and multi-organ toxicity. Toxicokinetic variability for perchloroethylene (perc) was previously characterized across 3 mouse strains and in 1 mouse strain with various degrees of liver steatosis. To further characterize the role of genetic variability in toxicokinetics of perc, we applied Bayesian population physiologically based pharmacokinetic (PBPK) modeling to the data on perc and metabolites in blood/plasma and tissues of male mice from 45 inbred strains from the Collaborative Cross (CC) mouse population. After identifying the most influential PBPK parameters based on global sensitivity analysis, we fit the model with a hierarchical Bayesian population analysis using Markov chain Monte Carlo simulation. We found that the data from 3 commonly used strains were not representative of the full range of variability in perc and metabolite blood/plasma and tissue concentrations across the CC population. Using interstrain variability as a surrogate for human interindividual variability, we calculated dose-dependent, chemical-, and tissue-specific toxicokinetic variability factors (TKVFs) as candidate science-based replacements for the default uncertainty factor for human toxicokinetic variability of 100.5. We found that toxicokinetic variability factors for glutathione conjugation metabolites of perc showed the greatest variability, often exceeding the default, whereas those for oxidative metabolites and perc itself were generally less than the default. Overall, we demonstrate how a combination of a population-based mouse model such as the CC with Bayesian population PBPK modeling can reduce uncertainty in human toxicokinetic variability and increase accuracy and precision in quantitative risk assessment.

Structural synthesis considering mixed discrete–continuous design variables: A Bayesian framework

In this work attention is directed to general structural optimization problems considering discrete–continuous design variables. The optimization problem is formulated as the minimization of an objective function subject to multiple design requirements. The mathematical programming statement is set into the framework of a Bayesian model updating problem. Constraints are handled directly within the proposed scheme, generating designs distributed over the feasible design space. Based on these samples, a set of designs lying in the vicinity of the optimal solution set is obtained. The Bayesian model updating problem is solved by an effective Markov chain Monte Carlo simulation scheme, where appropriate proposal distributions are introduced for the continuous and discrete design variables. The approach can efficiently estimate the sensitivity of the final design and constraints with respect to the design variables. In addition, the numerical implementation of the optimization algorithm depends on few control parameters. For illustration purposes, the general formulation is applied to an important class of problems, specifically, reliability-based design optimization of structural systems under stochastic excitation. Three numerical examples showing the effectiveness and potentiality of the approach reported herein are presented.

Derivation of a Human In Vivo Benchmark Dose for Perfluorooctanoic Acid From ToxCast In Vitro Concentration-Response Data Using a Computational Workflow for Probabilistic Quantitative In Vitro to In Vivo Extrapolation.

A computational workflow which integrates physiologically based kinetic (PBK) modeling, global sensitivity analysis (GSA), approximate Bayesian computation (ABC), and Markov Chain Monte Carlo (MCMC) simulation was developed to facilitate quantitative in vitro to in vivo extrapolation (QIVIVE). The workflow accounts for parameter and model uncertainty within a computationally efficient framework. The workflow was tested using a human PBK model for perfluorooctanoic acid (PFOA) and high throughput screening (HTS) in vitro concentration–response data, determined in a human liver cell line, from the ToxCast/Tox21 database. In vivo benchmark doses (BMDs) for PFOA intake (ng/kg BW/day) and drinking water exposure concentrations (µg/L) were calculated from the in vivo dose responses and compared to intake values derived by the European Food Safety Authority (EFSA). The intake benchmark dose lower confidence limit (BMDL5) of 0.82 was similar to 0.86 ng/kg BW/day for altered serum cholesterol levels derived by EFSA, whereas the intake BMDL5 of 6.88 was six-fold higher than the value of 1.14 ng/kg BW/day for altered antibody titer also derived by the EFSA. Application of a chemical-specific adjustment factor (CSAF) of 1.4, allowing for inter-individual variability in kinetics, based on biological half-life, gave an intake BMDL5 of 0.59 for serum cholesterol and 4.91 (ng/kg BW/day), for decreased antibody titer, which were 0.69 and 4.31 the EFSA-derived values, respectively. The corresponding BMDL5 for drinking water concentrations, for estrogen receptor binding activation associated with breast cancer, pregnane X receptor binding associated with altered serum cholesterol levels, thyroid hormone receptor α binding leading to thyroid disease, and decreased antibody titer (pro-inflammation from cytokines) were 0.883, 0.139, 0.086, and 0.295 ng/ml, respectively, with application of no uncertainty factors. These concentrations are 5.7-, 36-, 58.5-, and 16.9-fold lower than the median measured drinking water level for the general US population which is approximately, 5 ng/ml.

Digital Twin-driven framework for fatigue life prediction of steel bridges using a probabilistic multiscale model: Application to segmental orthotropic steel deck specimen

Accurate fatigue life prediction facilitates the fatigue maintenance of steel bridges. Since Digital Twin can simulate the lifecycle for physical objects at various scales, this study aims to provide a Digital Twin-driven framework for non-deterministic fatigue life prediction of steel bridges. A probabilistic multiscale model was developed to depict the fatigue evolution throughout the bridge lifecycle. The small crack initiation period was well described by the modified Fine and Bhat model considering microstructure uncertainties. After obtaining the critical model parameter via crystal plastic finite element simulation, the modified model was further calibrated using the assumed historical fatigue data in Digital Twin database. Based on the initiated half-penny-shaped small crack, the small crack initiation period was connected to the macrocrack extension period. Given the uncertainties of macrocrack propagation, the Paris’ law with random growth parameters was adopted. The Bayesian inference of the growth parameters realized the real-time calibration of the macrocrack growth model using Markov chain Monte Carlo simulation. The feasibility of the proposed framework was demonstrated through fatigue tests on a segmental steel deck specimen with mixed-mode deformed U-rib to diaphragm welded joints. The results show that the predicted fatigue initiation life and residual fatigue life are in good agreement with the experimentally observed life results. In summary, the proposed framework enhances our understanding of the fatigue evolution mechanism throughout the bridge lifecycle and provides an entirely new approach to accurately predict the fatigue life of steel bridges under various sources of uncertainties.

Quantification of the Flexibility Potential through Smart Charging of Battery Electric Vehicles and the Effects on the Future Electricity Supply System in Germany

Electrification offers an opportunity to decarbonize the transport sector, but it might also increase the need for flexibility options in the energy system, as the uncoordinated charging process of battery electric vehicles (BEV) can lead to a demand with high simultaneity. However, coordinating BEV charging by means of smart charging control can also offer substantial flexibility potential. This potential is limited by restrictions resulting from individual mobility behavior and preferences. It cannot be assumed that storage capacity will be available at times when the impact of additional flexibility potential is highest from a systemic point of view. Hence, it is important to determine the flexibility available per vehicle in high temporal (and spatial) resolution. Therefore, in this paper a Markov-Chain Monte Carlo simulation is carried out based on a vast empirical data set to quantify mobility profiles as accurately as possible and to subsequently derive charging load profiles. An hourly flexibility potential is derived and integrated as load shift potential into a linear optimization model for the simultaneous cost-optimal calculation of the dispatch of technology options and long-term capacity planning to meet a given electricity demand. It is shown that the costs induced by BEV charging are largely determined by the profile costs from the combination of the profiles of charging load and renewable generation, and not only by the additional energy and capacity demand. If the charging process can be flexibly controlled, the storage requirement can be reduced and generation from renewable energies can be better integrated.

Quantifying the small-area spatio-temporal dynamics of the Covid-19 pandemic in Scotland during a period with limited testing capacity

Modelling the small-area spatio-temporal dynamics of the Covid-19 pandemic is of major public health importance, because it allows health agencies to better understand how and why the virus spreads. However, in Scotland during the first wave of the pandemic testing capacity was severely limited, meaning that large numbers of infected people were not formally diagnosed as having the virus. As a result, data on confirmed cases are unlikely to represent the true infection rates, and due to the small numbers of positive tests these data are not available at the small-area level for confidentiality reasons. Therefore to estimate the small-area dynamics in Covid-19 incidence this paper analyses the spatio-temporal trends in telehealth data relating to Covid-19, because during the first wave of the pandemic the public were advised to call the national telehealth provider NHS 24 if they experienced symptoms of the virus. Specifically, we propose a multivariate spatio-temporal correlation model for modelling the proportions of calls classified as either relating to Covid-19 directly or having related symptoms, and provide software for fitting the model in a Bayesian setting using Markov chain Monte Carlo simulation. The model was developed in partnership with the national health agency Public Health Scotland, and here we use it to analyse the spatio-temporal dynamics of the first wave of the Covid-19 pandemic in Scotland between March and July 2020, specifically focusing on the spatial variation in the peak and the end of the first wave.

Analysis of Child Mortality for Muslim Women of Uttar Pradesh, India: An Application of Bayesian Frailty Model

In this paper an attempt has been made to analyze the child mortality by use of a hazard model in Bayesian environment, family effect through multiplicative random effect is also incorporated in the model. For fitting this model real data has taken from District Level Household and Facility Survey (DLHS)-3. The largest state (in population) of India i.e. Uttar Pradesh data is taken for analysis. Deviance information criteria are used for comparison of models. It found that the model with family frailty gives better fit. All the analysis is performed in winBUGS software, which is used Markov chain monte carlo simulation under gibbs sampling.

The Discrete Analogue of the Weibull G Family: Properties, Different Applications, Bayesian and Non-Bayesian Estimation Methods

In this work, we propose and study a new discrete analogue of the Weibull class. Many useful properties such as ordinary moments; moment generating function; cumulant generating function; probability generating function; central moments and dispersion index are derived. Two special discrete versions are discussed theoretically, graphically, and numerically. The hazard rate function of the new family can be "upside down", "increasing", "decreasing", "constant", "J-hazard rate function" and "double upside down" and "increasing-constant". Non-Bayesian estimation methods such as the maximum likelihood estimation; Cramer-von Mises estimation; the ordinary least square estimation and the weighted least square estimation are considered. The Bayesian estimation procedure under the squared error loss function is also presented. The Markov chain Monte Carlo simulations for comparing non-Bayesian and Bayesian estimation are performed using the Gibbs sampler and Metropolis Hastings algorithm. The flexibility of the new family is illustrated by four real datasets. The new family (through two special discrete versions) provided a better fit than sixteen competitive distributions.

Updating the models and uncertainty of mechanical parameters for rock tunnels using Bayesian inference

Rock mechanical parameters and their uncertainties are critical to rock stability analysis, engineering design, and safe construction in rock mechanics and engineering. The back analysis is widely adopted in rock engineering to determine the mechanical parameters of the surrounding rock mass, but this does not consider the uncertainty. This problem is addressed here by the proposed approach by developing a system of Bayesian inferences for updating mechanical parameters and their statistical properties using monitored field data, then integrating the monitored data, prior knowledge of geotechnical parameters, and a mechanical model of a rock tunnel using Markov chain Monte Carlo (MCMC) simulation. The proposed approach is illustrated by a circular tunnel with an analytical solution, which was then applied to an experimental tunnel in Goupitan Hydropower Station, China. The mechanical properties and strength parameters of the surrounding rock mass were modeled as random variables. The displacement was predicted with the aid of the parameters updated by Bayesian inferences and agreed closely with monitored displacements. It indicates that Bayesian inferences combined the monitored data into the tunnel model to update its parameters dynamically. Further study indicated that the performance of Bayesian inferences is improved greatly by regularly supplementing field monitoring data. Bayesian inference is a significant and new approach for determining the mechanical parameters of the surrounding rock mass in a tunnel model and contributes to safe construction in rock engineering.

Hybrid Censoring Schemes with Mixture Gamma Failure Distribution

Censoring schemes have received much attention over the past decades. Hybrid censoring schemes are censoring schemes mixed of type-I (T-1) and type-II (T-2) censoring schemes, a most popular area of study in life-testing or reliability experiments. More precisely, hybrid censoring can be described as a mixture of T-I and T-2 schemes. Gamma distribution is widely used, and its connection has more distributions. Mixture and single gamma distribution will be studied to estimate parameters, based on type-II hybrid censoring schemes (T-2HCS). We will apply algorithms to compute the maximum likelihood (ML) estimators and Bayesian approaches, using statistics, such as Markov chain Monte Carlo methods. Bayes estimators and corresponding highest posterior density confidence intervals will be tabled. Also, Markov chain Monte Carlo simulation is implemented to compare the performances of the different methods and the real dataset is analyzed for illustrative purposes.

A super-Earth on a close-in orbit around the M1V star GJ 740

Context. M-dwarfs have proven to be ideal targets for planetary radial velocity (RV) searches due to their higher planet-star mass contrast, which favors the detection of low-mass planets. The abundance of super-Earth and Earth-like planets detected around this type of star motivates further such research on hosts without reported planetary companions. Aims. The HADES and CARMENES programs are aimed at carrying out extensive searches of exoplanetary systems around M-type stars in the northern hemisphere, allowing us to address, in a statistical sense, the properties of the planets orbiting these objects. In this work, we perform a spectroscopic and photometric study of one of the program stars (GJ 740), which exhibits a short-period RV signal that is compatible with a planetary companion. Methods. We carried out a spectroscopic analysis based on 129 HARPS-N spectra taken over a time span of 6 yr combined with 57 HARPS spectra taken over 4 yr, as well as 32 CARMENES spectra taken during more than 1 yr, resulting in a dataset with a time coverage of 10 yr. We also relied on 459 measurements from the public ASAS survey with a time-coverage of 8 yr, along with 5 yr of photometric magnitudes from the EXORAP project taken in the V, B, R, and I filters to carry out a photometric study. Both analyses were made using Markov chain Monte Carlo simulations and Gaussian process regression to model the activity of the star. Results. We present the discovery of a short-period super-Earth with an orbital period of 2.37756−0.00011+0.00013 d and a minimum mass of 2.96−0.48+0.50 M⊕. We offer an update to the previously reported characterization of the magnetic cycle and rotation period of the star, obtaining values of Prot = 35.563 ± 0.071 d and Pcycle = 2800 ± 150 d. Furthermore, the RV time series exhibits a possibly periodic long-term signal, which might be related to a Saturn-mass planet of ~100 M⊕.

Spatial clustering of drug-resistant tuberculosis in Hunan province, China: an ecological study

ObjectiveThis study aimed to investigate the spatial distribution of drug-resistant tuberculosis (DR-TB) in Hunan province, China.MethodsAn ecological study was conducted using DR-TB data collected from the Tuberculosis Control Institute of...

Modelling the Spatial Distribution and the Factors Associated with Under-Five Mortality in Nigeria

Globally, the risk of a child dying before celebrating their fifth birthday is still high at 5.3 million deaths in 2018 alone. Nigeria is among the few countries that are yet to achieve the Sustainable Development Goal Target of keeping under-5 death to as low as 25 deaths per 1000 live births by 2030. A recent study found that the under-5 mortality rate in Nigeria is still high with 1 in 8 Nigerian children dying before reaching the age of 5. In this study, the effect of a child’s spatial location in Nigeria on their likelihood of dying before age 5 was examined alongside other key covariates. Bayesian geo-additive regression models were fitted to the 2018 Nigeria Demographic and Health Surveys data. Statistical inference was based on the Bayesian paradigm via Markov chain Monte Carlo simulation methods, and models were assessed using the deviance information criterion. Under-five mortality rate varied significantly across spatial locations in Nigeria with Kebbi, Jigawa, Kaduna, Kogi and Gombe states having the highest rates. The likelihood of a child dying before age 5 increased among women with primary education and women aged 38 years and over. Other characteristics associated with high under-5 death are poverty, male child, low birth weight and multiple births. The current study has helped to identify geographical ‘hotspots’ as well as the key factors driving under-5 deaths in Nigeria to inform the effective design and implementation of timely and efficient interventions.

Shield tunnel grouting layer estimation using sliding window probabilistic inversion of GPR data

The ground penetrating radar (GPR) is an effective tool to detect the grouting layer behind shield tunnel linings, yet to estimate the thickness from GPR data is always difficult. We herein present a probabilistic inversion method to infer the grouting layer thickness together with its relative permittivity and electric conductivity values from GPR waveform data. This method uses a sliding window and Markov chain Monte Carlo (MCMC) simulation with Bayesian inference to explore the posterior distribution of model parameters. The inversion results of a synthetic example demonstrate that the proposed method successfully estimates the grouting layer thickness. We also investigate the impact of the modeling error on the inversion results, and use a modified likelihood function to eliminate the modeling error. With the modeling error corrected, the posterior model parameters converge correctly to their true values, and the associated uncertainties are quantified.