Markov Chain Monte Carlo Simulation Research Articles

Inference of Onset Age of Preclinical State and Sojourn Time for Breast Cancer.

Accurate estimation of the three key parameters (sensitivity, time duration in disease-free state and sojourn time in preclinical state) in cancer screening are critical. Likelihood method with a new link function was applied to the Health Insurance Plan of Greater New York (HIP) breast cancer screening data, to estimate the onset age of preclinical state and the sojourn time in the preclinical state for breast cancer. A new link function to model sensitivity as a function of time in the preclinical state and the sojourn time was adopted. Markov Chain Monte Carlo simulations were used to obtain posterior samples and make inference on the three key parameters. Maximum likelihood estimate was also used for comparison. The onset age of the preclinical state has a wide range for breast cancer; the peak onset age was 65.07 years (95% credible interval [C.I.], 55.76 to 73.02). The mean sojourn time was 2.00 years (95% C.I., 0.85 to 2.95). The 95 % C.I. for the sojourn time was 0.16 to 5.53 years. Sensitivity at onset of the preclinical state was 0.75 (95% C.I., 0.54 to 0.88); and sensitivity at the end of the preclinical state was 0.84 (95% C.I., 0.67 to 0.88). The HIP study was the oldest breast cancer mass screening. The estimates reflect key parameters in those days with lower screening sensitivity. However, it is helpful to know other parameters in the planning for future breast cancer screening.

Optimal Planning of Parking Lots of PEVs Incorporating V2G for Reliability Improvement of Distribution Systems

The number of plug-in electric vehicles (PEV) increased significantly over the past few years and is expected to increase further in the next years due to environmental concerns and fossil fuel depletion. Distribution systems were not originally designed to accommodate this continuous prevalence of PEVs, challenging system planners to install parking lots (PLs) that support PEV charging. The literature has presented many studies for planning PLs, although it did not consider the vehicle-to-grid (V2G) contribution to improving system reliability. This paper proposes an optimal planning framework for allocating and sizing the PLs of PEVs incorporating V2G to improve the reliability of distribution systems. A combined probabilistic model of Markov Chain Monte Carlo simulation (MCMCS) and Monte Carlo simulation (MCS) is applied to capture the stochastic existence of PEVs in PLs. Reliability is evaluated based on a group of energy-oriented indices and the customer’s annual cost of interruption. A comprehensive investigation is presented to test the proposed framework on a distribution system for grid-to-vehicle (G2V) and V2G case studies. The results show the efficiency of the proposed framework in improving the reliability indices by 12% and reducing the customer cost of interruption by 10.06% while prioritizing critical customers.

CH3-Terminated Carbon Chains in the GOTHAM Survey of TMC-1: Evidence of Interstellar CH3C7N

Abstract We report a systematic study of all known methyl carbon chains toward TMC-1 using the second data release of the GOTHAM survey, as well as a search for larger species. Using Markov Chain Monte Carlo simulations and spectral line stacking of over 30 rotational transitions, we report statistically significant emission from methylcyanotriacetylene (CH3C7N) at a confidence level of 4.6σ, and use it to derive a column density of ∼1011 cm−2. We also searched for the related species, methyltetraacetylene (CH3C8H), and place upper limits on the column density of this molecule. By carrying out the above statistical analyses for all other previously detected methyl-terminated carbon chains that have emission lines in our survey, we assess the abundances, excitation conditions, and formation chemistry of methylpolyynes (CH3C2n H) and methylcyanopolyynes (CH3C2n-1N) in TMC-1, and compare those with predictions from a chemical model. Based on our observed trends in column density and relative populations of the A and E nuclear spin isomers, we find that the methylpolyyne and methylcyanopolyyne families exhibit stark differences from one another, pointing to separate interstellar formation pathways, which is confirmed through gas–grain chemical modeling with nautilus.

A spatio-temporal analysis of cause-specific mortality in São Paulo State, Brazil.

Using five cause-specific mortality data sourced by the Brazilian Ministry of Health, and over 17 years period, we applied Bayesian spatio-temporal models on 644 municipalities of the state of São Paulo, using logistic model to the binary outcome that specifies whether or not the death was from a specific cause. We modeled the temporal mortality effects using B-splines, while the spatial components were considered through Gaussian and Markov random field, and inference was based on Markov chain Monte Carlo simulation. The results demonstrate consistent downward trend in mortality from infectious and parasitic diseases and external causes, while those from neoplasms and respiratory are rising. Cardiovascular is the only cause-specific death that is kept constant in time. All the causes of death considered show heterogeneous spatial and temporal variations among the municipalities, which sometimes change considerably within successive years. Mortality from infectious diseases clustered around the Northwestern municipalities in 2000, but changes to the Southeastern part in 2016, a similar development as external death causes. The study identifies areas with increased and decreased odds mortality and could be useful in disease monitoring, especially if we consider small spatial units.

Clustering Point Process Based Network Topology Structure Constrained Urban Road Extraction From Remote Sensing Images

To extract complicated road network from remote sensing images on urban scenes, this article presents a clustering point process (CPP) based network topology structure constrained road extraction algorithm. Firstly, the CPP is constructed to model the feature points, such as endpoints, bends, and crossroads in a road system. Based on that, an initial network topology structure is constructed by connecting the points with lines. Then, according to the network structure characteristic and the spectral characteristic of road, a network topology structure constraining model and a spectral measurement constraining model are constructed, respectively. By combining the models above, a road extraction model is built under the framework of Bayes’ theorem. Finally, to simulate from the road extraction model and extract an optimal road network, a solution strategy, reversible jump Markov Chain Monte Carlo (RJMCMC) simulation algorithm with related transfer operations, is designed according to the CPP and network topology structure. Several high-resolution remote sensing images on urban scenes are tested. According to a buffer evaluation method, and compared with the comparing algorithms, accuracy and extraction rate of results from the proposed algorithm are increased by 10.86% and 8.75% on average, respectively. It is proved that the proposed algorithm can extract the complicated road network effectively.

Marine insurance claims analysis using the Weibull and log-normal models: Compensation for oil spill pollution due to tanker accidents

In marine insurance, the identification of the distribution of the claim size processes from given observations is of major importance. We evaluate the claim amounts due to accidental oil spill volume from tankers. Previous studies on oil spills were mainly concentrating on the relation between spill amounts and some accident factors. The trend of the spill claims is a major concern to the sustainability of insurance funds, tanker shipping and the whole oil industry. By analysing the real claim data series of IOPC (International Oil Pollution Compensation Funds), we identify the trends and reveal findings which enable policy-makers and insurers for the sufficient financial protection from oil spill damage. This study introduces the Weibull model and the log-normal model to the framework for oil spill claims. The Weibull model and the log-normal model are obtained with Markov chain Monte Carlo (MCMC) simulation method. The statistical properties of oil spill claims are determined in the time series of oil spill claims. Moreover, the relations among claim properties of different settings are examined. The log-normal of 3 groups of gross tonnage is found the best fit according to R-squared statistics and the mean squared errors.

On the reliability characteristics of the standard two-sided power distribution

In this study, the standard two-sided power (STSP) distribution is considered with regard to statistical reliability analysis in detail. For this purpose, along with the reliability and hazard functions of the distribution, particular reliability indices that are useful in maintenance and replacement policies are obtained and they are evaluated with their plots. The STSP distribution is classified based on aging according to various cases of its parameters. Then, we studied the classical and Bayesian estimations of the reliability and hazard functions. In Bayesian estimation, symmetric and different asymmetric loss functions are considered. For obtaining the Bayes estimates, Monte Carlo Markov Chain simulation using the Gibbs algorithm is performed. Various simulation schemes are performed for comparing the performances of the estimators. Further, the Bayesian predictions of the future observations based on the observed samples are obtained. A real data example is used to illustrate the theoretical outcomes.

Development of a stochastic bioeconomic model for the red octopus fishery on the Yucatan Peninsula: Implications for management

Although much effort has been dedicated to the management of the red octopus fishery on the Yucatan Peninsula (Mexico), managers have yet to incorporate economic aspects to ensure sustainable and profitable exploitation of this fishery resource. We developed a bioeconomic model that incorporated the uncertainty for the r and K parameters. We fit 3 models (Schaefer, Fox, and Pella–Tomlinson) to abundance index survey data and used the Akaike information criterion for model selection. The best fit corresponded to the Schaefer model. We built deterministic and stochastic versions of the Gordon–Schaefer model. Economic data (costs and prices) were determined from inter[1]views with fishermen. To estimate the posterior distributions of parameters and indicators, we used Bayesian methods with Markov chain Monte Carlo (MCMC) simulations. The deterministic results suggested that the maximum sustainable income was Mex$851.70 million, with a fishing effort of 3,650 fishing boats, while the maximum sustainable profit was $390.8 million, with a fishing effort of 2,472 fishing boats. The equilibrium point corresponded to an effort of 4,945 fishing boats. Regarding the stochastic model, the MCMC simulation results suggest that the maximum sustainable income distribution was not normal; its average was $856.1 million (SE 1.8) and the most likely value was $849.50 million. The most likely fishing effort at equilibrium was 4,970 fishing boats. Our results suggest the fishery could be operating close to the economic equilibrium point; if this is the case, fishing effort must decrease in order for annual profit to increase. Our approach will help make periodical re-evaluations of the fishery and establish management strategies to ensure the profitable and sustainable exploitation of the red octopus on the Yucatan Peninsula.

Bayesian and Classical Inference for Generalized Stress-Strength Parameter Under Generalized Logistic Distribution

In this paper, we study generalized stress-strength model for generalized logistic distribution. The maximum likelihood estimator of this quantity is obtained and then a confidence interval is presented for it. Bayesian and bootstrap methods are also applied for the recommended model. A Markov Chain Monte Carlo (MCMC) simulation study for assessing the estimation methods is performed via the Metropolis-Hastings algorithm in each step of Gibbs algorithm. An application to real data set is addressed.

Predicting Winter Wheat Heading Date: A Simple Model and Its Validation in Kansas

Abstract Accurate prediction of winter wheat (Triticum aestivum L.) heading date is important for determining the potential incidence of diseases and abiotic stresses such as freeze or heat events. Wheat phenological modeling requires cultivar- and crop-zone-specific vernalization and photoperiod knowledge. Previous models applied in Kansas showed that the uncertainties of predicting heading date were large and could be improved. In this study, a modification to the Scientific Impact Assessment and Modeling Platform for Advanced Crop and Ecosystem Management (SIMPLACE) model was developed and implemented to improve the accuracy of winter wheat heading date estimation. The cultivar- and crop-zone-specific model parameters were calculated using a Markov chain Monte Carlo simulation. The modified models were calibrated by using the longest observation site to cover all cultivars planted in each crop zone. Model performance was then evaluated for seven winter wheat cultivars at eight experiment sites distributed across four crop zones in Kansas. Our modified model (MS) had a root-mean-square error (RMSE) between predicted and observed heading date of 4 days, which reflects an improved accuracy by 5–8 days on average compared to the Agricultural Production Systems Simulator (APSIM) or the original SIMPLACE models. There was a clear correlation between the uncertainty of the modeled heading date and the sowing date in previous models. Our modified model demonstrates that integrating nonlinear temperature response functions, temperature stress factors, and sowing date information improved prediction of the heading date in winter wheat across Kansas.

Exploration of the Polarization Curve for Proton-Exchange Membrane Fuel Cells.

The polarization curve is the most important profile to evaluate the performance of proton-exchange membrane fuel cells (PEMFCs). To explore the important thermodynamic parameters and their correlation with the composition, fabrication, and operational settings, a comprehensive data set consisting of 446 polarization curves from 191 perfluorosulfonate and 255 sulfonated hydrocarbon-based PEMs is collected. Then, a Markov chain Monte Carlo simulation within the Bayesian frame provides higher than 93% confidence to extract six important thermodynamic parameters including open-circuit potential, the transfer coefficient, the current loss, the reference exchange current density, the internal resistance, and the limiting current density. An extreme gradient boosting algorithm affords a mean determinative coefficient of 0.89 to predict the whole polarization curve and a confidence of 94% to predict the peak power density (PPD). Both approaches to explore the polarization curve for PEMFCs show good robustness in the blind test. Overall, the PPD is positively correlated with the ion-exchange capacity of the polymer, operational temperature, and humidity and is negatively affected by internal resistance, membrane thickness, and the loading of the catalyst. The flow rate of fuels can effectively enhance them, while the increase of catalyst loading or fuel concentration shows deleterious impacts.

LTD064402+245919: A Subgiant with a 1–3 M ⊙ Undetected Companion Identified from LAMOST-TD Data

Abstract Single-line spectroscopic binaries have recently contributed to stellar-mass black hole discovery, independently of the X-ray transient method. We report the identification of a single-line binary system, LTD064402+245919, with an orbital period of 14.50 days. The observed component is a subgiant with a mass of 2.77 ± 0.68 M ⊙, radius 15.5 ± 2.5 R ⊙, effective temperature T eff 4500 ± 200 K, and surface gravity log g 2.5 ± 0.25 dex. The discovery makes use of the Large Sky Area Multi-Object fiber Spectroscopic Telescope time-domain and Zwicky Transient Facility survey. Our general-purpose software pipeline applies a Lomb–Scargle periodogram to determine the orbital period and uses machine learning to classify the variable type from the folded light curves. We apply a combined model to estimate the orbital parameters from both the light and radial velocity curves, taking constraints on the primary star mass, mass function, and detection limit of secondary luminosity into consideration. We obtain a radial velocity semiamplitude of 44.6 ± 1.5 km s−1, mass ratio of 0.73 ± 0.07, and an undetected component mass of 2.02 ± 0.49 M ⊙ when the type of the undetected component is not set. We conclude that the inclination is not well constrained, and that the secondary mass is larger than 1 M ⊙ when the undetected component is modeled as a compact object. According to our investigations using a Monte Carlo Markov Chain simulation, increasing the spectra signal-to-noise ratio by a factor of 3 would enable the secondary light to be distinguished (if present). The algorithm and software in this work are able to serve as general-purpose tools for the identification of compact objects quiescent in X-rays.

Extended reduced-order surrogate models for scalar-tensor gravity in the strong field and applications to binary pulsars and gravitational waves

Statistically sound tests of scalar-tensor gravity theories in the strong-field regime usually involves computationally intensive calculations. In this study, we construct a reduced order surrogate model for the scalar-tensor gravity of Damour and Esposito-Far\`ese (DEF) with spontaneous scalarization phenomena developed for neutron stars (NSs). This model allows us to perform a rapid and comprehensive prediction of NS properties, including mass, radius, moment of inertia, effective scalar coupling, and two extra coupling parameters. We code the model in the pySTGROMX package, as an extension of our previous work, that speeds up the calculations at two and even three orders of magnitude and yet still keeps accuracy of $\sim1\%$. Using the model, we can calculate all the post-Keplerian parameters in the timing of binary pulsars conveniently, which provides a quick approach for us to place comprehensive constraints on the DEF theory. We perform Markov-chain Monte Carlo simulations with the model to constrain the parameters of the DEF theory with well-timed binary pulsars. Utilizing five NS-white dwarf and three NS-NS binaries, we obtain the most stringent constraints on the DEF theory up to now. Our work provides a public tool for quick evaluation of NSs' derived parameters to test gravity in the strong-field regime.

Parameters Estimation Sensitivity of the Linear Mixed Model To Alternative Prior Distribution Specifications

Markov chain Monte Carlo (MCMC) is the most widely used method for estimating joint posterior distributions in Bayesian analysis. The Markov chain Monte Carlo technique has been used in order to estimate the model parameters based on the different prior distributions. MCMC simulations were carried out in order to evaluate the linear mixed model using different parameters of the prior distribution. In this paper, we established the linear mixed model with different types of variables. The proposed parameters of the prior distribution are different from the traditional parameters of the prior distribution. We assumed special parameters for the prior distribution based on some background or information about the data science. This work aims to estimate the parameters using a point estimator or find a confidence interval (credible interval) for the unknown parameters. Also, a specific hypothesis about these parameters can be tested using a random sample from the posterior distribution. The performance of each prior is measured based on the effective sample size (ESS) for the estimated model. The results showed that the estimated linear mixed model with proposed parameters of the prior distribution performed very well in comparison with the standard or traditional prior (inverse-Wishart prior for random effect component). Based on the scale reduction factors, the estimated model with proposed parameters performed better in comparison with scale reduction factors for the traditional model.

One-step dynamic analysis of growth kinetics of Bacillus cereus from spores in simulated fried rice – Model development, validation, and Marko Chain Monte Carlo simulation

Bacillus cereus is a spore-forming pathogen capable of producing an emetic toxin and several diarrheal enterotoxins that may cause outbreaks of foodborne illness often associated with rice-based and other farinaceous foods. Therefore, the objective of this study was to investigate the growth kinetics of B. cereus from spores in simulated egg fried rice.The growth of B. cereus was observed under dynamic conditions. Three independent growth curves were analyzed simultaneously using a one-step dynamic analysis (OSDA) to determine the kinetic parameters. The results showed that the minimum, optimum, and maximum growth temperatures were 11.8, 40.8, and 50.6 °C, respectively, with an optimum specific growth rate of 2.4 per h. The root-mean-square-error (RMSE) of model development was 0.4 log CFU/g. Deterministic validation with another 3 independent dynamic temperature profiles showed a RMSE of 0.5 log CFU/g. With Markov Chain Monte Carlo simulation, the RMSE of prediction was only 0.3 log CFU/g.This study proved that OSDA is an effective and efficient method for quickly developing integrated predictive models and estimating kinetic parameters. The resulting integrated model can be used to accurately predict the growth of B. cereus and for managing its risks associated with egg fried rice. The developed kinetic models also can be used to guide restaurant owners and catering establishments to properly prepare and store egg fried rice and other related products to prevent the growth of B. cereus. According to the model, the growth of mesophilic B. cereus is unlikely to occur if the food is stored below 10 °C.

A Bivariate Analysis of the Spatial Distributions of Stunting and Wasting Among Children Under-Five in Nigeria

Stunting and wasting are major malnutrition issues among children under five years of age and have continued to remain unacceptably high in Nigeria leading to high rates of child morbidity and mortality. Evidence-based strategies are required by government and non-governmental agencies to mitigate the suffering of these children, and this could be realised when the association between the determinants and the geographical distributions are fully understood. Using data from four waves of the Nigerian Demographic and Health Survey, we employed a distributional bivariate probit model to examine the geographical distributions of the levels and linear association between acute and chronic malnutrition in Nigeria after accounting for possible observed determinants. Bayesian inference was based on Markov chain Monte Carlo simulation. The findings reveal substantial spatial variations in stunting and wasting among under-five children in Nigeria, indicating a north–south divide. The findings show negative linear association between the two malnutrition indicators among children in some northern fringe states but positive for Akwa Ibom, Ebonyi and Anambra. The correlation also peaks around age 20 months indicating that during the first 2 years of life, the children have an increasing likelihood of suffering from stunting and wasting.

Asymptotic Bayesian Optimization: A Markov sampling-based framework for design optimization

This paper presents a Markov sampling-based framework, called Asymptotic Bayesian Optimization, for solving a class of constrained design optimization problems. The optimization problem is converted into a unified two-phase sample generation problem which is solved by an effective Markov chain Monte Carlo simulation scheme. First, an exploration phase generates designs distributed over the feasible design space. Based on this information, an exploitation phase obtains a set of designs lying in the vicinity of the optimal solution set. The proposed formulation can handle continuous, discrete, or mixed discrete-continuous design variables. Appropriate adaptive proposal distributions for the continuous and discrete design variables are suggested. The set of optimal solutions provides valuable sensitivity information of the different quantities involved in the problem with respect to the design variables. Representative examples including an analytical problem involving nonlinear benchmark functions, a classical engineering design problem, and a performance-based design optimization problem of a structural system under stochastic excitation are presented to show the effectiveness and potentiality of the proposed optimization scheme. Validation calculations show that the scheme is a flexible, efficient and competitive choice for solving a wide range of classical and complex engineering design problems.

Inverse methods for consistent quantification of seafloor anoxia using uranium isotope data from marine sediments

Uranium isotopes (δ238U) have quickly become one of the most widely-used redox proxies in paleoceanographic studies. The quantitative power of the δ238U proxy derives from the long marine residence time of uranium and the dominance of reduction in fractionating uranium isotopes during removal from seawater. The seawater δ238U value is therefore sensitive to the size of the anoxic sink, and by extension, the area of the seafloor overlain by anoxic waters. Leveraging the ability of carbonates to record and retain the seawater δ238U value, and the ubiquity of carbonate sediments in the geologic record, numerous studies have quantified seafloor anoxia across ocean anoxic events, mass extinctions, and global climatic changes. In most cases, forward models of marine uranium isotope mass balance have been used, illustrating potential histories of seafloor anoxia during these events.Here we show that there are multiple ways in which such forward modeling can lead to spurious inferences of anoxia, including (i) the poor sensitivity of the δ238U proxy when fractional anoxia is high, and (ii) the inherent bias in generating illustrative forward model outputs in stratigraphic sections with expected anoxic intervals. We thus explore inverse modeling approaches to constrain the most likely history of seafloor anoxia for a given δ238U dataset, and ultimately develop a framework for doing so using Bayesian inference via Markov Chain Monte Carlo simulation. We show that this approach can recover simulated trends, and further reconstruct marine anoxia for eight published δ238U datasets. We find that some previous interpretations of anoxic seafloor extent were inaccurate, either because steady state was improperly assumed, or because the illustrative forward models used were poor fits to the data. In order to overcome these issues in future work with the δ238U redox proxy, we have made this model publicly available, and also offer suggestions for the judicious use of forward models. By building on this framework, the future quantification of marine anoxia during transient environmental perturbations can be performed consistently, thereby facilitating robust comparison of anoxic extent between events.

Distance-based reconstruction of protein quaternary structures from inter-chain contacts.

Predicting the quaternary structure of protein complex is an important problem. Inter‐chain residue‐residue contact prediction can provide useful information to guide the ab initio reconstruction of quaternary structures. However, few methods have been developed to build quaternary structures from predicted inter‐chain contacts. Here, we develop the first method based on gradient descent optimization (GD) to build quaternary structures of protein dimers utilizing inter‐chain contacts as distance restraints. We evaluate GD on several datasets of homodimers and heterodimers using true/predicted contacts and monomer structures as input. GD consistently performs better than both simulated annealing and Markov Chain Monte Carlo simulation. Starting from an arbitrarily quaternary structure randomly initialized from the tertiary structures of protein chains and using true inter‐chain contacts as input, GD can reconstruct high‐quality structural models for homodimers and heterodimers with average TM‐score ranging from 0.92 to 0.99 and average interface root mean square distance from 0.72 Å to 1.64 Å. On a dataset of 115 homodimers, using predicted inter‐chain contacts as restraints, the average TM‐score of the structural models built by GD is 0.76. For 46% of the homodimers, high‐quality structural models with TM‐score ≥ 0.9 are reconstructed from predicted contacts. There is a strong correlation between the quality of the reconstructed models and the precision and recall of predicted contacts. Only a moderate precision or recall of inter‐chain contact prediction is needed to build good structural models for most homodimers. Moreover, GD improves the quality of quaternary structures predicted by AlphaFold2 on a Critical Assessment of Techniques for Protein Structure Prediction–Critical Assessments of Predictions of Interactions dataset.

Parallel power posterior analyses for fast computation of marginal likelihoods in phylogenetics.

In Bayesian phylogenetic inference, marginal likelihoods can be estimated using several different methods, including the path-sampling or stepping-stone-sampling algorithms. Both algorithms are computationally demanding because they require a series of power posterior Markov chain Monte Carlo (MCMC) simulations. Here we introduce a general parallelization strategy that distributes the power posterior MCMC simulations and the likelihood computations over available CPUs. Our parallelization strategy can easily be applied to any statistical model despite our primary focus on molecular substitution models in this study. Using two phylogenetic example datasets, we demonstrate that the runtime of the marginal likelihood estimation can be reduced significantly even if only two CPUs are available (an average performance increase of 1.96x). The performance increase is nearly linear with the number of available CPUs. We record a performance increase of 13.3x for cluster nodes with 16 CPUs, representing a substantial reduction to the runtime of marginal likelihood estimations. Hence, our parallelization strategy enables the estimation of marginal likelihoods to complete in a feasible amount of time which previously needed days, weeks or even months. The methods described here are implemented in our open-source software RevBayes which is available from http://www.RevBayes.com.