Utilizing Bayesian Modeling and MCMC for Accurate Characterization of Naturally Occurring Radionuclides Reference Background Levels in Mining Areas

Statistical biases may be introduced by imprecisely quantifying background radiation reference levels. It is, therefore, imperative to devise a simple, adaptable approach for precisely describing the reference background levels of naturally occurring radionuclides (NOR) in mining sites. As a substitute statistical method, we suggest using Bayesian modeling in this work to examine the spatial distribution of NOR. For naturally occurring gamma-induced radionuclides like 232Th, 40K, and 238U, statistical parameters are inferred using the Markov Chain Monte Carlo (MCMC) method. After obtaining an accurate subsample using bootstrapping, we exclude any possible outliers that fall outside of the Highest Density Interval (HDI). We use MCMC to build a Bayesian model with the resampled data and make predictions about the posterior distribution of radionuclides produced by gamma irradiation. This method offers a strong and dependable way to describe NOR reference background values, which is important for managing and evaluating radiation risks in mining contexts.

Discrimination for minimal hepatic encephalopathy based on Bayesian modeling of default mode network

In order to classify the minimal hepatic encephalopathy （MHE） patients from healthy controls, the independent component analysis （ICA） is used to generate the default mode network （DMN） from resting-state functional magnetic resonance imaging （fMRI）. Then a Bayesian voxel- wised method, graphical-model-based multivariate analysis （GAMMA）, is used to explore the associations between abnormal functional integration within DMN and clinical variable. Without any prior knowledge, five machine learning methods, namely, support vector machines （SVMs）, classification and regression trees （ CART ）, logistic regression, the Bayesian network, and C4.5, are applied to the classification. The functional integration patterns were alternative within DMN, which have the power to predict MHE with an accuracy of 98%. The GAMMA method generating functional integration patterns within DMN can become a simple, objective, and common imaging biomarker for detecting MIIE and can serve as a supplement to the existing diagnostic methods.

Improving the accuracy of precipitation estimates in a typical inland arid area of China using a dynamic Bayesian model averaging approach

Xinjiang Uygur Autonomous Region is a typical inland arid area in China with a sparse and uneven distribution of meteorological stations,limited access to precipitation data,and significant water scarcity.Evaluating and integrating precipitation datasets from different sources to accurately characterize precipitation patterns has become a challenge to provide more accurate and alternative precipitation information for the region,which can even improve the performance of hydrological modelling.This study evaluated the applicability of widely used five satellite-based precipitation products(Climate Hazards Group InfraRed Precipitation with Station(CHIRPS),China Meteorological Forcing Dataset(CMFD),Climate Prediction Center morphing method(CMORPH),Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks-Climate Data Record(PERSIANN-CDR),and Tropical Rainfall Measuring Mission Multi-satellite Precipitation Analysis(TMPA))and a reanalysis precipitation dataset(ECMWF Reanalysis v5-Land Dataset(ERA5-Land))in Xinjiang using ground-based observational precipitation data from a limited number of meteorological stations.Based on this assessment,we proposed a framework that integrated different precipitation datasets with varying spatial resolutions using a dynamic Bayesian model averaging(DBMA)approach,the expectation-maximization method,and the ordinary Kriging interpolation method.The daily precipitation data merged using the DBMA approach exhibited distinct spatiotemporal variability,with an outstanding performance,as indicated by low root mean square error(RMSE=1.40 mm/d)and high Person's correlation coefficient(CC=0.67).Compared with the traditional simple model averaging(SMA)and individual product data,although the DBMA-fused precipitation data were slightly lower than the best precipitation product(CMFD),the overall performance of DBMA was more robust.The error analysis between DBMA-fused precipitation dataset and the more advanced Integrated Multi-satellite Retrievals for Global Precipitation Measurement Final(IMERG-F)precipitation product,as well as hydrological simulations in the Ebinur Lake Basin,further demonstrated the superior performance of DBMA-fused precipitation dataset in the entire Xinjiang region.The proposed framework for solving the fusion problem of multi-source precipitation data with different spatial resolutions is feasible for application in inland arid areas,and aids in obtaining more accurate regional hydrological information and improving regional water resources management capabilities and meteorological research in these regions.

Comparison of isotope-based linear and Bayesian mixing models in determining moisture recycling ratio

Stable water isotopes are natural tracers quantifying the contribution of moisture recycling to local precipitation,i.e.,the moisture recycling ratio,but various isotope-based models usually lead to different results,which affects the accuracy of local moisture recycling.In this study,a total of 18 stations from four typical areas in China were selected to compare the performance of isotope-based linear and Bayesian mixing models and to determine local moisture recycling ratio.Among the three vapor sources including advection,transpiration,and surface evaporation,the advection vapor usually played a dominant role,and the contribution of surface evaporation was less than that of transpiration.When the abnormal values were ignored,the arithmetic averages of differences between isotope-based linear and the Bayesian mixing models were 0.9%for transpiration,0.2%for surface evaporation,and–1.1%for advection,respectively,and the medians were 0.5%,0.2%,and–0.8%,respectively.The importance of transpiration was slightly less for most cases when the Bayesian mixing model was applied,and the contribution of advection was relatively larger.The Bayesian mixing model was found to perform better in determining an efficient solution since linear model sometimes resulted in negative contribution ratios.Sensitivity test with two isotope scenarios indicated that the Bayesian model had a relatively low sensitivity to the changes in isotope input,and it was important to accurately estimate the isotopes in precipitation vapor.Generally,the Bayesian mixing model should be recommended instead of a linear model.The findings are useful for understanding the performance of isotope-based linear and Bayesian mixing models under various climate backgrounds.

Bayesian partial pooling to reduce uncertainty in overcoring rock stress estimation

The state of in situ stress is a crucial parameter in subsurface engineering,especially for critical projects like nuclear waste repository.As one of the two ISRM suggested methods,the overcoring(OC)method is widely used to estimate the full stress tensors in rocks by independent regression analysis of the data from each OC test.However,such customary independent analysis of individual OC tests,known as no pooling,is liable to yield unreliable test-specific stress estimates due to various uncertainty sources involved in the OC method.To address this problem,a practical and no-cost solution is considered by incorporating into OC data analysis additional information implied within adjacent OC tests,which are usually available in OC measurement campaigns.Hence,this paper presents a Bayesian partial pooling(hierarchical)model for combined analysis of adjacent OC tests.We performed five case studies using OC test data made at a nuclear waste repository research site of Sweden.The results demonstrate that partial pooling of adjacent OC tests indeed allows borrowing of information across adjacent tests,and yields improved stress tensor estimates with reduced uncertainties simultaneously for all individual tests than they are independently analysed as no pooling,particularly for those unreliable no pooling stress estimates.A further model comparison shows that the partial pooling model also gives better predictive performance,and thus confirms that the information borrowed across adjacent OC tests is relevant and effective.

Measurement Research Based on Bayesian Structural Equation Cognitive Model

The Bayesian structural equation model integrates the principles of Bayesian statistics, providing a more flexible and comprehensive modeling framework. In exploring complex relationships between variables, handling uncertainty, and dealing with missing data, the Bayesian structural equation model demonstrates unique advantages. Therefore, Bayesian methods are used in this paper to establish a structural equation model of innovative talent cognition, with the measurement of college students’ cognition of innovative talent being studied. An in-depth analysis is conducted on the effects of innovative self-efficacy, social resources, innovative personality traits, and school education, aiming to explore the factors influencing college students’ innovative talent. The results indicate that innovative self-efficacy plays a key role in perception, social resources are significantly positively correlated with the perception of innovative talents, innovative personality tendencies and school education are positively correlated with the perception of innovative talents, but the impact is not significant.

Automated soil resources mapping based on decision tree and Bayesian predictive modeling

This article presents two approaches for automated building of knowledge bases of soil resources mapping. These methods used decision tree and Bayesian predictive modeling, respectively to generate knowledge from training data. With these methods, building a knowledge base for automated soil mapping is easier than using the conventional knowledge acquisition approach. The knowledge bases built by these two methods were used by the knowledge classifier for soil type classification of the Longyou area, Zhejiang Province, China using TM bi-temporal imageries and GIS data. To evaluate the performance of the resultant knowledge bases, the classification results were compared to existing soil map based on field survey. The accuracy assessment and analysis of the resultant soil maps suggested that the knowledge bases built by these two methods were of good quality for mapping distribution model of soil classes over the study area.

Development of a novel critical nitrogen concentration-cumulative transpiration curve for optimizing nitrogen management under varying irrigation conditions in winter wheat

Accurate nitrogen(N)nutrition diagnosis is essential for improving N use efficiency in crop production.The widely used critical N(Nc)dilution curve traditionally depends solely on agronomic variables,neglecting crop water status.With three-year field experiments with winter wheat,encompassing two irrigation levels(rainfed and irrigation at jointing and anthesis)and three N levels(0,180,and 270 kg ha1),this study aims to establish a novel approach for determining the Nc dilution curve based on crop cumulative transpiration(T),providing a comprehensive analysis of the interaction between N and water availability.The Nc curves derived from both crop dry matter(DM)and T demonstrated N concentration dilution under different conditions with different parameters.The equation Nc=6.43T0.24 established a consistent relationship across varying irrigation regimes.Independent test results indicated that the nitrogen nutrition index(NNI),calculated from this curve,effectively identifies and quantifies the two sources of N deficiency:insufficient N supply in the soil and insufficient soil water concentration leading to decreased N availability for root absorption.Additionally,the NNI calculated from the Nc-DM and Nc-T curves exhibited a strong negative correlation with accumulated N deficit(Nand)and a positive correlation with relative grain yield(RGY).The NNI derived from the Nc-T curve outperformed the NNI derived from the Nc-DM curve concerning its relationship with Nand and RGY,as indicated by larger R2 values and smaller AIC.The novel Nc curve based on T serves as an effective diagnostic tool for assessing winter wheat N status,predicting grain yield,and optimizing N fertilizer management across varying irrigation conditions.These findings would provide new insights and methods to improve the simulations of water-N interaction relationship in crop growth models.

Response of Growing Season Gross Primary Production to El Nino in Different Phases of the Pacific Decadal Oscillation over Eastern China Based on Bayesian Model Averaging

Gross primary production(GPP) plays a crucial part in the carbon cycle of terrestrial ecosystems.A set of validated monthly GPP data from 1957 to 2010 in 0.5°× 0.5° grids of China was weighted from the Multi-scale Terrestrial Model Intercomparison Project using Bayesian model averaging(BMA).The spatial anomalies of detrended BMA GPP during the growing seasons of typical El Nino years indicated that GPP response to El Nino varies with Pacific Decadal Oscillation(PDO) phases: when the PDO was in the cool phase,it was likely that GPP was greater in northern China(32°–38°N,111°–122°E) and less in the Yangtze River valley(28°–32°N,111°–122°E);in contrast,when PDO was in the warm phase,the GPP anomalies were usually reversed in these two regions.The consistent spatiotemporal pattern and high partial correlation revealed that rainfall dominated this phenomenon.The previously published findings on how El Nino during different phases of PDO affecting rainfall in eastern China make the statistical relationship between GPP and El Nino in this study theoretically credible.This paper not only introduces an effective way to use BMA in grids that have mixed plant function types,but also makes it possible to evaluate the carbon cycle in eastern China based on the prediction of El Nino and PDO.

Landslide hazards mapping using uncertain Na?ve Bayesian classification method

Landslide hazard mapping is a fundamental tool for disaster management activities in Loess terrains. Aiming at major issues with these landslide hazard assessment methods based on Naive Bayesian classification technique, which is difficult in quantifying those uncertain triggering factors, the main purpose of this work is to evaluate the predictive power of landslide spatial models based on uncertain Naive Bayesian classification method in Baota district of Yan＇an city in Shaanxi province, China. Firstly, thematic maps representing various factors that are related to landslide activity were generated. Secondly, by using field data and GIS techniques, a landslide hazard map was performed. To improve the accuracy of the resulting landslide hazard map, the strategies were designed, which quantified the uncertain triggering factor to design landslide spatial models based on uncertain Naive Bayesian classification method named NBU algorithm. The accuracies of the area under relative operating characteristics curves（AUC） in NBU and Naive Bayesian algorithm are 87.29% and 82.47% respectively. Thus, NBU algorithm can be used efficiently for landslide hazard analysis and might be widely used for the prediction of various spatial events based on uncertain classification technique.

A Novel Approach for QoS Prediction Based on Bayesian Combinational Model

As an important factor in evaluating service,QoS(Quality of Service) has drawn more and more concerns with the rapid increasing of Web services. However,due to the great volatility of services in Mobile Internet environments,such as internet of vehicles,Web services often do not work as announced and thus cause unacceptable problems. QoS prediction can avoid failure before it takes place,which is considered a more effective way to assure quality. However,Current QoS prediction approaches neither consider the highly dynamic of Web services,nor maintain good prediction performance all the time. Consequently we propose a novel Bayesian combinational model to predict QoS by continuously adjusting credit values of the basic models so as to keep good prediction accuracy. QoS attributes such as response time,throughput and reliability are used to validate the proposed model. Experimental results show that the model can provide stable prediction results in Mobile Internet environments.

Bayesian Rayleigh wave inversion with an unknown number of layers

Surface wave methods have received much attention due to their efficient, flexible and convenient characteristics. However, there are still critical issues regarding a key step in surface wave inversion. In most existing methods, the number of layers is assumed to be known prior to the process of inversion. However, improper assignment of this parameter leads to erroneous inversion results. A Bayesian nonparametric method for Rayleigh wave inversion is proposed herein to address this problem. In this method, each model class represents a particular number of layers with unknown S-wave velocity and thickness of each layer. As a result, determination of the number of layers is equivalent to selection of the most applicable model class. Regarding each model class, the optimization search of S-wave velocity and thickness of each layer is implemented by using a genetic algorithm. Then, each model class is assessed in view of its efficiency under the Bayesian framework and the most efficient class is selected. Simulated and actual examples verify that the proposed Bayesian nonparametric approach is reliable and efficient for Rayleigh wave inversion, especially for its capability to determine the number of layers.

Application of Bayesian regularized BP neural network model for analysis of aquatic ecological data—A case study of chlorophyll-a prediction in Nanzui water area of Dongting Lake

Bayesian regularized BP neural network（BRBPNN） technique was applied in the chlorophyll-α prediction of Nanzui water area in Dongting Lake. Through BP network interpolation method, the input and output samples of the network were obtained. After the selection of input variables using stepwise/multiple linear regression method in SPSS i1.0 software, the BRBPNN model was established between chlorophyll-α and environmental parameters, biological parameters. The achieved optimal network structure was 3-11-1 with the correlation coefficients and the mean square errors for the training set and the test set as 0.999 and 0.000？8426, 0.981 and 0.0216 respectively. The sum of square weights between each input neuron and the hidden layer of optimal BRBPNN models of different structures indicated that the effect of individual input parameter on chlorophyll- α declined in the order of alga amount 〉 secchi disc depth（SD） 〉 electrical conductivity （EC）. Additionally, it also demonstrated that the contributions of these three factors were the maximal for the change of chlorophyll-α concentration, total phosphorus（TP） and total nitrogen（TN） were the minimal. All the results showed that BRBPNN model was capable of automated regularization parameter selection and thus it may ensure the excellent generation ability and robustness. Thus, this study laid the foundation for the application of BRBPNN model in the analysis of aquatic ecological data（chlorophyll-α prediction） and the explanation about the effective eutrophication treatment measures for Nanzui water area in Dongting Lake.

Local and regional flood frequency analysis based on hierarchical Bayesian model in Dongting Lake Basin,China

This study developed a hierarchical Bayesian(HB)model for local and regional flood frequency analysis in the Dongting Lake Basin,in China.The annual maximum daily flows from 15 streamflow-gauged sites in the study area were analyzed with the HB model.The generalized extreme value(GEV)distribution was selected as the extreme flood distribution,and the GEV distribution location and scale parameters were spatially modeled through a regression approach with the drainage area as a covariate.The Markov chain Monte Carlo(MCMC)method with Gibbs sampling was employed to calculate the posterior distribution in the HB model.The results showed that the proposed HB model provided satisfactory Bayesian credible intervals for flood quantiles,while the traditional delta method could not provide reliable uncertainty estimations for large flood quantiles,due to the fact that the lower confidence bounds tended to decrease as the return periods increased.Furthermore,the HB model for regional analysis allowed for a reduction in the value of some restrictive assumptions in the traditional index flood method,such as the homogeneity region assumption and the scale invariance assumption.The HB model can also provide an uncertainty band of flood quantile prediction at a poorly gauged or ungauged site,but the index flood method with L-moments does not demonstrate this uncertainty directly.Therefore,the HB model is an effective method of implementing the flexible local and regional frequency analysis scheme,and of quantifying the associated predictive uncertainty.

Improving microwave brightness temperature predictions based on Bayesian model averaging ensemble approach

The choices of the parameterizations for each component in a microwave emission model have significant effects on the quality of brightness temperature （Tb） sim- ulation. How to reduce the uncertainty in the Tb simulation is investigated by adopting a statistical post-processing procedure with the Bayesian model averaging （BMA） ensemble approach. The simulations by the community microwave emission model （CMEM） cou- pled with the community land model version 4.5 （CLM4.5） over China's Mainland are con- ducted by the 24 configurations from four vegetation opacity parameterizations （VOPs）, three soil dielectric constant parameterizations （SDCPs）, and two soil roughness param- eterizations （SRPs）. Compared with the simple arithmetical averaging （SAA） method, the BMA reconstructions have a higher spatial correlation coefficient （larger than 0.99） than the C-band satellite observations of the advanced microwave scanning radiometer on the Earth observing system （AMSR-E） at the vertical polarization. Moreover, the BMA product performs the best among the ensemble members for all vegetation classes, with a mean root-mean-square difference （RMSD） of 4 K and a temporal correlation coefficient of 0.64.

Improving the simulation of terrestrial water storage anomalies over China using a Bayesian model averaging ensemble approach

The ability to estimate terrestrial water storage(TWS)is essential for monitoring hydrological extremes(e.g.,droughts and floods)and predicting future changes in the hydrological cycle.However,inadequacies in model physics and parameters,as well as uncertainties in meteorological forcing data,commonly limit the ability of land surface models(LSMs)to accurately simulate TWS.In this study,the authors show how simulations of TWS anomalies(TWSAs)from multiple meteorological forcings and multiple LSMs can be combined in a Bayesian model averaging(BMA)ensemble approach to improve monitoring and predictions.Simulations using three forcing datasets and two LSMs were conducted over China's Mainland for the period 1979–2008.All the simulations showed good temporal correlations with satellite observations from the Gravity Recovery and Climate Experiment during 2004–08.The correlation coefficient ranged between 0.5 and 0.8 in the humid regions(e.g.,the Yangtze river basin,Huaihe basin,and Zhujiang basin),but was much lower in the arid regions(e.g.,the Heihe basin and Tarim river basin).The BMA ensemble approach performed better than all individual member simulations.It captured the spatial distribution and temporal variations of TWSAs over China's Mainland and the eight major river basins very well;plus,it showed the highest R value(>0.5)over most basins and the lowest root-mean-square error value(<40 mm)in all basins of China.The good performance of the BMA ensemble approach shows that it is a promising way to reproduce long-term,high-resolution spatial and temporal TWSA data.

Climate change in the Tianshan and northern Kunlun Mountains based on GCM simulation ensemble with Bayesian model averaging

Climate change in mountainous regions has significant impacts on hydrological and ecological systems. This research studied the future temperature, precipitation and snowfall in the 21^（st） century for the Tianshan and northern Kunlun Mountains（TKM） based on the general circulation model（GCM） simulation ensemble from the coupled model intercomparison project phase 5（CMIP5） under the representative concentration pathway（RCP） lower emission scenario RCP4.5 and higher emission scenario RCP8.5 using the Bayesian model averaging（BMA） technique. Results show that（1） BMA significantly outperformed the simple ensemble analysis and BMA mean matches all the three observed climate variables;（2） at the end of the 21^（st） century（2070–2099） under RCP8.5, compared to the control period（1976–2005）, annual mean temperature and mean annual precipitation will rise considerably by 4.8°C and 5.2%, respectively, while mean annual snowfall will dramatically decrease by 26.5%;（3） precipitation will increase in the northern Tianshan region while decrease in the Amu Darya Basin. Snowfall will significantly decrease in the western TKM. Mean annual snowfall fraction will also decrease from 0.56 of 1976–2005 to 0.42 of 2070–2099 under RCP8.5; and（4） snowfall shows a high sensitivity to temperature in autumn and spring while a low sensitivity in winter, with the highest sensitivity values occurring at the edge areas of TKM. The projections mean that flood risk will increase and solid water storage will decrease.

The applications of Bayesian models in real-world studies of traditional Chinese medicine:a primer

Real-world study is valuable for traditional Chinese medicine.However,there are no gold standards of statistical approaches for analyzing data from real-world study of traditional Chinese medicine.With the development of computer technology,researchers have increasingly paid attention to Bayesian statistics in the biomedical field.In present study,real-world study and Bayesian statistics were introduced.It was discussed that why and when to use Bayesian analysis and the challenge in the real-world study of traditional Chinese medicine.

Ontology Mapping Based on Bayesian Network

Ontology mapping is a key interoperability enabler for the semantic web. In this paper,a new ontology mapping approach called ontology mapping based on Bayesian network( OM-BN) is proposed. OM-BN combines the models of ontology and Bayesian Network,and applies the method of Multi-strategy to computing similarity. In OM-BN,the characteristics of ontology,such as tree structure and semantic inclusion relations among concepts,are used during the process of translation from ontology to ontology Bayesian network( OBN). Then the method of Multi-strategy is used to create similarity table( ST) for each concept-node in OBN. Finally,the iterative process of mapping reasoning is used to deduce new mappings from STs,repeatedly.

Bayesian meta-analysis of regional biomass factors for Quercus mongolica forests in South Korea

Indirect approaches to estimation of biomass factors are often applied to measure carbon flux in the forestry sector. An assumption underlying a country-level carbon stock estimate is the representativeness of these factors. Although intensive studies have been conducted to quantify biomass factors, each study typically covers a limited geographic area. The goal of this study was to employ a meta-analysis approach to develop regional bio- mass factors for Quercus mongolica forests in South Korea. The biomass factors of interest were biomass conversion and expansion factor （BCEF）, biomass expansion factor （BEF） and root-to-shoot ratio （RSR）. Our objectives were to select probability density functions （PDFs） that best fitted the three biomass factors and to quantify their means and uncertainties. A total of 12 scientific publications were selected as data sources based on a set of criteria. Fromthese publications we chose 52 study sites spread out across South Korea. The statistical model for the meta- analysis was a multilevel model with publication （data source） as the nesting factor specified under the Bayesian framework. Gamma, Log-normal and Weibull PDFs were evaluated. The Log-normal PDF yielded the best quanti- tative and qualitative fit for the three biomass factors. However, a poor fit of the PDF to the long right tail of observed BEF and RSR distributions was apparent. The median posterior estimates for means and 95 % credible intervals for BCEF, BEF and RSR across all 12 publica- tions were 1.016 （0.800-1.299）, 1.414 （1.304-1.560） and 0.260 （0.200-0.335）, respectively. The Log-normal PDF proved useful for estimating carbon stock of Q. mongolica forests on a regional scale and for uncertainty analysis based on Monte Carlo simulation.