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...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.展开更多
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,...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.展开更多
patients with PPF.TCM treatments are typically diverse and individualized,requiring urgent development of efficient and precise design strategies to identify effective treatment options.We designed an innovative Bayes...patients with PPF.TCM treatments are typically diverse and individualized,requiring urgent development of efficient and precise design strategies to identify effective treatment options.We designed an innovative Bayesian adaptive two-stage trial,hoping to provide new ideas for the rapid evaluation of the effectiveness of TCM in PPF.An open-label,two-stage,adaptive Bayesian randomized controlled trial will be conducted in China.Based on Bayesian methods,the trial will employ response-adaptive randomization to allocate patients to study groups based on data collected over the course of the trial.The adaptive Bayesian trial design will employ a Bayesian hierarchical model with“stopping”and“continuation”criteria once a predetermined posterior probability of superiority or futility and a decision threshold are reached.The trial can be implemented more efficiently by sharing the master protocol and organizational management mechanisms of the sub-trial we have implemented.The primary patient-reported outcome is a change in the Leicester Cough Questionnaire score,reflecting an improvement in cough-specific quality of life.The adaptive Bayesian trial design may be a promising method to facilitate the rapid clinical evaluation of TCM effectiveness for PPF,and will provide an example for how to evaluate TCM effectiveness in rare and refractory diseases.However,due to the complexity of the trial implementation,sufficient simulation analysis by professional statistical analysts is required to construct a Bayesian response-adaptive randomization procedure for timely response.Moreover,detailed standard operating procedures need to be developed to ensure the feasibility of the trial implementation.展开更多
Recently,machine learning has become a powerful tool for predicting nuclear charge radius RC,providing novel insights into complex physical phenomena.This study employs a continuous Bayesian probability(CBP)estimator ...Recently,machine learning has become a powerful tool for predicting nuclear charge radius RC,providing novel insights into complex physical phenomena.This study employs a continuous Bayesian probability(CBP)estimator and Bayesian model averaging(BMA)to optimize the predictions of RCfrom sophisticated theoretical models.The CBP estimator treats the residual between the theoretical and experimental values of RCas a continuous variable and derives its posterior probability density function(PDF)from Bayesian theory.The BMA method assigns weights to models based on their predictive performance for benchmark nuclei,thereby accounting for the unique strengths of each model.In global optimization,the CBP estimator improved the predictive accuracy of the three theoretical models by approximately 60%.The extrapolation analyses consistently achieved an improvement rate of approximately 45%,demonstrating the robustness of the CBP estimator.Furthermore,the combination of the CBP and BMA methods reduces the standard deviation to below 0.02 fm,effectively reproducing the pronounced shell effects on RCof the Ca and Sr isotope chains.The studies in this paper propose an efficient method to accurately describe RCof unknown nuclei,with potential applications in research on other nuclear properties.展开更多
Background:The short term forecasts regarding different parameters of the COVID-19 are very important to make informed decisions.However,majority of the earlier contributions have used classical time series models,suc...Background:The short term forecasts regarding different parameters of the COVID-19 are very important to make informed decisions.However,majority of the earlier contributions have used classical time series models,such as auto regressive integrated moving average(ARIMA)models,to obtain the said forecasts for Iran and its neighbors.In addition,the impacts of lifting the lockdowns in the said countries have not been studied.The aim of this paper is to propose more flexible Bayesian structural time series(BSTS)models for forecasting the future trends of the COVID-19 in Iran and its neighbors,and to compare the predictive power of the BSTS models with frequently used ARIMA models.The paper also aims to investigate the casual impacts of lifting the lockdown in the targeted countries using proposed models.Methods:We have proposed BSTS models to forecast the patterns of this pandemic in Iran and its neighbors.The predictive power of the proposed models has been compared with ARIMA models using different forecast accuracy criteria.We have also studied the causal impacts of resuming commercial/social activities in these countries using intervention analysis under BSTS models.The forecasts for next thirty days were obtained by using the data from March 16 to July 22,2020.These data have been obtained from Our World in Data and Humanitarian Data Exchange(HDX).All the numerical results have been obtained using R software.Results:Different measures of forecast accuracy advocated that forecasts under BSTS models were better than those under ARIMA models.Our forecasts suggested that the active numbers of cases are expected to decrease in Iran and its neighbors,except Afghanistan.However,the death toll is expected to increase at more pace in majority of these countries.The resuming of commercial/social activities in these countries has accelerated the surges in number of positive cases.Conclusions:The serious efforts would be needed to make sure that these expected figures regarding active number of cases come true.Iran and its neighbors need to improve their extensive healthcare infrastructure to cut down the higher expected death toll.Finally,these countries should develop and implement the strict SOPs for the commercial activities in order to prevent the expected second wave of the pandemic.展开更多
To ensure agreement between theoretical calculations and experimental data,parameters to selected nuclear physics models are perturbed and fine-tuned in nuclear data evaluations.This approach assumes that the chosen s...To ensure agreement between theoretical calculations and experimental data,parameters to selected nuclear physics models are perturbed and fine-tuned in nuclear data evaluations.This approach assumes that the chosen set of models accurately represents the‘true’distribution of considered observables.Furthermore,the models are chosen globally,indicating their applicability across the entire energy range of interest.However,this approach overlooks uncertainties inherent in the models themselves.In this work,we propose that instead of selecting globally a winning model set and proceeding with it as if it was the‘true’model set,we,instead,take a weighted average over multiple models within a Bayesian model averaging(BMA)framework,each weighted by its posterior probability.The method involves executing a set of TALYS calculations by randomly varying multiple nuclear physics models and their parameters to yield a vector of calculated observables.Next,computed likelihood function values at each incident energy point were then combined with the prior distributions to obtain updated posterior distributions for selected cross sections and the elastic angular distributions.As the cross sections and elastic angular distributions were updated locally on a per-energy-point basis,the approach typically results in discontinuities or“kinks”in the cross section curves,and these were addressed using spline interpolation.The proposed BMA method was applied to the evaluation of proton-induced reactions on ^(58)Ni between 1 and 100 MeV.The results demonstrated a favorable comparison with experimental data as well as with the TENDL-2023 evaluation.展开更多
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 a...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.展开更多
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 u...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.展开更多
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 backgro...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.展开更多
This study examines the relationship between macroeconomic variables and stock price indices of four prominent OPEC oil-exporting members.Bayesian model averaging(BMA)and regularized linear regression(RLR)are employed...This study examines the relationship between macroeconomic variables and stock price indices of four prominent OPEC oil-exporting members.Bayesian model averaging(BMA)and regularized linear regression(RLR)are employed to address uncertainties arising from different estimation models and variable selection.Jointness is utilized to determine the nature of relationships among variable pairs.The case study spans macroeconomic variables and stock prices from 1996 to 2018.BMA findings reveal a strong positive association between stock price indices and both consumer price index(CPI)and broad money growth in each analyzed OPEC country.Additionally,the study suggests a weak negative correlation between OPEC oil prices and the stock price index.RLR results align with BMA analysis,offering insights valuable for policymakers and international wealth managers.展开更多
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 u...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.展开更多
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 functi...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.展开更多
Temperate rainforests have historically been considered highly vulnerable to disturbance.Climate change,which is expected to increase the intensity,frequency,and impacts of disturbance events,is consequently a signifi...Temperate rainforests have historically been considered highly vulnerable to disturbance.Climate change,which is expected to increase the intensity,frequency,and impacts of disturbance events,is consequently a significant threat to their long-term persistence.However,data describing the long-term response of temperate rainforests to disturbance is rare.In the cool temperate rainforests of northern New South Wales,Australia,Nothofagus moorei is considered especially vulnerable to climate change due to a decreasing number of mature individuals,limited remaining suitable habitat,and low rates of sexual regeneration.In this study,we used over 50 years of empirical data from silvicultural experiments with multiple thinning intensities to characterise the demographic responses(i.e.,growth,mortality,and recruitment)of cool temperate rainforest species,including N.moorei,to disturbance over time.Cool temperate rainforest species showed resilience to disturbance,predominantly through their widespread ability to basally coppice.Nothofagus moorei,in particular,demonstrated higher rates of successful sexual and vegetative recruitment and grew faster in response to higher intensities of disturbance,in comparison to very low rates of recruitment pre-disturbance.These results challenge successional models that position rainforests as disturbance-sensitive ecosystems and identify N.moorei as a species that requires large-scale disturbance to successfully regenerate.Management regimes that actively exclude disturbance from these forests risk the local loss of disturbance-dependent rainforest species such as N.moorei.展开更多
Biomass burning(BB)emits carbonaceous aerosols that significantly influence air quality in Southwest China during spring.To further understand the characteristics of spring BB and its original contribution to organic ...Biomass burning(BB)emits carbonaceous aerosols that significantly influence air quality in Southwest China during spring.To further understand the characteristics of spring BB and its original contribution to organic carbon(OC),daily fine particulate matter(PM_(2.5))samples were collected from March to May 2022 in Pu'er,Southwest China.The concentrations of OC,elemental carbon(EC),levoglucosan(Lev),and potassium from BB(K+BB)during the study period ranged from 5.3 to 31.2μg/m^(3),0.86-13.1μg/m^(3),0.06-0.82μg/m^(3),and 0.05-2.88μg/m^(3),respectively.To eliminate the effects of Lev degradation,this study uses the Aging of Air Mass(AAM)index to correct the atmospheric concentration of Lev and combines Bayesian mixture modeling with a molecular tracer method to assess the original contribution of BB to OC.The results indicated that the AAM index was 0.18±0.05,indicating that the degradation of Lev reached 82%.When considering the degradation of levoglucosan in the atmosphere,the primary source of BB aerosols was crop-straw combustion(71.1%),followed by the combustion of certain hardwoods and softwoods(24.9%)and grasses(4.0%).The original contribution of BB to OC was 62.4%,which was much greater than the contribution when levoglucosan degradation(23.7%)was ignored.The air mass inverse trajectories and Moderate Resolution Imaging Spectroradiometer(MODIS)fire hotspots indicated that the BB plume from Southeast Asia during spring could influence PM_(2.5)long-range transport in remote locations,and the contribution could reach 82%in Southwest China.展开更多
Background:There is the limited evidence available from randomized controlled trials on the dose-response relationship of NiuHuangJiangYa capsule for hypertension.The objective of this study is to investigate the dose...Background:There is the limited evidence available from randomized controlled trials on the dose-response relationship of NiuHuangJiangYa capsule for hypertension.The objective of this study is to investigate the dose-response relationship of NiuHuangJiangYa capsule for hypertension based on multiple N-of-1 trials.Methods:This study was a secondary analysis of the data from a series of N-of-1 trials examining the efficacy of high-dose versus low-dose NiuHuangJiangYa capsule for hypertension.Hierarchical Bayesian models were used to aggregate these N-of-1 trials for estimating the population and individual treatment effects synchronously.Results:It showed that overall population estimates of the posterior mean difference in Systolic Blood Pressure reduction,Diastolic Blood Pressure reduction,and traditional Chinese medicine symptom score reduction were 3.18 mmHg(95%CIs:-4.69 to 9.04,posterior probability(>0):83.33%),0.8636 mmHg(95%CIs:-5.19 to 6.79,posterior probability(>0):63.38%),and 0.8384(95%CIs:-2.21 to 3.84,posterior probability(>0):77.05%)respectively.Individual posterior mean difference ranged from 1.237 to 5.628 with posterior probability(>0)ranging from 63.63%to 92.95%in Systolic Blood Pressure reduction,-0.714 to 3.423 with posterior probability(>0)ranging from 43.03%to 84.04%in Diastolic Blood Pressure reduction,and-0.5179 to 2.733 with posterior probability(>0)ranging from 27.02%to 97.73%in traditional Chinese medicine symptom score reduction.Conclusion:The efficacy of high-dose versus low-dose NiuHuangJiangYa capsule for hypertension may be various across patients.Further studies are warranted to investigate these findings.Moreover,Bayesian N-of-1 trial may be helpful to explore the optimal and personalized dosage of anti-hypertensive drugs.展开更多
Respiratory diseases and air pollution are the goals of many scientific works, but studies of the relations between these diseases and cane field burning pollution are still not well studied in the literature. In this...Respiratory diseases and air pollution are the goals of many scientific works, but studies of the relations between these diseases and cane field burning pollution are still not well studied in the literature. In this work, we consider the times between days of extrapolations of the number of daily hospitalizations due to respiratory diseases as our data. To analyze this data set, we introduce different statistical models related to burning focus pollution and their relations with the counting of hospitalizations due to respiratory diseases. Under a Bayesian approach and with the help of the free available WinBUGS software, we get posterior summaries of interest using standard MCMC (Markov Chain Monte Carlo) methods.展开更多
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 ...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.展开更多
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 techniq...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.展开更多
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 envir...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.展开更多
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 exist...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.展开更多
基金the project of National Natural Science Foundation of China(grant numbers 81273935,81303093,81602930).
文摘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.
基金This study was supported by the National Natural Science Foundation of China(42261008,41971034)the Natural Science Foundation of Gansu Province,China(22JR5RA074).
文摘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.
基金supported by National Natural Science Foundation of China(No.81973713)。
文摘patients with PPF.TCM treatments are typically diverse and individualized,requiring urgent development of efficient and precise design strategies to identify effective treatment options.We designed an innovative Bayesian adaptive two-stage trial,hoping to provide new ideas for the rapid evaluation of the effectiveness of TCM in PPF.An open-label,two-stage,adaptive Bayesian randomized controlled trial will be conducted in China.Based on Bayesian methods,the trial will employ response-adaptive randomization to allocate patients to study groups based on data collected over the course of the trial.The adaptive Bayesian trial design will employ a Bayesian hierarchical model with“stopping”and“continuation”criteria once a predetermined posterior probability of superiority or futility and a decision threshold are reached.The trial can be implemented more efficiently by sharing the master protocol and organizational management mechanisms of the sub-trial we have implemented.The primary patient-reported outcome is a change in the Leicester Cough Questionnaire score,reflecting an improvement in cough-specific quality of life.The adaptive Bayesian trial design may be a promising method to facilitate the rapid clinical evaluation of TCM effectiveness for PPF,and will provide an example for how to evaluate TCM effectiveness in rare and refractory diseases.However,due to the complexity of the trial implementation,sufficient simulation analysis by professional statistical analysts is required to construct a Bayesian response-adaptive randomization procedure for timely response.Moreover,detailed standard operating procedures need to be developed to ensure the feasibility of the trial implementation.
基金supported by the National Natural Science Foundation of China(Nos.12475135,12035011,and 12475119)the Shandong Provincial Natural Science Foundation,China(No.ZR2020MA096)the Fundamental Research Funds for the Central Universities(No.22CX03017A)。
文摘Recently,machine learning has become a powerful tool for predicting nuclear charge radius RC,providing novel insights into complex physical phenomena.This study employs a continuous Bayesian probability(CBP)estimator and Bayesian model averaging(BMA)to optimize the predictions of RCfrom sophisticated theoretical models.The CBP estimator treats the residual between the theoretical and experimental values of RCas a continuous variable and derives its posterior probability density function(PDF)from Bayesian theory.The BMA method assigns weights to models based on their predictive performance for benchmark nuclei,thereby accounting for the unique strengths of each model.In global optimization,the CBP estimator improved the predictive accuracy of the three theoretical models by approximately 60%.The extrapolation analyses consistently achieved an improvement rate of approximately 45%,demonstrating the robustness of the CBP estimator.Furthermore,the combination of the CBP and BMA methods reduces the standard deviation to below 0.02 fm,effectively reproducing the pronounced shell effects on RCof the Ca and Sr isotope chains.The studies in this paper propose an efficient method to accurately describe RCof unknown nuclei,with potential applications in research on other nuclear properties.
文摘Background:The short term forecasts regarding different parameters of the COVID-19 are very important to make informed decisions.However,majority of the earlier contributions have used classical time series models,such as auto regressive integrated moving average(ARIMA)models,to obtain the said forecasts for Iran and its neighbors.In addition,the impacts of lifting the lockdowns in the said countries have not been studied.The aim of this paper is to propose more flexible Bayesian structural time series(BSTS)models for forecasting the future trends of the COVID-19 in Iran and its neighbors,and to compare the predictive power of the BSTS models with frequently used ARIMA models.The paper also aims to investigate the casual impacts of lifting the lockdown in the targeted countries using proposed models.Methods:We have proposed BSTS models to forecast the patterns of this pandemic in Iran and its neighbors.The predictive power of the proposed models has been compared with ARIMA models using different forecast accuracy criteria.We have also studied the causal impacts of resuming commercial/social activities in these countries using intervention analysis under BSTS models.The forecasts for next thirty days were obtained by using the data from March 16 to July 22,2020.These data have been obtained from Our World in Data and Humanitarian Data Exchange(HDX).All the numerical results have been obtained using R software.Results:Different measures of forecast accuracy advocated that forecasts under BSTS models were better than those under ARIMA models.Our forecasts suggested that the active numbers of cases are expected to decrease in Iran and its neighbors,except Afghanistan.However,the death toll is expected to increase at more pace in majority of these countries.The resuming of commercial/social activities in these countries has accelerated the surges in number of positive cases.Conclusions:The serious efforts would be needed to make sure that these expected figures regarding active number of cases come true.Iran and its neighbors need to improve their extensive healthcare infrastructure to cut down the higher expected death toll.Finally,these countries should develop and implement the strict SOPs for the commercial activities in order to prevent the expected second wave of the pandemic.
基金funding from the Paul ScherrerInstitute,Switzerland through the NES/GFA-ABE Cross Project。
文摘To ensure agreement between theoretical calculations and experimental data,parameters to selected nuclear physics models are perturbed and fine-tuned in nuclear data evaluations.This approach assumes that the chosen set of models accurately represents the‘true’distribution of considered observables.Furthermore,the models are chosen globally,indicating their applicability across the entire energy range of interest.However,this approach overlooks uncertainties inherent in the models themselves.In this work,we propose that instead of selecting globally a winning model set and proceeding with it as if it was the‘true’model set,we,instead,take a weighted average over multiple models within a Bayesian model averaging(BMA)framework,each weighted by its posterior probability.The method involves executing a set of TALYS calculations by randomly varying multiple nuclear physics models and their parameters to yield a vector of calculated observables.Next,computed likelihood function values at each incident energy point were then combined with the prior distributions to obtain updated posterior distributions for selected cross sections and the elastic angular distributions.As the cross sections and elastic angular distributions were updated locally on a per-energy-point basis,the approach typically results in discontinuities or“kinks”in the cross section curves,and these were addressed using spline interpolation.The proposed BMA method was applied to the evaluation of proton-induced reactions on ^(58)Ni between 1 and 100 MeV.The results demonstrated a favorable comparison with experimental data as well as with the TENDL-2023 evaluation.
基金supported by The Technology Innovation Team(Tianshan Innovation Team),Innovative Team for Efficient Utilization of Water Resources in Arid Regions(2022TSYCTD0001)the National Natural Science Foundation of China(42171269)the Xinjiang Academician Workstation Cooperative Research Project(2020.B-001).
文摘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.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(2023A1515011244).
文摘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.
文摘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.
文摘This study examines the relationship between macroeconomic variables and stock price indices of four prominent OPEC oil-exporting members.Bayesian model averaging(BMA)and regularized linear regression(RLR)are employed to address uncertainties arising from different estimation models and variable selection.Jointness is utilized to determine the nature of relationships among variable pairs.The case study spans macroeconomic variables and stock prices from 1996 to 2018.BMA findings reveal a strong positive association between stock price indices and both consumer price index(CPI)and broad money growth in each analyzed OPEC country.Additionally,the study suggests a weak negative correlation between OPEC oil prices and the stock price index.RLR results align with BMA analysis,offering insights valuable for policymakers and international wealth managers.
文摘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.
基金The National Natural Science Foundation of China(No.8123003481271739+2 种基金81501453)the Special Program of Medical Science of Jiangsu Province(No.BL2013029)the Natural Science Foundation of Jiangsu Province(No.BK20141342)
文摘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.
基金supported by the Bushfire and Natural Hazards Cooperative Research Centre and New South Wales National Parks and Wildlife Service.
文摘Temperate rainforests have historically been considered highly vulnerable to disturbance.Climate change,which is expected to increase the intensity,frequency,and impacts of disturbance events,is consequently a significant threat to their long-term persistence.However,data describing the long-term response of temperate rainforests to disturbance is rare.In the cool temperate rainforests of northern New South Wales,Australia,Nothofagus moorei is considered especially vulnerable to climate change due to a decreasing number of mature individuals,limited remaining suitable habitat,and low rates of sexual regeneration.In this study,we used over 50 years of empirical data from silvicultural experiments with multiple thinning intensities to characterise the demographic responses(i.e.,growth,mortality,and recruitment)of cool temperate rainforest species,including N.moorei,to disturbance over time.Cool temperate rainforest species showed resilience to disturbance,predominantly through their widespread ability to basally coppice.Nothofagus moorei,in particular,demonstrated higher rates of successful sexual and vegetative recruitment and grew faster in response to higher intensities of disturbance,in comparison to very low rates of recruitment pre-disturbance.These results challenge successional models that position rainforests as disturbance-sensitive ecosystems and identify N.moorei as a species that requires large-scale disturbance to successfully regenerate.Management regimes that actively exclude disturbance from these forests risk the local loss of disturbance-dependent rainforest species such as N.moorei.
基金supported by the Basic Research Key Project of Science and Technology Department of Yunnan Province(No.202401AS070116)the National Natural Science Foundation of China(No.21966016)。
文摘Biomass burning(BB)emits carbonaceous aerosols that significantly influence air quality in Southwest China during spring.To further understand the characteristics of spring BB and its original contribution to organic carbon(OC),daily fine particulate matter(PM_(2.5))samples were collected from March to May 2022 in Pu'er,Southwest China.The concentrations of OC,elemental carbon(EC),levoglucosan(Lev),and potassium from BB(K+BB)during the study period ranged from 5.3 to 31.2μg/m^(3),0.86-13.1μg/m^(3),0.06-0.82μg/m^(3),and 0.05-2.88μg/m^(3),respectively.To eliminate the effects of Lev degradation,this study uses the Aging of Air Mass(AAM)index to correct the atmospheric concentration of Lev and combines Bayesian mixture modeling with a molecular tracer method to assess the original contribution of BB to OC.The results indicated that the AAM index was 0.18±0.05,indicating that the degradation of Lev reached 82%.When considering the degradation of levoglucosan in the atmosphere,the primary source of BB aerosols was crop-straw combustion(71.1%),followed by the combustion of certain hardwoods and softwoods(24.9%)and grasses(4.0%).The original contribution of BB to OC was 62.4%,which was much greater than the contribution when levoglucosan degradation(23.7%)was ignored.The air mass inverse trajectories and Moderate Resolution Imaging Spectroradiometer(MODIS)fire hotspots indicated that the BB plume from Southeast Asia during spring could influence PM_(2.5)long-range transport in remote locations,and the contribution could reach 82%in Southwest China.
基金This study was supported by the National Natural Science Foundation of China.(No.81973705).
文摘Background:There is the limited evidence available from randomized controlled trials on the dose-response relationship of NiuHuangJiangYa capsule for hypertension.The objective of this study is to investigate the dose-response relationship of NiuHuangJiangYa capsule for hypertension based on multiple N-of-1 trials.Methods:This study was a secondary analysis of the data from a series of N-of-1 trials examining the efficacy of high-dose versus low-dose NiuHuangJiangYa capsule for hypertension.Hierarchical Bayesian models were used to aggregate these N-of-1 trials for estimating the population and individual treatment effects synchronously.Results:It showed that overall population estimates of the posterior mean difference in Systolic Blood Pressure reduction,Diastolic Blood Pressure reduction,and traditional Chinese medicine symptom score reduction were 3.18 mmHg(95%CIs:-4.69 to 9.04,posterior probability(>0):83.33%),0.8636 mmHg(95%CIs:-5.19 to 6.79,posterior probability(>0):63.38%),and 0.8384(95%CIs:-2.21 to 3.84,posterior probability(>0):77.05%)respectively.Individual posterior mean difference ranged from 1.237 to 5.628 with posterior probability(>0)ranging from 63.63%to 92.95%in Systolic Blood Pressure reduction,-0.714 to 3.423 with posterior probability(>0)ranging from 43.03%to 84.04%in Diastolic Blood Pressure reduction,and-0.5179 to 2.733 with posterior probability(>0)ranging from 27.02%to 97.73%in traditional Chinese medicine symptom score reduction.Conclusion:The efficacy of high-dose versus low-dose NiuHuangJiangYa capsule for hypertension may be various across patients.Further studies are warranted to investigate these findings.Moreover,Bayesian N-of-1 trial may be helpful to explore the optimal and personalized dosage of anti-hypertensive drugs.
文摘Respiratory diseases and air pollution are the goals of many scientific works, but studies of the relations between these diseases and cane field burning pollution are still not well studied in the literature. In this work, we consider the times between days of extrapolations of the number of daily hospitalizations due to respiratory diseases as our data. To analyze this data set, we introduce different statistical models related to burning focus pollution and their relations with the counting of hospitalizations due to respiratory diseases. Under a Bayesian approach and with the help of the free available WinBUGS software, we get posterior summaries of interest using standard MCMC (Markov Chain Monte Carlo) methods.
基金supported by the National Key Research and Development Program of China (Grant Nos.2016YFA0602501 and 2018YFA0606004)the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos.XDA20040301 and XDA20020201)。
文摘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.
基金Projects(41362015,51164012) supported by the National Natural Science Foundation of ChinaProject(2012AA061901) supported by the National High-tech Research and Development Program of China
文摘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.
基金supported by National Natural Science Foundation of China (61572171,61202097,61202136)Research Fund for the Doctoral Program of Higher Education of China (20120094120009)+2 种基金Fundamental Research Funds for the Central Universities of China (B15020191)the national college students innovation training program (No.201511460012)by Jiangsu Province,and key special funds of efficient utilization of water resources (No.2016YFC0402710)
文摘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.
基金Science and Technology Development Fund of the Macao SAR under research grant SKL-IOTSC-2018-2020the Research Committee of University of Macao under Research Grant MYRG2016-00029-FST。
文摘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.
