This study investigated the impacts of random negative training datasets(NTDs)on the uncertainty of machine learning models for geologic hazard susceptibility assessment of the Loess Plateau,northern Shaanxi Province,...This study investigated the impacts of random negative training datasets(NTDs)on the uncertainty of machine learning models for geologic hazard susceptibility assessment of the Loess Plateau,northern Shaanxi Province,China.Based on randomly generated 40 NTDs,the study developed models for the geologic hazard susceptibility assessment using the random forest algorithm and evaluated their performances using the area under the receiver operating characteristic curve(AUC).Specifically,the means and standard deviations of the AUC values from all models were then utilized to assess the overall spatial correlation between the conditioning factors and the susceptibility assessment,as well as the uncertainty introduced by the NTDs.A risk and return methodology was thus employed to quantify and mitigate the uncertainty,with log odds ratios used to characterize the susceptibility assessment levels.The risk and return values were calculated based on the standard deviations and means of the log odds ratios of various locations.After the mean log odds ratios were converted into probability values,the final susceptibility map was plotted,which accounts for the uncertainty induced by random NTDs.The results indicate that the AUC values of the models ranged from 0.810 to 0.963,with an average of 0.852 and a standard deviation of 0.035,indicating encouraging prediction effects and certain uncertainty.The risk and return analysis reveals that low-risk and high-return areas suggest lower standard deviations and higher means across multiple model-derived assessments.Overall,this study introduces a new framework for quantifying the uncertainty of multiple training and evaluation models,aimed at improving their robustness and reliability.Additionally,by identifying low-risk and high-return areas,resource allocation for geologic hazard prevention and control can be optimized,thus ensuring that limited resources are directed toward the most effective prevention and control measures.展开更多
The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally average...The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally averaged spatial distributions under different temperatures are calculated to evaluate the stabilities of(H2)n@C70(n = 1, 2, 3). The results show that(H2)2@C70is more stable than H2@C70. The interaction energy slowly changes in a large temperature range,so temperature has little effect on the stability of the system. For H2@C70and(H2)2@C70, the interaction energies keep negative; however, when three H2 molecules are in the cage, the interaction energy rapidly increases to a positive value.This implies that at most two H2 molecules can be trapped by C70. With an increase of temperature, the peak of the spatial distribution gradually shifts away from the center of the cage, but the maximum distance from the center of H2 molecule to the cage center is much smaller than the average radius of C70.展开更多
Nonlinear dynamical stochastic models are ubiquitous in different areas.Their statistical properties are often of great interest,but are also very challenging to compute.Many excitable media models belong to such type...Nonlinear dynamical stochastic models are ubiquitous in different areas.Their statistical properties are often of great interest,but are also very challenging to compute.Many excitable media models belong to such types of complex systems with large state dimensions and the associated covariance matrices have localized structures.In this article,a mathematical framework to understand the spatial localization for a large class of stochastically coupled nonlinear systems in high dimensions is developed.Rigorous mathematical analysis shows that the local effect from the diffusion results in an exponential decay of the components in the covariance matrix as a function of the distance while the global effect due to the mean field interaction synchronizes different components and contributes to a global covariance.The analysis is based on a comparison with an appropriate linear surrogate model,of which the covariance propagation can be computed explicitly.Two important applications of these theoretical results are discussed.They are the spatial averaging strategy for efficiently sampling the covariance matrix and the localization technique in data assimilation.Test examples of a linear model and a stochastically coupled Fitz Hugh-Nagumo model for excitable media are adopted to validate the theoretical results.The latter is also used for a systematical study of the spatial averaging strategy in efficiently sampling the covariance matrix in different dynamical regimes.展开更多
One of the key research problems in financial markets is the investigation of inter-stock dependence.A good understanding in this regard is crucial for portfolio optimization.To this end,various econometric models hav...One of the key research problems in financial markets is the investigation of inter-stock dependence.A good understanding in this regard is crucial for portfolio optimization.To this end,various econometric models have been proposed.Most of them assume that the random noise associated with each subject is independent.However,dependence might still exist within this random noise.Ignoring this valuable information might lead to biased estimations and inaccurate predictions.In this article,we study a spatial autoregressive moving average model with exogenous covariates.Spatial dependence from both response and random noise is considered simultaneously.A quasi-maximum likelihood estimator is developed,and the estimated parameters are shown to be consistent and asymptotically normal.We then conduct an extensive analysis of the proposed method by applying it to the Chinese stock market data.展开更多
基金supported by a project entitled Loess Plateau Region-Watershed-Slope Geological Hazard Multi-Scale Collaborative Intelligent Early Warning System of the National Key R&D Program of China(2022YFC3003404)a project of the Shaanxi Youth Science and Technology Star(2021KJXX-87)public welfare geological survey projects of Shaanxi Institute of Geologic Survey(20180301,201918,202103,and 202413).
文摘This study investigated the impacts of random negative training datasets(NTDs)on the uncertainty of machine learning models for geologic hazard susceptibility assessment of the Loess Plateau,northern Shaanxi Province,China.Based on randomly generated 40 NTDs,the study developed models for the geologic hazard susceptibility assessment using the random forest algorithm and evaluated their performances using the area under the receiver operating characteristic curve(AUC).Specifically,the means and standard deviations of the AUC values from all models were then utilized to assess the overall spatial correlation between the conditioning factors and the susceptibility assessment,as well as the uncertainty introduced by the NTDs.A risk and return methodology was thus employed to quantify and mitigate the uncertainty,with log odds ratios used to characterize the susceptibility assessment levels.The risk and return values were calculated based on the standard deviations and means of the log odds ratios of various locations.After the mean log odds ratios were converted into probability values,the final susceptibility map was plotted,which accounts for the uncertainty induced by random NTDs.The results indicate that the AUC values of the models ranged from 0.810 to 0.963,with an average of 0.852 and a standard deviation of 0.035,indicating encouraging prediction effects and certain uncertainty.The risk and return analysis reveals that low-risk and high-return areas suggest lower standard deviations and higher means across multiple model-derived assessments.Overall,this study introduces a new framework for quantifying the uncertainty of multiple training and evaluation models,aimed at improving their robustness and reliability.Additionally,by identifying low-risk and high-return areas,resource allocation for geologic hazard prevention and control can be optimized,thus ensuring that limited resources are directed toward the most effective prevention and control measures.
基金supported by the National Natural Science Foundation of China(Grant Nos.11474207 and 11374217)
文摘The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally averaged spatial distributions under different temperatures are calculated to evaluate the stabilities of(H2)n@C70(n = 1, 2, 3). The results show that(H2)2@C70is more stable than H2@C70. The interaction energy slowly changes in a large temperature range,so temperature has little effect on the stability of the system. For H2@C70and(H2)2@C70, the interaction energies keep negative; however, when three H2 molecules are in the cage, the interaction energy rapidly increases to a positive value.This implies that at most two H2 molecules can be trapped by C70. With an increase of temperature, the peak of the spatial distribution gradually shifts away from the center of the cage, but the maximum distance from the center of H2 molecule to the cage center is much smaller than the average radius of C70.
基金supported by the Office of Vice Chancellor for Research and Graduate Education(VCRGE)at University of Wisconsin-Madisonthe Office of Naval Research Grant ONR MURI N00014-16-1-2161+1 种基金the Center for Prototype Climate Modeling(CPCM)at New York University Abu Dhabi Research InstituteNUS Grant R-146-000-226-133
文摘Nonlinear dynamical stochastic models are ubiquitous in different areas.Their statistical properties are often of great interest,but are also very challenging to compute.Many excitable media models belong to such types of complex systems with large state dimensions and the associated covariance matrices have localized structures.In this article,a mathematical framework to understand the spatial localization for a large class of stochastically coupled nonlinear systems in high dimensions is developed.Rigorous mathematical analysis shows that the local effect from the diffusion results in an exponential decay of the components in the covariance matrix as a function of the distance while the global effect due to the mean field interaction synchronizes different components and contributes to a global covariance.The analysis is based on a comparison with an appropriate linear surrogate model,of which the covariance propagation can be computed explicitly.Two important applications of these theoretical results are discussed.They are the spatial averaging strategy for efficiently sampling the covariance matrix and the localization technique in data assimilation.Test examples of a linear model and a stochastically coupled Fitz Hugh-Nagumo model for excitable media are adopted to validate the theoretical results.The latter is also used for a systematical study of the spatial averaging strategy in efficiently sampling the covariance matrix in different dynamical regimes.
基金supported by the Major Program of the National Natural Science Foundation of China (Grant No. 11731101)National Natural Science Foundation of China (Grant No. 11671349)+6 种基金supported by National Natural Science Foundation of China (Grant No. 72171226)the Beijing Municipal Social Science Foundation (Grant No. 19GLC052)the National Statistical Science Research Project (Grant No. 2020LZ38)supported by National Natural Science Foundation of China (Grant Nos. 71532001, 11931014, 12171395 and 71991472)the Joint Lab of Data Science and Business Intelligence at Southwestern University of Finance and Economicssupported by National Natural Science Foundation of China (Grant No. 11831008)the Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science (Grant No. Klatasds-Moe-EcnuKlatasds2101)
文摘One of the key research problems in financial markets is the investigation of inter-stock dependence.A good understanding in this regard is crucial for portfolio optimization.To this end,various econometric models have been proposed.Most of them assume that the random noise associated with each subject is independent.However,dependence might still exist within this random noise.Ignoring this valuable information might lead to biased estimations and inaccurate predictions.In this article,we study a spatial autoregressive moving average model with exogenous covariates.Spatial dependence from both response and random noise is considered simultaneously.A quasi-maximum likelihood estimator is developed,and the estimated parameters are shown to be consistent and asymptotically normal.We then conduct an extensive analysis of the proposed method by applying it to the Chinese stock market data.
