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
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
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 simu...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.展开更多
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 ph...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.展开更多
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 ...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.展开更多
In this paper, a model averaging method is proposed for varying-coefficient models with response missing at random by establishing a weight selection criterion based on cross-validation. Under certain regularity condi...In this paper, a model averaging method is proposed for varying-coefficient models with response missing at random by establishing a weight selection criterion based on cross-validation. Under certain regularity conditions, it is proved that the proposed method is asymptotically optimal in the sense of achieving the minimum squared error.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
Bayesian model averaging (BMA) is a popular and powerful statistical method of taking account of uncertainty about model form or assumption. Usually the long run (frequentist) performances of the resulted estimator ar...Bayesian model averaging (BMA) is a popular and powerful statistical method of taking account of uncertainty about model form or assumption. Usually the long run (frequentist) performances of the resulted estimator are hard to derive. This paper proposes a mixture of priors and sampling distributions as a basic of a Bayes estimator. The frequentist properties of the new Bayes estimator are automatically derived from Bayesian decision theory. It is shown that if all competing models have the same parametric form, the new Bayes estimator reduces to BMA estimator. The method is applied to the daily exchange rate Euro to US Dollar.展开更多
In several instances of statistical practice, it is not uncommon to use the same data for both model selection and inference, without taking account of the variability induced by model selection step. This is usually ...In several instances of statistical practice, it is not uncommon to use the same data for both model selection and inference, without taking account of the variability induced by model selection step. This is usually referred to as post-model selection inference. The shortcomings of such practice are widely recognized, finding a general solution is extremely challenging. We propose a model averaging alternative consisting on taking into account model selection probability and the like-lihood in assigning the weights. The approach is applied to Bernoulli trials and outperforms Akaike weights model averaging and post-model selection estimators.展开更多
Ridge regression is an effective tool to handle multicollinearity in regressions.It is also an essential type of shrinkage and regularization methods and is widely used in big data and distributed data applications.Th...Ridge regression is an effective tool to handle multicollinearity in regressions.It is also an essential type of shrinkage and regularization methods and is widely used in big data and distributed data applications.The divide and conquer trick,which combines the estimator in each subset with equal weight,is commonly applied in distributed data.To overcome multicollinearity and improve estimation accuracy in the presence of distributed data,we propose a Mallows-type model averaging method for ridge regressions,which combines estimators from all subsets.Our method is proved to be asymptotically optimal allowing the number of subsets and the dimension of variables to be divergent.The consistency of the resultant weight estimators tending to the theoretically optimal weights is also derived.Furthermore,the asymptotic normality of the model averaging estimator is demonstrated.Our simulation study and real data analysis show that the proposed model averaging method often performs better than commonly used model selection and model averaging methods in distributed data cases.展开更多
Counting data without zero category often occurs in many fields,such as social studies,clinical trials and economic phenomenon analyses.Researchers usually show interest in describing the characteristics of the observ...Counting data without zero category often occurs in many fields,such as social studies,clinical trials and economic phenomenon analyses.Researchers usually show interest in describing the characteristics of the observed counts and the Poisson distribution is often preferred to model the counted data.Nevertheless,making marginal inference on the population mean is a challenging job when missing zero class occurs and the Poisson mean is considered as an alternative.In this paper,based on a so-called marginalized zero-truncated Poisson(ZTP)regression model,a novel SR-based EMFS algorithm is proposed to facilitate parameter estimation.To improve the prediction accuracy,this paper proposes a zero-truncated Poisson model averaging prediction that selects the optimal weight combination by minimizing a Kullback-Leibler(KL)divergence criterion.It is shown that the weight criterion is approximately unbiased about the expected KL loss.We further prove that the proposed prediction is asymptotically optimal in the sense that the KL-type loss and prediction risk are asymptotically identical to those of the infeasible best possible averaged prediction.Simulations and two empirical data applications are conducted to illustrate the proposed method.展开更多
Multivariate time series forecasting holds substantial practical significance,facilitates precise predictions,and informs decision-making.The complexity of nonlinear relationships and the presence of higher-order feat...Multivariate time series forecasting holds substantial practical significance,facilitates precise predictions,and informs decision-making.The complexity of nonlinear relationships and the presence of higher-order features in multivariate time series data have sparked a burgeoning interest in leveraging deep learning approaches for such forecasting tasks.Existing methods often use pre-scaled neural networks,whose reliability and generalization can pose a challenge.In this study,the authors propose an instance-wise graph-based Mallows model averaging(IGMMA)framework for multivariate time series prediction.The framework incorporates a model averaging module into the network,where extracted features are utilized as inputs for candidate linear models.These linear models are combined with weights to create a new linear layer,forming a novel graph neural network model.Moreover,the network loss function is modified based on the Mallows criterion,where penalties are imposed on the parameters and the weights separately.The authors use the proposed method to predict multicommodity futures prices,and the empirical results show that IGMMA has superior predictive accuracy even when small neural networks are used.This indicates that the model averaging module significantly reduces the parameters required for deep learning training,which enables the training of multiple small models as an alternative to training a large model.展开更多
KaKs_Calculator is a software package that calculates nonsynonymous （Ka） and synonymous （Ks） substitution rates through model selection and model averaging. Since existing methods for this estimation adopt their s...KaKs_Calculator is a software package that calculates nonsynonymous （Ka） and synonymous （Ks） substitution rates through model selection and model averaging. Since existing methods for this estimation adopt their specific mutation （substitution） models that consider different evolutionary features, leading to diverse estimates, KaKs_Calculator implements a set of candidate models in a maximum likelihood framework and adopts the Akaike information criterion to measure fitness between models and data, aiming to include as many features as needed for accurately capturing evolutionary information in protein-coding sequences. In addition, several existing methods for calculating Ka and Ks are also incorporated into this software. KaKs_Calculator, including source codes, compiled executables, and documentation, is freely available for academic use at http：//evolution.genomics.org.cn/software.htm.展开更多
In applications, the traditional estimation procedure generally begins with model selection.Once a specific model is selected, subsequent estimation is conducted under the selected model withoutconsideration of the un...In applications, the traditional estimation procedure generally begins with model selection.Once a specific model is selected, subsequent estimation is conducted under the selected model withoutconsideration of the uncertainty from the selection process. This often leads to the underreportingof variability and too optimistic confidence sets. Model averaging estimation is an alternative to thisprocedure, which incorporates model uncertainty into the estimation process. In recent years, therehas been a rising interest in model averaging from the frequentist perspective, and some importantprogresses have been made. In this paper, the theory and methods on frequentist model averagingestimation are surveyed. Some future research topics are also discussed.展开更多
A probabilistic precipitation forecasting model using generalized additive models （GAMs） and Bayesian model averaging （BMA） was proposed in this paper. GAMs were used to fit the spatial-temporal precipitation mode...A probabilistic precipitation forecasting model using generalized additive models （GAMs） and Bayesian model averaging （BMA） was proposed in this paper. GAMs were used to fit the spatial-temporal precipitation models to individual ensemble member forecasts. The distributions of the precipitation occurrence and the cumulative precipitation amount were represented simultaneously by a single Tweedie distribution. BMA was then used as a post-processing method to combine the individual models to form a more skillful probabilistic forecasting model. The mixing weights were estimated using the expectation-maximization algorithm. The residual diagnostics was used to examine if the fitted BMA forecasting model had fully captured the spatial and temporal variations of precipitation. The proposed method was applied to daily observations at the Yishusi River basin for July 2007 using the National Centers for Environmental Prediction ensemble forecasts. By applying scoring rules, the BMA forecasts were verified and showed better performances compared with the empirical probabilistic ensemble forecasts, particularly for extreme precipitation. Finally, possible improvements and a^plication of this method to the downscaling of climate change scenarios were discussed.展开更多
The varying-coefficient single-index model(VCSIM)is widely used in economics,statistics and biology.A model averaging method for VCSIM based on a Mallows-type criterion is proposed to improve prodictive capacity,which...The varying-coefficient single-index model(VCSIM)is widely used in economics,statistics and biology.A model averaging method for VCSIM based on a Mallows-type criterion is proposed to improve prodictive capacity,which allows the number of candidate models to diverge with sample size.Under model misspecification,the asymptotic optimality is derived in the sense of achieving the lowest possible squared errors.The authors compare the proposed model averaging method with several other classical model selection methods by simulations and the corresponding results show that the model averaging estimation has a outstanding performance.The authors also apply the method to a real dataset.展开更多
Frequentist model averaging has received much attention from econometricians and statisticians in recent years.A key problem with frequentist model average estimators is the choice of weights.This paper develops a new...Frequentist model averaging has received much attention from econometricians and statisticians in recent years.A key problem with frequentist model average estimators is the choice of weights.This paper develops a new approach of choosing weights based on an approximation of generalized cross validation.The resultant least squares model average estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors.Especially,the optimality is built under both discrete and continuous weigh sets.Compared with the existing approach based on Mallows criterion,the conditions required for the asymptotic optimality of the proposed method are more reasonable.Simulation studies and real data application show good performance of the proposed estimators.展开更多
Bayesian model averaging(BMA) is a recently proposed statistical method for calibrating forecast ensembles from numerical weather models.However,successful implementation of BMA requires accurate estimates of the weig...Bayesian model averaging(BMA) is a recently proposed statistical method for calibrating forecast ensembles from numerical weather models.However,successful implementation of BMA requires accurate estimates of the weights and variances of the individual competing models in the ensemble.Two methods,namely the Expectation-Maximization(EM) and the Markov Chain Monte Carlo(MCMC) algorithms,are widely used for BMA model training.Both methods have their own respective strengths and weaknesses.In this paper,we first modify the BMA log-likelihood function with the aim of removing the addi-tional limitation that requires that the BMA weights add to one,and then use a limited memory quasi-Newtonian algorithm for solving the nonlinear optimization problem,thereby formulating a new approach for BMA(referred to as BMA-BFGS).Several groups of multi-model soil moisture simulation experiments from three land surface models show that the performance of BMA-BFGS is similar to the MCMC method in terms of simulation accuracy,and that both are superior to the EM algo-rithm.On the other hand,the computational cost of the BMA-BFGS algorithm is substantially less than for MCMC and is al-most equivalent to that for EM.展开更多
Linear mixed-effects models are a powerful tool for the analysis of longitudinal data. The aim of this paper is to study model averaging for linear mixed-effects models. The asymptotic distribution of the frequentist ...Linear mixed-effects models are a powerful tool for the analysis of longitudinal data. The aim of this paper is to study model averaging for linear mixed-effects models. The asymptotic distribution of the frequentist model average estimator is derived, and a confidence interval procedure with an actual coverage probability that tends to the nominal level in large samples is developed. The two confidence intervals based on the model averaging and based on the full model are shown to be asymptotically equivalent. A simulation study shows good finite sample performance of the model average estimators.展开更多
In recent years,Kriging model has gained wide popularity in various fields such as space geology,econometrics,and computer experiments.As a result,research on this model has proliferated.In this paper,the authors prop...In recent years,Kriging model has gained wide popularity in various fields such as space geology,econometrics,and computer experiments.As a result,research on this model has proliferated.In this paper,the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method,with consideration for the model uncertainty.The authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method.First,the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction risk.Second,the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models.The effectiveness of the proposed method is verified through numerical analyses.展开更多
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Project supported by the China Special Fund for Meteorological Research in the Public Interest(No.GYHY201306045)the National Natural Science Foundation of China(Nos.41305066 and41575096)
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.41405083 and 91437220)the Natural Science Foundation of Hunan Province,China(Grant No.2015JJ3098)+1 种基金the Key Research Program of Frontier Sciences,CAS(QYZDY-SSW-DQC012)the Fund Project for The Education Department of Hunan Province(Grant No.16A234)
文摘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.
基金supported by the Thousand Youth Talents Plan(Xinjiang Project)the National Natural Science Foundation of China(41630859)the West Light Foundation of Chinese Academy of Sciences(2016QNXZB12)
文摘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.
文摘In this paper, a model averaging method is proposed for varying-coefficient models with response missing at random by establishing a weight selection criterion based on cross-validation. Under certain regularity conditions, it is proved that the proposed method is asymptotically optimal in the sense of achieving the minimum squared error.
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.
文摘Bayesian model averaging (BMA) is a popular and powerful statistical method of taking account of uncertainty about model form or assumption. Usually the long run (frequentist) performances of the resulted estimator are hard to derive. This paper proposes a mixture of priors and sampling distributions as a basic of a Bayes estimator. The frequentist properties of the new Bayes estimator are automatically derived from Bayesian decision theory. It is shown that if all competing models have the same parametric form, the new Bayes estimator reduces to BMA estimator. The method is applied to the daily exchange rate Euro to US Dollar.
文摘In several instances of statistical practice, it is not uncommon to use the same data for both model selection and inference, without taking account of the variability induced by model selection step. This is usually referred to as post-model selection inference. The shortcomings of such practice are widely recognized, finding a general solution is extremely challenging. We propose a model averaging alternative consisting on taking into account model selection probability and the like-lihood in assigning the weights. The approach is applied to Bernoulli trials and outperforms Akaike weights model averaging and post-model selection estimators.
基金partially supported by the Research Foundation of Shenzhen Polytechnic University (Grant No. 6023312034K)the Post-doctoral Later-stageof Shenzhen Polytechnic University(Grant No. 6023271021K)+2 种基金partially supported by the National Natural Science Foundation of China (Grant No. 71973116)partially supported by the National Natural Science Foundation of China (Grant Nos. 11971323 and 12031016)the Beijing Natural Science Foundation (Grant No. Z210003)
文摘Ridge regression is an effective tool to handle multicollinearity in regressions.It is also an essential type of shrinkage and regularization methods and is widely used in big data and distributed data applications.The divide and conquer trick,which combines the estimator in each subset with equal weight,is commonly applied in distributed data.To overcome multicollinearity and improve estimation accuracy in the presence of distributed data,we propose a Mallows-type model averaging method for ridge regressions,which combines estimators from all subsets.Our method is proved to be asymptotically optimal allowing the number of subsets and the dimension of variables to be divergent.The consistency of the resultant weight estimators tending to the theoretically optimal weights is also derived.Furthermore,the asymptotic normality of the model averaging estimator is demonstrated.Our simulation study and real data analysis show that the proposed model averaging method often performs better than commonly used model selection and model averaging methods in distributed data cases.
基金the Editor-in-chief,an AE and two referees for their helpful comments and suggestions,which result in a significant improvement of the manuscriptthe National Natural Science Foundation of China(Grant No.12171483)+3 种基金the Fundamental Research Funds for the Central Universities(2722022BY020)National Natural Science Foundation of China(Grant Nos.71925007,72091212,12288201)the CAS Project for Young Scientists in Basic Research(Grant No.YSBR-008)a joint grant from Academy for Multidisciplinary Studies,Capital Normal University.
文摘Counting data without zero category often occurs in many fields,such as social studies,clinical trials and economic phenomenon analyses.Researchers usually show interest in describing the characteristics of the observed counts and the Poisson distribution is often preferred to model the counted data.Nevertheless,making marginal inference on the population mean is a challenging job when missing zero class occurs and the Poisson mean is considered as an alternative.In this paper,based on a so-called marginalized zero-truncated Poisson(ZTP)regression model,a novel SR-based EMFS algorithm is proposed to facilitate parameter estimation.To improve the prediction accuracy,this paper proposes a zero-truncated Poisson model averaging prediction that selects the optimal weight combination by minimizing a Kullback-Leibler(KL)divergence criterion.It is shown that the weight criterion is approximately unbiased about the expected KL loss.We further prove that the proposed prediction is asymptotically optimal in the sense that the KL-type loss and prediction risk are asymptotically identical to those of the infeasible best possible averaged prediction.Simulations and two empirical data applications are conducted to illustrate the proposed method.
基金supported by the Research Foundation of Shenzhen Polytechnic University under Grant No.6023312034Kthe Post-doctoral Later-Stageof Shenzhen Polytechnic University under Grant No.6023271021K+3 种基金the National Science Foundation of Guangdong Province of China under Grant No.2024A1515011542the Guangdong Provincial Ordinary Universities Youth Innovative Talent Project(Natural Science)under Grant No.2023KQNCX064the National Natural Science Foundation of China under Grant No.12371448the National Key R&D Program of China under Grant No.2023YFE0126800。
文摘Multivariate time series forecasting holds substantial practical significance,facilitates precise predictions,and informs decision-making.The complexity of nonlinear relationships and the presence of higher-order features in multivariate time series data have sparked a burgeoning interest in leveraging deep learning approaches for such forecasting tasks.Existing methods often use pre-scaled neural networks,whose reliability and generalization can pose a challenge.In this study,the authors propose an instance-wise graph-based Mallows model averaging(IGMMA)framework for multivariate time series prediction.The framework incorporates a model averaging module into the network,where extracted features are utilized as inputs for candidate linear models.These linear models are combined with weights to create a new linear layer,forming a novel graph neural network model.Moreover,the network loss function is modified based on the Mallows criterion,where penalties are imposed on the parameters and the weights separately.The authors use the proposed method to predict multicommodity futures prices,and the empirical results show that IGMMA has superior predictive accuracy even when small neural networks are used.This indicates that the model averaging module significantly reduces the parameters required for deep learning training,which enables the training of multiple small models as an alternative to training a large model.
基金grants from the Ministry of Science and Technology of China （No. 2001AA231061） the National Natural Science Foundation of China （No. 30270748）
文摘KaKs_Calculator is a software package that calculates nonsynonymous （Ka） and synonymous （Ks） substitution rates through model selection and model averaging. Since existing methods for this estimation adopt their specific mutation （substitution） models that consider different evolutionary features, leading to diverse estimates, KaKs_Calculator implements a set of candidate models in a maximum likelihood framework and adopts the Akaike information criterion to measure fitness between models and data, aiming to include as many features as needed for accurately capturing evolutionary information in protein-coding sequences. In addition, several existing methods for calculating Ka and Ks are also incorporated into this software. KaKs_Calculator, including source codes, compiled executables, and documentation, is freely available for academic use at http：//evolution.genomics.org.cn/software.htm.
基金supported by the National Natural Science Foundation of China under Grant Nos. 70625004, 10721101, and 70221001
文摘In applications, the traditional estimation procedure generally begins with model selection.Once a specific model is selected, subsequent estimation is conducted under the selected model withoutconsideration of the uncertainty from the selection process. This often leads to the underreportingof variability and too optimistic confidence sets. Model averaging estimation is an alternative to thisprocedure, which incorporates model uncertainty into the estimation process. In recent years, therehas been a rising interest in model averaging from the frequentist perspective, and some importantprogresses have been made. In this paper, the theory and methods on frequentist model averagingestimation are surveyed. Some future research topics are also discussed.
基金Supported by the National Basic Research and Development (973) Program of China (2010CB428402)China Meteorological Administration Special Public Welfare Research Fund (GYHY200706001)
文摘A probabilistic precipitation forecasting model using generalized additive models （GAMs） and Bayesian model averaging （BMA） was proposed in this paper. GAMs were used to fit the spatial-temporal precipitation models to individual ensemble member forecasts. The distributions of the precipitation occurrence and the cumulative precipitation amount were represented simultaneously by a single Tweedie distribution. BMA was then used as a post-processing method to combine the individual models to form a more skillful probabilistic forecasting model. The mixing weights were estimated using the expectation-maximization algorithm. The residual diagnostics was used to examine if the fitted BMA forecasting model had fully captured the spatial and temporal variations of precipitation. The proposed method was applied to daily observations at the Yishusi River basin for July 2007 using the National Centers for Environmental Prediction ensemble forecasts. By applying scoring rules, the BMA forecasts were verified and showed better performances compared with the empirical probabilistic ensemble forecasts, particularly for extreme precipitation. Finally, possible improvements and a^plication of this method to the downscaling of climate change scenarios were discussed.
基金supported by the National Nature Science Foundation of Chinaunder Grant Nos.12001559and 11971324+1 种基金the Ministry of Education of Humanities and Social Science projectunder Grant No.19YJC910008。
文摘The varying-coefficient single-index model(VCSIM)is widely used in economics,statistics and biology.A model averaging method for VCSIM based on a Mallows-type criterion is proposed to improve prodictive capacity,which allows the number of candidate models to diverge with sample size.Under model misspecification,the asymptotic optimality is derived in the sense of achieving the lowest possible squared errors.The authors compare the proposed model averaging method with several other classical model selection methods by simulations and the corresponding results show that the model averaging estimation has a outstanding performance.The authors also apply the method to a real dataset.
基金by National Key R&D Program of China(2020AAA0105200)the Ministry of Science and Technology of China(Grant no.2016YFB0502301)+1 种基金the National Natural Science Foundation of China(Grant nos.11871294,12031016,11971323,71925007,72042019,72091212 and 12001559)a joint grant from the Academy for Multidisciplinary Studies,Capital Normal University.
文摘Frequentist model averaging has received much attention from econometricians and statisticians in recent years.A key problem with frequentist model average estimators is the choice of weights.This paper develops a new approach of choosing weights based on an approximation of generalized cross validation.The resultant least squares model average estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors.Especially,the optimality is built under both discrete and continuous weigh sets.Compared with the existing approach based on Mallows criterion,the conditions required for the asymptotic optimality of the proposed method are more reasonable.Simulation studies and real data application show good performance of the proposed estimators.
基金supported by National Basic Research Program of China (Grant No. 2010CB428403)National Natural Science Foundation of China (Grant No.41075076)Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No.KZCX2-EW-QN207)
文摘Bayesian model averaging(BMA) is a recently proposed statistical method for calibrating forecast ensembles from numerical weather models.However,successful implementation of BMA requires accurate estimates of the weights and variances of the individual competing models in the ensemble.Two methods,namely the Expectation-Maximization(EM) and the Markov Chain Monte Carlo(MCMC) algorithms,are widely used for BMA model training.Both methods have their own respective strengths and weaknesses.In this paper,we first modify the BMA log-likelihood function with the aim of removing the addi-tional limitation that requires that the BMA weights add to one,and then use a limited memory quasi-Newtonian algorithm for solving the nonlinear optimization problem,thereby formulating a new approach for BMA(referred to as BMA-BFGS).Several groups of multi-model soil moisture simulation experiments from three land surface models show that the performance of BMA-BFGS is similar to the MCMC method in terms of simulation accuracy,and that both are superior to the EM algo-rithm.On the other hand,the computational cost of the BMA-BFGS algorithm is substantially less than for MCMC and is al-most equivalent to that for EM.
文摘Linear mixed-effects models are a powerful tool for the analysis of longitudinal data. The aim of this paper is to study model averaging for linear mixed-effects models. The asymptotic distribution of the frequentist model average estimator is derived, and a confidence interval procedure with an actual coverage probability that tends to the nominal level in large samples is developed. The two confidence intervals based on the model averaging and based on the full model are shown to be asymptotically equivalent. A simulation study shows good finite sample performance of the model average estimators.
基金supported by the National Natural Science Foundation of China under Grant Nos.71973116 and 12201018the Postdoctoral Project in China under Grant No.2022M720336+2 种基金the National Natural Science Foundation of China under Grant Nos.12071457 and 11971045the Beijing Natural Science Foundation under Grant No.1222002the NQI Project under Grant No.2022YFF0609903。
文摘In recent years,Kriging model has gained wide popularity in various fields such as space geology,econometrics,and computer experiments.As a result,research on this model has proliferated.In this paper,the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method,with consideration for the model uncertainty.The authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method.First,the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction risk.Second,the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models.The effectiveness of the proposed method is verified through numerical analyses.
