基于核密度估计的AM-MCMC算法在径流模拟中的应用
|
摘要
无资料或资料稀缺地区的径流概率模拟,是目前水文研究难点问题之一。基于此,利用Kernal核密度估计法估算出流量的月径流概率密度函数,采用基于自适应采样算法(Adaptive Metropolis algorithm,AM)的马尔可夫链蒙特卡罗(Markov Chain Monte Carlo,MCMC)模拟方法求解,最后给出月径流量的模拟预测。实例表明基于Kernel核密度估计的AM-MCMC算法模型计算结果精度较高,有良好的应用价值,可在资料较少地区推广使用。
The simulation of runoff probability in an area in lack of runoff data is a difficulty in hydrological research. In this article,we try to establish the probability density function of monthly runoff flow by adopting kernal density estimation method,and give the solution by Markov Chain Monte Carlo( MCMC) simulation method based on Adaptive Metropolis( AM) algorithm. Case study shows that the AM-MCMC algorithm model based on kernel density estimation is of high accuracy and good application value. It can be used in areas in lack of data.
The simulation of runoff probability in an area in lack of runoff data is a difficulty in hydrological research. In this article,we try to establish the probability density function of monthly runoff flow by adopting kernal density estimation method,and give the solution by Markov Chain Monte Carlo( MCMC) simulation method based on Adaptive Metropolis( AM) algorithm. Case study shows that the AM-MCMC algorithm model based on kernel density estimation is of high accuracy and good application value. It can be used in areas in lack of data.
引文
[1]邢贞相,芮孝芳,崔海燕,等.基于AM-MCMC算法的贝叶斯概率洪水预报模型[J].水利学报,2007,38(12):1500-1506.
[2]ROSENBLATT M.Remarks on Some Nonparametric Estimates of a Density Function[J].Annals of Mathematical Statistics,1956,27(3):832-837.
[3]PARZEN E.On Estimation of a Probability Density Function and Mode[J].Annals of Mathematical Statistics,1962,33(3):1065-1076.
[4]SCOTT D W,WHITTAKER G.Multivariate Applications of the ASH in Regression[J].Communications in Statistics—Theory and Methods,1996,25(11):2521-2530.
[5]RUPPERT D,CLINE D B.Bias Reduction in Kernel Density Estimation by Smoothed Empirical Transformations[J].The Annals of Statistics,1994:185-210,doi:10.1214/aos/1176325365.
[6]崔恒建,王雪峰.核密度估计及其在直径分布研究中的应用[J].北京林业大学学报,1996,18(2):67-72.
[7]刘锐,胡伟平,王红亮,等.基于核密度估计的广佛都市区路网演变分析[J].地理科学,2011,31(1):81-86.
[8]赵渊,沈智健,周念成,等.基于序贯仿真和非参数核密度估计的大电网可靠性评估[J].电力系统自动化,2008,32(6):14-19.
[9]凌建国,刘尔琦,梁海燕,等.基于核密度估计的红外目标提取方法[J].红外与毫米波学报,2006,25(6):434-438.
[10]唐林俊,杨虎,张洪阳.核密度估计在预测风险价值中的应用[J].数学的实践与认识,2006,35(10):29-35.
[11]王文圣,丁晶.单变量核密度估计模型及其在径流随机模拟中的应用[J].水科学进展,2001,12(3):367-372.
[12]JONES M C,MARRON J S,SHEATHER S J.A Brief Survey of Bandwidth Selection for Density Estimation[J].Journal of the American Statistical Association,1996,91(433):401-407.
[13]SAIN S R,BAGGERLY K A,SCOTT D W.Cross-validation of Multivariate Densities[J].Journal of the American Statistical Association,1994,89(427):807-817.
[14]BOLANCC,GUILLEN M,NIELSEN J P.Kernel Density Estimation of Actuarial Loss Functions[J].Insurance:Mathematics and Economics,2003,32(1):19-36.
[15]FUKUNAGA K,HOSTETLER L.The Estimation of the Gradient of a Density Function,with Applications in Pattern Recognition[J].IEEE Transactions on Information Theory,1975,21(1):32-40.
[16]SMITH A F,ROBERTS G O.Bayesian Computation via the Gibbs Sampler and Related Markov Chain Monte Carlo Methods[J].Journal of the Royal Statistical Society.Series B(Methodological),1993:3-23,doi:10.2307/2346063.
[17]CHIB S,GREENBERG E.Understanding the MetropolisHastings Algorithm[J].The American Statistician,1995,49(4):327-335.
[18]HAARIO H,SAKSMAN E,TAMMINEN J.An Adaptive Metropolis Algorithm[J].Bernoulli,2001,7(2):223-242.
[19]GELMAN A,RUBIN D B.Inference from Iterative Simulation Using Multiple Sequences[J].Statistical Science,1992,7(4):457-472.
[2]ROSENBLATT M.Remarks on Some Nonparametric Estimates of a Density Function[J].Annals of Mathematical Statistics,1956,27(3):832-837.
[3]PARZEN E.On Estimation of a Probability Density Function and Mode[J].Annals of Mathematical Statistics,1962,33(3):1065-1076.
[4]SCOTT D W,WHITTAKER G.Multivariate Applications of the ASH in Regression[J].Communications in Statistics—Theory and Methods,1996,25(11):2521-2530.
[5]RUPPERT D,CLINE D B.Bias Reduction in Kernel Density Estimation by Smoothed Empirical Transformations[J].The Annals of Statistics,1994:185-210,doi:10.1214/aos/1176325365.
[6]崔恒建,王雪峰.核密度估计及其在直径分布研究中的应用[J].北京林业大学学报,1996,18(2):67-72.
[7]刘锐,胡伟平,王红亮,等.基于核密度估计的广佛都市区路网演变分析[J].地理科学,2011,31(1):81-86.
[8]赵渊,沈智健,周念成,等.基于序贯仿真和非参数核密度估计的大电网可靠性评估[J].电力系统自动化,2008,32(6):14-19.
[9]凌建国,刘尔琦,梁海燕,等.基于核密度估计的红外目标提取方法[J].红外与毫米波学报,2006,25(6):434-438.
[10]唐林俊,杨虎,张洪阳.核密度估计在预测风险价值中的应用[J].数学的实践与认识,2006,35(10):29-35.
[11]王文圣,丁晶.单变量核密度估计模型及其在径流随机模拟中的应用[J].水科学进展,2001,12(3):367-372.
[12]JONES M C,MARRON J S,SHEATHER S J.A Brief Survey of Bandwidth Selection for Density Estimation[J].Journal of the American Statistical Association,1996,91(433):401-407.
[13]SAIN S R,BAGGERLY K A,SCOTT D W.Cross-validation of Multivariate Densities[J].Journal of the American Statistical Association,1994,89(427):807-817.
[14]BOLANCC,GUILLEN M,NIELSEN J P.Kernel Density Estimation of Actuarial Loss Functions[J].Insurance:Mathematics and Economics,2003,32(1):19-36.
[15]FUKUNAGA K,HOSTETLER L.The Estimation of the Gradient of a Density Function,with Applications in Pattern Recognition[J].IEEE Transactions on Information Theory,1975,21(1):32-40.
[16]SMITH A F,ROBERTS G O.Bayesian Computation via the Gibbs Sampler and Related Markov Chain Monte Carlo Methods[J].Journal of the Royal Statistical Society.Series B(Methodological),1993:3-23,doi:10.2307/2346063.
[17]CHIB S,GREENBERG E.Understanding the MetropolisHastings Algorithm[J].The American Statistician,1995,49(4):327-335.
[18]HAARIO H,SAKSMAN E,TAMMINEN J.An Adaptive Metropolis Algorithm[J].Bernoulli,2001,7(2):223-242.
[19]GELMAN A,RUBIN D B.Inference from Iterative Simulation Using Multiple Sequences[J].Statistical Science,1992,7(4):457-472.