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新疆大学数学与系统科学学院
Published:2020
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[1]郑良芳,胡锡健.拉普拉斯逼近方法在复杂函数积分中的应用[J].新疆大学学报(自然科学版)(中英文),2020,37(01):1-7.
[1]郑良芳,胡锡健.拉普拉斯逼近方法在复杂函数积分中的应用[J].新疆大学学报(自然科学版)(中英文),2020,37(01):1-7. DOI: 10.13568/j.cnki.651094.651316.2019.07.11.0004.
DOI:10.13568/j.cnki.651094.651316.2019.07.11.0004.
在常见的积分计算问题中
复杂函数的积分通常难以计算或是计算过程复杂
计算时间长.拉普拉斯逼近方法通过将复杂函数进行二阶泰勒展开
将满足一定条件的被积函数近似为正态分布密度函数的形式
并对其进行积分.从而求解出复杂函数积分的近似结果.文章基于正态分布良好的计算性质
通过实例分析拉普拉斯逼近方法在复杂函数积分中的应用
验证了拉普拉斯逼近方法具有计算方便
快捷
并且逼近结果较为精确的特点.
In the common integral calculation problem
the integral of complex functions is usually difficult to calculate or the calculation process is complicated and the calculation time is long. The Laplace approximation method approximates the integrand function satisfying certain conditions to a normal distribution by performing a second-order Taylor expansion of the complex function
and integrates the corresponding normal distribution density function to solve the approximate result of complex function integral. Due to the good computational properties of normal distribution
the application of Laplace approximation method in complex function integration is considered. The analysis of several examples shows that the Laplace approximation method is convenient
fast
and accurate.
DE LAPLACE P S.M′emoire sur la probabilite′des causes par les′ev′enements[J].Me′mde math et physpre′sent′es`al’Acad roy des sci,1774,6:621-656.
ROBERT C, CASELLA G. Monte Carlo statistical methods[M]. Berlin:Springer Science&Business Media, 2013.
AZEVEDO-FILHO A, SHACHTER R D. Laplace’s method approximations for probabilistic inference in belief networks with continuous variables[J]. Uncertainty Proceedings, 1994:28-36.
BAGHISHANI H, MOHAMMADZADEH M. Asymptotic normality of posterior distributions for generalized linear mixed models[J]. Journal of Multivariate Analysis, 2012, 111:66-77.
LIN X H. Variance component testing in generalised linear models with random effects[J]. Biometrika, 1997, 84(2):309-326.
MARTINO S, AKERKAR R, RUE H. Approximate bayesian inference for survival models[J]. Scandinavian Journal of Statistics,2011, 38(3):514-528.
RULI E, SARTORI N, VENTURA L. A note on marginal posterior simulation via higher-order tail area approximations[J].Bayesian Analysis, 2012, 9(1):129-146.
MUNOZ-GONZALEZ L, LAZARO-GREDILLA M, FIGUEIRAS-VIDAL A R. Laplace approximation for divisive gaussian processes for nonstationary regression[J]. IEEE Transactions on Pattern Analysis, Machine Intelligence, 2016, 38(3):618-624.
韦来生,张伟平.贝叶斯分析[M].北京:中国科技大学出版社, 2013.WEI L S, ZHANG W P. Bayesian Analysis[M]. Beijing:China University of Science and Technology Press, 2013.(in Chinese)
TIERNEY L, KADANE J. Accurate approximations for posterior moments and marginal densities[J]. Publications of the American Statistical Association, 1986, 81(393):82-86.
LEONARD T. Comment on A simple predictive density function[J]. Journal of the American Statistical Association, 1982,77(379):657-658.
KASS R E, RAFTERY A E. Bayes factors[J]. Journal of the American Statistical Association, 1995, 90:773-795.
RUE H, MARTINO S, CHOPIN N. Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations[J]. Journal of the Royal Statistical Society:Series B 2009, 71:319-392.
FRIEL N, WYSE, J. Estimating the evidence a review[J]. Statistica Neerlandica, 2012, 66(3):288-308.
孙彬.基于物流大数据有向图的客户资源聚类研究[J].新疆大学学报(自然科学版), 2017, 34(2):187-194.SUN B. Study on Clustering of Customer Resources Based on Directed Graph of Logistics Big Data[J]. Journal of Xinjiang University(Natural Science Edition), 2017, 34(2):187-194.(in Chinese)
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