自适应抽样算法及其R包开发

发布时间：2018-01-18 05:23

本文关键词：自适应抽样算法及其R包开发　出处：《华东师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：随机数抽样对于统计学科意义重大。目前为止,常规分布的随机数生成可由计算机软件如R直接操作完成,但对于非常规分布而言尚缺少统计软件的支持。另一方面,自适应性算法具有其根据条件改善算法自身从而提高精度的优良性质,因此可被用于随机数抽样算法之中。本文首先介绍了若干自适应改进下的随机数生成算法:对于概率密度函数具有对数凹函数性质的目标分布,可依据自适应拒绝算法在支撑点处建立切线方程构造目标概率密度函数的分段指数型包络函数加以抽样。对于其他分布,可根据改进自适应拒绝算法,在对数凹区间上建立切线方程,并在对数凸区间上建立割线方程构造包络函数并抽样;亦可使用凹凸分解自适应拒绝算法将有限定义域上的目标分布分解成凹凸两部分并分别构造包络函数;还可根据自适应切片算法建立水平切片进行切片抽样。最后,自适应拒绝Metropolis抽样算法还可实现多元分布抽样。针对上述算法,我们设计并开发一款名为AdapSamp的R功能包来实现自适应随机数抽样。其中,rARS,rMARS,rCCARS,rASS与rARMS函数可分别实现上述功能。经过案例分析,我们得出该功能包所生成的随机数皆来自给定分布的结论。此外,rARMS与rASS函数由于循环和判断次数少于其他函数,因此速度快且具有广泛的实用性。相比而言,rMARS函数则耗时过长导致效率较低。我们开发的新的R包整合了许多优秀的自适应抽样算法,能够解决几乎所有的分布的抽样,是现有R功能包中常规分布抽样函数的有效补充。因其普遍的适用性与使用的便利性,此R包一定会受到广大统计专业人员的欢迎。
[Abstract]:Random number sampling is of great significance to statistical science. So far, the generation of random numbers of conventional distribution can be directly operated by computer software such as R. On the other hand, the adaptive algorithm has the excellent property of improving the algorithm itself according to the condition and improving the precision. Therefore, it can be used in random number sampling algorithms. Firstly, this paper introduces some adaptive improved random number generation algorithms: the distribution of objects with logarithmic concave function for probability density function. According to the adaptive rejection algorithm, the tangent equation can be established at the support point to construct the piecewise exponential envelope function of the probability density function of the target to be sampled. For the other distributions, the improved adaptive rejection algorithm can be used. The tangent equation is established on the logarithmic concave interval and the tangent equation is established on the logarithmic convex interval to construct the envelope function and sampling. An adaptive rejection algorithm based on convex and concave decomposition can be used to decompose the distribution of objects in a finite domain into concave and convex parts and construct envelope functions respectively. Finally, the adaptive rejection Metropolis sampling algorithm can be used to realize multivariate distribution sampling. We design and develop a R function package called AdapSamp to realize adaptive random number sampling. The rASS function and the rARMS function can realize the above functions respectively. Through the case study, we draw the conclusion that the random numbers generated by the function package are all from the given distribution. RARMS and rASS functions are faster and more practical than other functions because the number of cycles and judgments is less than other functions. RMARS function is time-consuming and inefficient. Our new R package integrates many excellent adaptive sampling algorithms and can solve almost all of the distribution of sampling. It is an effective supplement to the conventional distribution sampling function in the existing R function package. Due to its universal applicability and convenience, the R package will be welcomed by the majority of statistical professionals.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.2

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