Adaptive Sampling Algorithms And Its R Package Development

Sampling plays an important role in statistics.Sampling from conventional distri-butions can be done directly by statistics softwares such as R while it is hard for uncon-ventional distributions.On the other hand,adaptive algorithm can be used for sampling owing to its good property of adapting itself for improving accuracy.We showed several sampling methods related to adaptive algorithm.For distributions whose probability densitry functions are log-concave,Adaptive Rejection Sampling(ARS)algorithm can be used to build tangent lines on support points as envelope functions for sampling.For others,we can use Modified Adaptive Rejection Sampling(MARS)algorithm for building tangent lines on log-concave intervals and secant lines on log-convex intervals as envelope functions.We can also decompose density functions into convex and concave parts and find envelope functions respectively by Concave-Convex Adaptive Rejection(CCARS)Sampling algorithm.Adaptive Slice Sampling(ASS)algorithm is also a good choice by calculating slices.At last.,Adaptive Rejection Metropolis Sampling(ARMS)can realize sampling for multivariate distributions.Then we designed an R package called AdapSamp for all the algorithms above.There are mainly 5 functions in this package:rARS,rMARS,rCCARS,rASS and rARMS.After some experimental analysis,we got a conclusion that samples generated by this package are all from target distributions correctly.Also function rARMS and rASS have a high efficiency and a wide practicability with less loops and judgements while rMARS has a slow speed.The new R package we developed contains many perfect adaptive algorithms and it can solve sampling problems for almost all distributions.Also,it is a worth addition of existing R packages for sampling from conventional distributions.AdapSamp will finally enjoy great popularity from statisticians due to its applicability and convenience.