# ars: Adaptive Rejection Sampling In ars: Adaptive Rejection Sampling

## Description

Adaptive Rejection Sampling from log-concave density functions

## Usage

 `1` ```ars(n=1,f,fprima,x=c(-4,1,4),ns=100,m=3,emax=64,lb=FALSE,ub=FALSE,xlb=0,xub=0,...) ```

## Arguments

 `n` sample size `f` function that computes log(f(u,...)), for given u, where f(u) is proportional to the density we want to sample from `fprima` d/du log(f(u,...)) `x` some starting points in wich log(f(u,...) is defined `ns` maximum number of points defining the hulls `m` number of starting points `emax` large value for which it is possible to compute an exponential `lb` boolean indicating if there is a lower bound to the domain `xlb` value of the lower bound `ub` boolean indicating if there is a upper bound to the domain `xub` value of the upper bound bound `...` arguments to be passed to f and fprima

## Details

ifault codes, subroutine initial

1. 0:successful initialisation

2. 1:not enough starting points

3. 2:ns is less than m

4. 3:no abscissae to left of mode (if lb = false)

5. 4:no abscissae to right of mode (if ub = false)

6. 5:non-log-concavity detect

ifault codes, subroutine sample

1. 0:successful sampling

2. 5:non-concavity detected

3. 6:random number generator generated zero

4. 7:numerical instability

## Value

a sampled value from density

## Author(s)

Paulino Perez Rodriguez, original C++ code from Arnost Komarek based on ars.f written by P. Wild and W. R. Gilks

## References

Gilks, W.R., P. Wild. (1992) Adaptive Rejection Sampling for Gibbs Sampling, Applied Statistics 41:337–348.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```library(ars) #Example 1: sample 20 values from the normal distribution N(2,3) f<-function(x,mu=0,sigma=1){-1/(2*sigma^2)*(x-mu)^2} fprima<-function(x,mu=0,sigma=1){-1/sigma^2*(x-mu)} mysample<-ars(20,f,fprima,mu=2,sigma=3) mysample hist(mysample) #Example 2: sample 20 values from a gamma(2,0.5) f1<-function(x,shape,scale=1){(shape-1)*log(x)-x/scale} f1prima<-function(x,shape,scale=1) {(shape-1)/x-1/scale} mysample1<-ars(20,f1,f1prima,x=4.5,m=1,lb=TRUE,xlb=0,shape=2,scale=0.5) mysample1 hist(mysample1) #Example 3: sample 20 values from a beta(1.3,2.7) distribution f2<-function(x,a,b){(a-1)*log(x)+(b-1)*log(1-x)} f2prima<-function(x,a,b){(a-1)/x-(b-1)/(1-x)} mysample2<-ars(20,f2,f2prima,x=c(0.3,0.6),m=2,lb=TRUE,xlb=0,ub=TRUE,xub=1,a=1.3,b=2.7) mysample2 hist(mysample2) ```

ars documentation built on May 2, 2019, 6:32 a.m.