| Title: | Adaptive Rejection Sampling |
| Version: | 0.8 |
| Date: | 2024-09-05 |
| Maintainer: | Paulino Perez Rodriguez <perpdgo@colpos.mx> |
| Depends: | R (≥ 3.1.2) |
| Description: | Adaptive Rejection Sampling, Original version. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| NeedsCompilation: | yes |
| Packaged: | 2024-09-05 20:26:20 UTC; pperez |
| Author: | Paulino Perez Rodriguez [aut, cre] (Original C++ code from Arnost Komarek based on ars.f written by P. Wild and W. R. Gilks) |
| Repository: | CRAN |
| Date/Publication: | 2024-09-06 15:30:05 UTC |
Adaptive Rejection Sampling
Description
Adaptive Rejection Sampling from log-concave density functions
Usage
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
- 0:
successful initialisation
- 1:
not enough starting points
- 2:
ns is less than m
- 3:
no abscissae to left of mode (if lb = false)
- 4:
no abscissae to right of mode (if ub = false)
- 5:
non-log-concavity detect
ifault codes, subroutine sample
- 0:
successful sampling
- 5:
non-concavity detected
- 6:
random number generator generated zero
- 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
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)