ars {ars} | R Documentation |
Adaptive Rejection Sampling from log-concave density functions
ars(n=1,f,fprima,x=c(-4,1,4),ns=100,m=3,emax=64,lb=FALSE,ub=FALSE,xlb=0,xub=0,...)
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 |
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
a sampled value from density
Paulino Perez Rodriguez, original C++ code from Arnost Komarek based on ars.f written by P. Wild and W. R. Gilks
Gilks, W.R., P. Wild. (1992) Adaptive Rejection Sampling for Gibbs Sampling, Applied Statistics 41:337–348.
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)