int ranhprob(int n, int a, int m)
// hypergeometric sampling
// rejection sampling. Devroye. Computing (1987) General method for log-concave densities
// where mode is known
/**
urn with n balls . a black balls. Pick m without replacement. Return number of black balls picked.
*/
{
double y ;
double pm, logpm, w, ru, rw, rat ;
int mode, x, zans ;
mode = modehprob(n, a, m) ;
logpm = loghprob(n, a, m, mode) ;
pm = exp(logpm) ;
w = 1 + pm ;
for (;;) {
ru = DRAND() ;
rw = DRAND() ;
if (ru <= w/(1+w)) y = DRAND()*w/pm ;
else y = (w+ranexp())/pm ;
x = nnint(y) ;
if (ranmod(2)==0) x = -x ;
zans = mode+x ;
if (zans<0) continue ;
if (zans>a) continue ;
rat = exp(loghprob(n, a, m, zans)-logpm) ;
rw *= MIN(1, exp(w-pm*y)) ;
if (rw <= rat) break ;
}
return zans ;
}
int ranhprob(int n, int a, int m)
// rejection sampling. Devroye
{
double v, y ;
double pm, logpm, w, ru, rw, rat ;
int mode, k, x, zans ;
v = (double) (a+1)*(m+1) / (double) (n+1) ;
mode = (int) v ;
/**
for (k=-5; k<=5; ++k) {
x = mode+k ;
y = exp(loghprob(n, a, m, x)) ;
printf("%4d %4d %12.6f\n", mode, x, y) ;
}
*/
logpm = loghprob(n, a, m, mode) ;
pm = exp(logpm) ;
w = 1 + pm ;
for (;;) {
ru = DRAND() ;
rw = DRAND() ;
if (ru <= w/(1+w)) y = DRAND()*w/pm ;
else y = (w+ranexp())/pm ;
x = nnint(y) ;
if (ranmod(2)==0) x = -x ;
zans = mode+x ;
if (zans<0) continue ;
if (zans>a) continue ;
rat = exp(loghprob(n, a, m, zans)-logpm) ;
rw *= MIN(1, exp(1.0-pm*y)) ;
if (rw <= rat) break ;
}
return zans ;
}
int main()
{
int n=50, m=16, a=5 ;
int k, t, iter ;
int hist[100] ;
double y ;
ivzero(hist, 100) ;
for (iter =1 ; iter <= 10000; ++iter) {
t = ranhprob(n, a, m) ;
++hist[t] ;
}
for (k=0; k<=a ; ++k) {
y = exp(loghprob(n, a, m, k)) ;
printf("%3d %3d %9.3f\n", k, hist[k], y) ;
}
}
