* Nom du fichier: pile_bayes.kumac
*
* KUMAC pour montrer a posteriori  Baysienne d'un parametre inconnu
*                                      MP 03/01
*              [n] essais de pile ou face
zone 2 2
n  = 128
*              Definitions du vecteur a contenir les v.a.
vec/cre rr([n]) r
*              Definitions du vecteur a contenir l'a posteriori
vec/cre q(20) r
*              Definitions du vecteur a contenir 1. partout
vec/cre tt([n]) r [n]*1.
*              Creer un vecteur rr de [n] pseudo-aleatoires 0 < rr < 1.
sigma rr = rndm(rr)
*              Creer un vecteur de [n] pseudo-aleatoires 0 (face) ou 1 (pile)
*              et les compter pour theta = 0.25
sigma nf =  sumv(rr gt 0.75)
sigma np =  sumv(tt) - nf
*              Calculer q apres coup 1
for/file 20 'pile_bayes1.eps'
meta     20 -113
sigma pp=np(1)
sigma ff=nf(1)
sigma theta=array(50,0.01#0.99)
sigma q=theta**pp*(1-theta)**ff
sigma q=q/maxv(q)
sigma q2=theta**2*q
sigma q2=q2/maxv(q2)
sigma q3=(1-theta)**2*q
sigma q3=q3/maxv(q3)
set ltyp 1
graph 50 theta q
set ltyp 2
graph 50 theta q2 c
set ltyp 3
graph 50 theta q3 c
atitle 'theta' 'q(theta|x)'
text .1 .9 'N=1' .5 0.
*              Calculer q apres coup 2
sigma pp=np(2)
sigma ff=nf(2)
sigma theta=array(50,0.01#0.99)
sigma q=theta**pp*(1-theta)**ff
sigma q=q/maxv(q)
sigma q2=theta**2*q
sigma q2=q2/maxv(q2)
sigma q3=(1-theta)**2*q
sigma q3=q3/maxv(q3)
set ltyp 1
graph 50 theta q
set ltyp 2
graph 50 theta q2 c
set ltyp 3
graph 50 theta q3 c
atitle 'theta' 'q(theta|x)'
text .1 .9 'N=2' .5 0.
*              Calculer q apres coup 4
sigma pp=np(4)
sigma ff=nf(4)
sigma theta=array(50,0.01#0.99)
sigma q=theta**pp*(1-theta)**ff
sigma q=q/maxv(q)
sigma q2=theta**2*q
sigma q2=q2/maxv(q2)
sigma q3=(1-theta)**2*q
sigma q3=q3/maxv(q3)
set ltyp 1
graph 50 theta q
set ltyp 2
graph 50 theta q2 c
set ltyp 3
graph 50 theta q3 c
atitle 'theta' 'q(theta|x)'
text .1 .9 'N=4' .5 0.
*              Calculer q apres coup 8
sigma pp=np(8)
sigma ff=nf(8)
sigma theta=array(50,0.01#0.99)
sigma q=theta**pp*(1-theta)**ff
sigma q=q/maxv(q)
sigma q2=theta**2*q
sigma q2=q2/maxv(q2)
sigma q3=(1-theta)**2*q
sigma q3=q3/maxv(q3)
set ltyp 1
graph 50 theta q
set ltyp 2
graph 50 theta q2 c
set ltyp 3
graph 50 theta q3 c
atitle 'theta' 'q(theta|x)'
text .1 .9 'N=8' .5 0.
for/close 20
wait
*              Calculer q apres coup 16
for/file 20 'pile_bayes2.eps'
meta     20 -113
sigma pp=np(16)
sigma ff=nf(16)
sigma theta=array(50,0.01#0.99)
sigma q=theta**pp*(1-theta)**ff
sigma q=q/maxv(q)
sigma q2=theta**2*q
sigma q2=q2/maxv(q2)
sigma q3=(1-theta)**2*q
sigma q3=q3/maxv(q3)
set ltyp 1
graph 50 theta q
set ltyp 2
graph 50 theta q2 c
set ltyp 3
graph 50 theta q3 c
atitle 'theta' 'q(theta|x)'
text .1 .9 'N=16' .5 0.
*              Calculer q apres coup 32
sigma pp=np(32)
sigma ff=nf(32)
sigma theta=array(50,0.01#0.99)
sigma q=theta**pp*(1-theta)**ff
sigma q=q/maxv(q)
sigma q2=theta**2*q
sigma q2=q2/maxv(q2)
sigma q3=(1-theta)**2*q
sigma q3=q3/maxv(q3)
set ltyp 1
graph 50 theta q
set ltyp 2
graph 50 theta q2 c
set ltyp 3
graph 50 theta q3 c
atitle 'theta' 'q(theta|x)'
text .1 .9 'N=32' .5 0.
*              Calculer q apres coup 64
sigma pp=np(64)
sigma ff=nf(64)
sigma theta=array(50,0.01#0.99)
sigma q=theta**pp*(1-theta)**ff
sigma q=q/maxv(q)
sigma q2=theta**2*q
sigma q2=q2/maxv(q2)
sigma q3=(1-theta)**2*q
sigma q3=q3/maxv(q3)
set ltyp 1
graph 50 theta q
set ltyp 2
graph 50 theta q2 c
set ltyp 3
graph 50 theta q3 c
atitle 'theta' 'q(theta|x)'
text .1 .9 'N=64' .5 0.
*              Calculer q apres coup 128
sigma pp=np(128)
sigma ff=nf(128)
sigma theta=array(50,0.01#0.99)
sigma q=theta**pp*(1-theta)**ff
sigma q=q/maxv(q)
sigma q2=theta**2*q
sigma q2=q2/maxv(q2)
sigma q3=(1-theta)**2*q
sigma q3=q3/maxv(q3)
set ltyp 1
graph 50 theta q
set ltyp 2
graph 50 theta q2 c
set ltyp 3
graph 50 theta q3 c
atitle 'theta' 'q(theta|x)'
text .1 .9 'N=128' .5 0.
for/close 20
return