# W&J Example page 47.

prior<-function(S) {return ( S^(-5/2)) } # "a priori"

vero<-function(f,S,sigma)  {return ( exp(-1/(2*sigma^2) * (f-S)^2) )} # Verossimilhança


flux<-seq(1,4,0.05)

 # A priori
pp <- prior(flux)					   
pp<-pp/sum(pp) * 1/0.05 #Normalização
plot(flux,pp,type="l",ylab="Densidade de Probabilidade",xlab="Fluxo")
text(1.0,1.6,"a priori",pos=4)


# Two data-points (2.0, 1.3) & prior
p1 <- prior(flux) * vero(2.0,flux,1.0) * vero(1.3,flux,1.0) 
p1<-p1/sum(p1) * 1/0.05   
lines(flux,p1,col="green")
text(1.15,1.2,"post.(2pts)",pos=4,col="green")

 # Four data-points (2.0, 1.3, 3.0, 1.5) & prior
p2 <- p1 * vero(3.0,flux,1.0) * vero(1.5,flux,1.0)         
p2<-p2/sum(p2) * 1/0.05 
lines(flux,p2,col="blue")
text(0.85,0.8,"post.(4pts)",pos=4,col="blue")

 # Six data-points (2.0, 1.3, 3.0, 1.5, 2.0, 1.8) & prior
p3 <- p2 * vero(2.0,flux,1.0) * vero(1.8,flux,1.0)         
p3<-p3/sum(p3) * 1/0.05 
lines(flux,p3,col="red")
text(1.4,1.0,"post.(6pts)",pos=4,col="red")

# Six data-points & no-prior
p4 <- p3/prior(flux)					    
p4<-p4/sum(p4) * 1/0.05 
lines(flux,p4,lty="dashed")
text(2.3,0.63,"post.(6pts) no-prior",pos=4)