1 - INFERÊNCIA NA NORMAL

mu0=0
v0=sqrt(2)
n=5
sigma=sqrt(10)
xbarra=10

mu=seq(-10,20,.1)

# cálculo da verossimilhança "padronizada"

vero=1/( sqrt( 2*pi*(sigma^2)/n ) * exp(n*((mu-xbarra)^2)/(2*(sigma^2))) )
plot(mu,vero,type="l",ylim=c(0,0.5))

a) ANÁLISE CONJUGADA (PRIORI NORMAL)

priori=1/(sqrt(2*pi*(v0^2))*exp(((mu-mu0)^2)/(2*(v0^2))))
lines(mu,priori)
v2=1/( ( 1/(v0^2) )  + ( n/ ( sigma^2 )  )  )
mu1= v2* ( ( mu0/(v0^2) )  + ( n * xbarra / ( sigma^2 )  )  )
post=1/(sqrt(2*pi*(v2))*exp(((mu-mu1)^2)/(2*(v2))))
lines(mu,post,col=3)

b) ANÁLISE NÃO-CONJUGADA (PRIORI CAUCHY)

prioriC= 1/( pi * .8 * v0 * ( 1 + ( ( (mu-mu0)^2 )/(.64*(v0^2)) )  )  )
lines(mu,prioriC,col=6)
postC=260*prioriC*vero
lines(mu,postC,col=6)


2 - INFERÊNCIA NA BINOMIAL

a=2
b=8
n=10
x=8

p=seq(0,1,0.01)

# cálculo da verossimilhança "padronizada"

vero=( p^x ) * ( ( 1-p )^( n-x ) )*gamma(n+2)/( gamma(x+1) * gamma(1+n-x) )
plot(p,vero,type="l",ylim=c(0,5))

ANÁLISE CONJUGADA (PRIORI BETA)

priori=( p^(a-1) ) * ( ( 1-p )^( b-1 ) )      *gamma(a+b)  /( gamma(a)   * gamma(b)     )
lines(p,priori,col=3)

post=( p^(a+x-1) ) * ( ( 1-p )^( b+n-(x+1) ) )*gamma(a+b+n)/( gamma(a+x) * gamma(b+n-x) )
lines(p,post,col=3)