# KOMMANDOER TIL FORELESNINGENE FOR UKE 9 

# ===============


# EKSEMEL 1 FRA HEFTET TIL STORVIK: NEDBRYTING AV MYONER

# Leser inn dataene:

x = c(0.41040018,0.91061564,-0.61106896,0.39736684,0.37997637,0.34565436 ,
0.01906680,-0.28765977,-0.33169289,0.99989810,-0.35203164,0.10360470 ,
0.30573300,0.75283842,-0.33736278,-0.91455101,-0.76222116,0.27150040 ,
-0.01257456,0.68492778,-0.72343908,0.45530570,0.86249107,0.52578673 ,
0.14145264,0.76645754,-0.65536275,0.12497668,0.74971197,0.53839119)

# Histogram av dataene:
hist(x)

# Beregner likelihooden:
alpha=seq(-1,1,0.01)
likelihood=rep(0,length(alpha))
for (i in 1:length(alpha))
likelihood[i]= prod((1+alpha[i]*x)/2)

# Plotter likelihooden:
plot(alpha,likelihood,type='l')



# ====================

# EKSEMEL 12.14 I D&B: CHALLENGER ULYKKEN

# Leser inn dataene:
challenger=read.table("http://www.uio.no/studier/emner/matnat/math/STK2120/v13/exmp12-14.txt",header=T)

# Trekker 70 fra alle temperaturm?lingene (som er i Farenheit-grader):
x=challenger$temp-70
y=challenger$fail

# Beregner og loglikelihood og likelihood:
b0 = seq(-4,2,0.1)
b1 = seq(-0.4,0,0.01)
loglik = matrix(nrow=length(b0),ncol=length(b1))
for(i in 1:length(b0))
for(j in 1:length(b1))
loglik[i,j] = sum((b0[i]+b1[j]*x)*y-log(1+exp(b0[i]+b1[j]*x)))
lik=exp(loglik)

#Plotter likelihooden:
persp(b0,b1,lik,theta=330,phi=45,shade=1,zlab="lik")
image(b0,b1,lik,col=gray((0:32)/32))


# Plotter estimert sannsynligheten for feil som en funksjon av temperatur
# (bruker at estimatene for beta0 og beta 1 blir 1.12 og -0.171)
b0=-1.12
b1=-0.171
temp=seq(53,81,1)
plot(temp,exp(b0+b1*(temp-70))/(1+exp(b0+b1*(temp-70))),type='l')