CS计算机代考程序代写 # Bayes factor example, discussed in class on Tue Feb 16

# Bayes factor example, discussed in class on Tue Feb 16

# H1: Y|theta ~ Binomial(20, theta) where theta = 0.5

# H2: Y|theta ~ Binomial(20, theta) where theta ~ Uniform(0,1)

rm(list=ls())

# First let’s do classical hypothesis test of

# Y ~ Binomial(n=20, theta)

# H0: theta = .5 versus H1: theta ^= .5

# for comparison

# For what y-values is p-value < .05? < .01? y <- 0:20 p.value <- c(2*pbinom(0:9, 20, .5), 1, 2*(1-pbinom(10:19, 20, .5))) plot(log10(p.value) ~ y, type="b") abline(h=log10(.05), col="blue") abline(h=log10(.01), col="red") legend("bottom", inset=.10, lty=1, col=c("blue","red"), legend=c("p-value<.05: y<=5 or y>=15″,
“p-value<.01: y<=3 or y>=17″))

# Calculate Bayes factor for each y

# BF = Pr(Y=y | H2) / Pr(Y=y | H1)

y <- 0:20 py.H2 <- 1 / 21 # Exercise: Prove this! py.H1 <- dbinom(y, 20, .5) # Obviously BF <- py.H2 / py.H1; plot(log10(BF) ~ y, type="b") abline(h=1, col="blue") abline(h=2, col="red") legend("top", inset=.10, lty=1, col=c("blue","red"), legend=c("BF> 10: y<=4 or y>=16″,
“BF>100: y<=2 or y>=18″))