###############################
# Prior Elicitation Example   #
###############################

#################################
### Example (TV-watching data)
#################################

## The variable of interest is the number of hours per week 
## of TV watched by college-age students in the U.S.

# The parameter of interest is the mean weekly number of hours.

# We will use a normal prior for this parameter.

# Suppose 5 experts named the most likely value for this weekly mean
# and also gave two numbers in between which they were 
# 80% sure the mean fell (i.e., the 0.1 and 0.9 quantiles).

# Expert 1:
med.1 <- 
q.1.1 <- 
q.9.1 <- 

# Expert 2:
med.2 <- 
q.1.2 <- 
q.9.2 <- 

# Expert 3:
med.3 <- 
q.1.3 <- 
q.9.3 <- 

# Expert 4:
med.4 <- 
q.1.4 <- 
q.9.4 <- 

# Expert 5:
med.5 <- 
q.1.5 <- 
q.9.5 <- 

expert.quantiles <- c(med.1,med.2,med.3,med.4,med.5,q.1.1,q.1.2,q.1.3,q.1.4,q.1.5,q.9.1,q.9.2,q.9.3,q.9.4,q.9.5)

z.quantiles <- c(rep(qnorm(0.5), times=5), rep(qnorm(0.1), times=5), rep(qnorm(0.9), times=5) )

coef( lm(expert.quantiles ~ z.quantiles) )

# We will use the estimated intercept as the prior mean and the estimated slope
# as the prior standard deviation.