Learning about a percentile
Suppose you want to learn about the 75th percentile of the sampling distribution defined by: $$Q75 = M + 0.674 S$$
This exercise is part of the course
Beginning Bayes in R
Exercise instructions
- Examine the code that simulates 1000 values from the posterior distribution of
(M, S)
. - Use the
coef()
andsigma.hat()
functions to extract simulated vectors ofM
andS
fromsim_fit
. - Compute simulated posterior values of the 75th percentile and save the result as
Q75
. - Construct a histogram of the posterior of
Q75
. - Find a 70% probability interval for
Q75
.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Collect reaction times: times
times <- c(240, 267, 308, 275, 271,
268, 258, 295, 315, 262)
# Fit a normal model: fit
fit <- lm(times ~ 1)
# Simulate 1000 from posterior: sim_fit
sim_fit <- sim(fit, n.sims = 1000)
# Extract the simulated values of M and S: M_sim, s_sim
M_sim <- ___
s_sim <- ___
# Compute values of the 75th percentile: Q75
# Construct histogram of the posterior of Q75
# Find a 70% probability interval for Q75