Normal-Normal priors

Researchers developed a test to evaluate the impact of sleep deprivation on reaction time. For subject \(i\), let \(Y\)_i be the change in reaction time (in ms) after 3 sleep deprived nights. Of course, people react differently to sleep deprivation. It's reasonable to assume that \(Y\)_i are Normally distributed around some average \(m\) with standard deviation \(s\): \(Y\)_i \(\sim N(m, s^2)\).

In the first step of your Bayesian analysis, you'll simulate the following prior models for parameters \(m\) and \(s\): \(m \sim N(50, 25^2)\) and \(s \sim Unif(0, 200)\). This requires the rnorm(n, mean, sd) and runif(n, min, max) functions.

Use rnorm(n, mean, sd) to sample 10,000 draws from the \(m\) prior. Assign the output to prior_m.
Use runif(n, min, max) to sample 10,000 draws from the \(s\) prior. Assign the output to prior_s.
After storing these results in the samples data frame, construct a density plot of the prior_m samples and a density plot of the prior_s samples.

Exercise

Normal-Normal priors

Instructions