DataCamp

Normal-Normal priors

likelihood: Y[i] ~ N(m, s^2)
priors: m ~ N(50, 25^2) and s ~ Unif(0, 200)

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 will 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() and runif() functions. rnorm() takes 3 arguments: sample size n and the mean and sd Normal parameters. runif() also takes sample size n and the min and max Uniform parameters.

Use rnorm() to sample 10,000 draws from the \(N(50, 25^2)\) prior for \(m\). Assign the output to prior_m.
Use runif() to sample 10,000 draws from the \(Unif(0, 200)\) prior for \(s\). Assign the output to prior_s.
Store the prior_m and prior_s samples in the samples data frame.
Construct a density plot of the prior_m samples and a density plot of the prior_s samples.

Take Hint (-30 XP)

Exercise

Normal-Normal priors

Instructions