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.

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Bayesian Modeling with RJAGS

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Instrucciones del ejercicio

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.

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# Take 10000 samples from the m prior


# Take 10000 samples from the s prior    


# Store samples in a data frame
samples <- data.frame(prior_m, prior_s)

# Density plots of the prior_m & prior_s samples    
ggplot(___, aes(x = ___)) + 
    ___()
ggplot(___, aes(x = ___)) + 
    ___()

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