Exercise

# Define, compile, & simulate the Normal-Normal

Upon observing the change in reaction time \(Y\)_{i} for each of the 18 subjects \(i\) enrolled in the sleep study, you can update your *posterior* model of the effect of sleep deprivation on reaction time. This requires the combination of insight from the likelihood and prior models:

**likelihood:**\(Y\)_{i}\(\sim N(m, s^2)\)**priors:**\(m \sim N(50, 25^2)\) and \(s \sim Unif(0, 200)\)

In this series of exercises, you'll **define**, **compile**, and **simulate** your Bayesian posterior. The observed `sleep_study`

data are in your work space.

Instructions 1/3

**undefined XP**

**DEFINE** your Bayesian model and store the *model string* as `sleep_model`

. In doing so, note that:

`dnorm(a, b)`

defines a \(N(a, b^{-1})\) model with**precision**(ie. inverse variance) \(b\).`dunif(a,b)`

defines a \(Unif(a,b)\) model.The model of \(Y\)

_{i}depends upon \(m\) and \(s\). The number of subjects \(i\) is defined by`length(Y)`

.