Goals for the Afternoon
Develop an activity that could be used in a course you teach
Be creative!
Brainstorm ideas for questions to answer using a Bayesian analysis
Identify data
Pinpoint how data can be used to address the question
Write down data model and prior
Develop code for modeling
Develop an approach for drawing inferences from the model
Example
Do individuals adapt to extended periods of sleep deprivation?
Sleep study data from lme4 R package, exploring whether the day 3 (first day of sleep deprivation) reaction times differ from the day 9 (7th day of sleep deprivation) reaction times
Take the difference between the 7th day and first day reaction times (7th-1st). Positive differences would imply that more consecutive days of sleep deprivation are related to longer reaction times. Negative differences would imply that reaction times are recovering a bit after individuals become acclimated to sleep deprivation over the week. Differences close to zero would imply no difference in reaction times of the first vs 7th day of sleep deprivation.
Take the difference between the 7th day and first day reaction times (7th-1st) and call it Y_i. Let Y_i \sim N(\mu,\sigma^2)
We could use a normal prior for the mean and a Cauchy prior for the standard deviation. Students can experiment with prior choices.
This can be adapted depending on choice of priors. We could use the brms packages for analysis, so that students have a “black box” method for simulating from the posterior.
We will first look at convergence diagnostics and assuming these are satisfactory, we will plot the posterior. Then we will calculate the posterior probability that the mean difference between response times after 7 days and 1 day of sleep deprivation is >0.