Bayesian workshop - STEP 2023
University of Alberta
By the end of this session you will:
brms
In the Bayesian framework, it’s a simple distinction:
For example:
Function that describes probabilities of the different values of a variable
Unknown values can be represented by a function like a probability distribution - called random variables
Bayesian probability:
Frequentist probability:
You flip a coin once and hide it. What is the probability that it is heads?
Frequentist:
Bayesian:
You flip a coin once and hide it. What is the probability that it is heads?
Frequentist: I don’t know the outcome, but it’s either heads or tails. I could only say what the probability of heads for many repeated flips would be.
Bayesian:
You flip a coin once and hide it. What is the probability that it is heads?
Frequentist: I don’t know the outcome, but it’s either heads or tails. I could only say what the probability of heads for many repeated flips would be.
Bayesian: 50%!
“Remember that using Bayes’ Theorem doesn’t make you a Bayesian. Quantifying uncertainty with probability makes you a Bayesian.” - Michael Betancourt
\(\theta\) is some parameter value (like the effect of frequency) \(D\) is the observed data
rt
with a normal distribution
Model assumes rt
comes from a normal distribution with:
We can write this succinctly as:
\(rt \sim Normal(\mu,\sigma)\)
Remember, for the model \(rt \sim Normal(\mu,\sigma)\)
Remember, for the model \(rt \sim Normal(\mu,\sigma)\)
We are now going to move to practice with this simple model.
Please open up script S1_E2_brms_intro.R