1. Lecture 2

3. Frequentist vs Bayesian statistics
We can draw stronger conclusions from Bayesian statistics!
Frequentist P-value:
P(observed data or more extreme | Ho )
Bayesian P-value:
P(Ho | data)
Concerns about Bayesian inference
We have to choose a prior and it is often very arbitrary.
prior
posterior
likelihood

4. A reindeer example The herders gather hundreds of reindeer each autumn
Save 20% of the heaviest calves
Variation between years
They have to decide directly after weighing whether to keep the calf or not

5. Looking back at previous years they can see that the average weight has been 45 kg
But quite large variance between years of 4.0
The variance within years is
Let X be the unkown weight of the first incoming calf; assumed normal
Will the first calf belong to the top 20% that day?
We need to make a guess of the mean weight that day, ie

6. Theory
Prior
Likelihood
Posterior mean
Easy to update