Intro To Bayesian Thinking

Question 1

Probability

Answer 1

In order to understand the rules of probability, we need to understand three kinds of probabilities

• marginal probabilities like p (A)
• joint probabilities like p (A,B)
• conditional probabilities like p (B\A)

Question 2

What are Bayes’ rule

Question 3

Bayesian model comparison - Bayes factor

Answer 3

The Bayes factor is a ratio of the likelihood of the data under two competing models. It quantifies how much more likely the data is under one model compared to another.

Question 4

Comparing the differences between frequentist vs Bayesian

Answer 4

Frequentist
- hypotheses are tested using p-values and confidence intervals. Hypotheses are either rejected or not rejected based on the data.

Bayesian
- hypotheses are assigned probabilities. Bayesian inference updaters the probability of a hypothesis as new data is introduced.

Question 5

Bayesian hypothesis testing

Answer 5

1. prior and posterior probabilities
2. Bayes factor
3. Credible intervals