Chapter 2: The Subjective Worlds of Frequentist and Bayesian Statistics

Question 1

What does Bayes rule tell us how to do?

Answer 1

Bayes’ rule tells us how to update our prior beliefs in order to derive better, more informed, beliefs about a situation in light of new data.

Question 2

What does θ represent in BS?

Answer 2

In Bayesian inference, we test hypotheses about the real world using these posterior beliefs. As part of this process, we estimate characteristics that interest us, which we call parameters, that are then used to test such hypotheses. We use θ to represent the unknown parameter(s) which we want to estimate.

Question 2

What does θ represent in BS?

Answer 2

In Bayesian inference, we test hypotheses about the real world using these posterior beliefs. As part of this process, we estimate characteristics that interest us, which we call parameters, that are then used to test such hypotheses. We use θ to represent the unknown parameter(s) which we want to estimate.

Question 3

What is Bayes’ rule?

Answer 3

p(θ | data ) = p(data | θ) x p(θ) / p(data)

where we use p to indicate a probability distribution which may represent either probabilities or, more usually, probability densities

Question 4

What name is given to the term Pr(data|θ)?

Answer 4

We call Pr(data|θ) the likelihood, which is common to both Frequentist and Bayesian analyses. This tells us the probability of generating the particular sample of data if the parameters in our statistical model were equal to θ.