Lecture 11

Question 1

What are probabilities?

Answer 1

relative frequencies of outcomes of repeatable random experiments

Question 2

What are bayesian probabilities?

Answer 2

plausibilities of propositions conditional on available information.

Question 3

What is the formula for Bayes theorem? and what does each component mean/ show?

Answer 3

Slide 14

Question 4

What is the prior probability distribution?

Answer 4

knowledge about some variable in the absence of data included in the likelihood term.

Question 5

The 95% credible interval is an interval of —– distribution containing —-% of the —–.

Answer 5

the posterior, 95, probability

Question 6

How can we find the 95% HPD interval?

Answer 6

It can be found by lowering a threashold density until the AUC where the density exceeds the threshold is 0.95.

Question 7

What is the meaning of the HPD interval? How is it different from the 95% confidence interval?

Answer 7

The probability of the unknown value falling in this region is 95% given the observed data. 95% confidence interval, is an interval produced by a method which generates truth containing intervals 95% of the time when averaging over all possible datasets.