Bayesian Statistics

Question 1

Bayesian statistics

Answer 1

Probability of an event expressed from 0-1

Question 2

Bayes theorem

Answer 2

Posterior = likelihood x prior / marginal

Question 3

Components of Bayes theorem

Answer 3

-Posterior- probability the hypothesis is true given the data
-Likelihood- how probable the data is given the hypothesis is true
-Prior- how probable was hypothesis before observing data
-Marginal- how likely you are to see this data regardless of the hypothesis

Question 4

Bayes factor

Answer 4

-Assessing the relative plausibilities of competing hypotheses H0 and H1
-Strength of evidence in favor of one hypothesis among two competing hypotheses
-More lower than 1 = H0
-More higher than 1 = H1
-Interpretation- 8 means there is 8 times more evidence for H1 than H0

Question 5

Similarities with frequentist

Answer 5

-Use some similar models
-Both can be used for estimation and hypothesis testing

Question 6

Differences from frequentist

Answer 6

-No p-values to interpret coefficients
-No reliance on null hypothesis
-Must explicitly state prior knowledge

Question 7

Advantages

Answer 7

-Realistic estimates
-Intuitive interpretations
-Requires you to know your area and be specific
-Tells us the answer to what we want to know