3-probability

Question 1

What is bayes rule?

Answer 1

P(A | B) = P(B | A) * P(A) / P(B)

Question 2

What is posterior probability?

Answer 2

P(A | B)
Degree of belief of A, having accounted for B

Question 3

What is prior probability?

Answer 3

P(A)
Initial degree in the belief of A
The probability of A occurring, given no additional knowledge about A

Question 4

What is likelihood?

Answer 4

P(B)
The support B provides A

Question 5

What are the parameters of gaussian distribution?

Answer 5

mu = mean
sigma = standard deviation

Question 6

What is the probability P of an event with probability p occurring exactly m out of n times?

Answer 6

(n choose m) * p^m *(1-p)^(n-m)

Question 7

What is multinomial distribution?

Answer 7

Multinomial distribution models the probability of counts of different events from a series of independent trials with more than two possible outcomes

Question 8

What is categorical distribution?

Answer 8

Categorical distribution models the probability of events resulting from a single trial

Question 9

What is marginilisation?

Answer 9

When we want to assess the probability of an event A, irrespective of the outcome of another event B

P(A) = Sum over B (P(A, B = b))

Question 10

What is maximum likelihood estimate?

Answer 10

When a parameter is chosen to maximise the probability of observed data, i.e. maximise theta

argmax over theta (P(X;theta;N))

Question 11

What is maximum a posteriori estimate?

Answer 11

Modifying the maximum likelihood estimate by multiplying by the prior belief of theta

argmax over theta (P(theta)*P(X|theta))