Week 4 Maximum Likelihood

Question 1

what is statistical interference

Answer 1

when you know the value of the bayes theorem equation and can test a hypothesis and fit a model to the data

Question 2

what is the likelihood function equation

Answer 2

L(x I a) = II L(xi I a)

Question 3

what is the maximum a posteriori

Answer 3

the most likely outcome of a

Question 4

what are the MAP equation for a value a -give only one

Answer 4

MAP(a) = argmax P(a I x) = [δP(a I x) / δa] = 0
MAP(a) = argmax ln[P(a I x) = [δlnP(a I x) / δa] = 0

Question 5

what is maximum likelihood estimation

Answer 5

MLE is the result of MAP when the prior probability is independent of value a

Question 6

what do we use to determine the efficiency of MLE

Answer 6

variance

Question 7

what is the RCF inequality equation

Answer 7

V(ahat) >= (1+δb/δa)^2 /

Question 8

what happens to the RCF when the estimator is unbiased

Answer 8

it just becomes the minimum variance bound

Question 9

what happens to the bias of an estimator as the number of trials increase

Answer 9

the bias vanishes

Question 10

what two things can be said of the MLE

Answer 10

the logarithmic likelihood near the MLE can be approximated with a parabola so the likelihood is a Gaussian in the MLE region
The standard deviation on the MLE can be found by finding the value of the parameter for which the likelihood change is 1/2 wrt the MLE