Week 7 Goodness of fit tests

Question 1

what is the most widely used goodness of fit test

Answer 1

chi-squared test

Question 2

what is the probability distribution of chi-squared equation

Answer 2

P(X^2; N) = 2^-(N/2) / Γ(N/2) X^(N-2)e^-(X^2/2)

N is the number of degrees of freedom

Question 3

what is one possible interpretation of the chi-squared tests

Answer 3

if you conduct a large number of fits with an appropriate model to independent, each with N degrees of freedom then the chi-squared probability corresponds to the fraction of fits that result in a chi-squared value greater than the threshold

Question 4

what is the most important criteria when selecting a specific model for best fit

Answer 4

its meaningfulness in terms of its physics interpretation

Question 5

what is the Akaike Information Criterion equation

Answer 5

AIC = -2ln[L(x I ahat, M)] + 2k

ahat is the parameter that maximises the likelihood for model M which has k parameters

Question 6

what is the Bayesian Information Criterion equation

Answer 6

BIC = -2ln[L(x I ahat, M)] +kln[n]

a is the parameter that maximises the likelihood for model M which has k parameters and n datasets

Question 7

why is BIC better than AIC

Answer 7

only BIC is guaranteed to identify the true model among a set of candidates

Question 8

what are the AIC and BIC chi-squared equations respectively

Answer 8

AIC = X^2 + 2k
BIC = X^2 +kln[n]

Question 9

when we have to compare two datasets what can we do if we know there deviation values

Answer 9

we compare the difference between two values with the combined uncertainty of the datasets

Question 10

what is the Kolmogorov-Smirnov KS test used for

Answer 10

comparing a distribution that is fully defined of data events to a given distribution

Question 11

what are the two equations associated with the KS test

Answer 11

D = max I cum(x)-cum(P) I
d = Dsqrt(N)
D is the largest difference between two distributions
d is the scaled difference
N is the number of trials