Statistics for Astronomy 2020

Question 1

What statement about MCMC is true?

Accepted Answer

MCMC makes a random walk through the parameter space

Question 2

Consider matrix M=(A C; C B) for a two par problem X & Y; what is the covariance matrix?

Accepted Answer

-M-1

Question 3

Given the expected number of alpacas in a barn, what distribution represents the nr of alpacas in a random barn?

Accepted Answer

Poisson distribution

Question 4

What is the goodness of fit test?

Accepted Answer

It tests if the data has unlikely high deviations

Question 5

In model comparison, the "Ockham factor" penalizes models that...

Accepted Answer

Have a large parameter space

Question 6

Considering the linear rank correlation coefficient, what is true?

Accepted Answer

It measures if two parameters correlate

Question 7

What about the chi2 distribution is true?

Accepted Answer

The sum of squared standard normal values is χ2 distributed

Question 8

What is true about the Student T distribution?

Accepted Answer

It arises when estimating the mean without knowing the certainty

Question 9

Consider the chi2-test, what is true?

Accepted Answer

It requires binned data

Question 10

In the context of statistics, what is bootstrapping?

Accepted Answer

It creates multiple data sets from a single data set

Question 11

The Cauchy distribution has an undefined mean

Accepted Answer

True

Question 12

The mean of the Poisson distribution is equal to square root of its variance.

Accepted Answer

False

Question 13

The central limit theorem says that all probability distributions tend towards a Gaussian distribution for large N

Accepted Answer

False

Question 14

A Poisson distrib. is an appropriate likelihood function for binned data when you know the expected signal in each bin

Accepted Answer

True

Question 15

Ockham's theory states that, in some situations, summing independent random variables tends to a normal distribution

Accepted Answer

False

Question 16

What is the Levenberg-Macquard method?

Accepted Answer

A method for fitting parameters to a non-linear model

Question 17

Given a coin with bias H, with N throws and R heads, what is true?

Accepted Answer

P(H | N, R) ∝HR (1 - H)N-R

Question 18

Which equation defines the singular value decomposition?

Accepted Answer

A = U Σ VH

Question 19

What can the Singular Value Decomposition be used for?

Accepted Answer

Degenerate linear problems

Question 20

Given data y and model f(x), what is the definition of the χ2 function?

Accepted Answer

sum [(yi - f(xi))/σi]^2

Question 21

How is <X>, the expected value of X , defined?

Accepted Answer

<X> = ∫ X P(X) dx

Question 22

What distribution has the PDF: P(N) = λN e-λ / (N!)

Accepted Answer

Poisson

Question 23

What about the Kolmogorov-Smirnov test is true?

Accepted Answer

It is defined as the maximum distance of two CDFs

Question 24

Which of these choices is an example of transitivity?

Accepted Answer

A>B and B>C implies A>C

Question 25

What is the best estimate for the mean of N samples {xi} with different uncertainties σi

Accepted Answer

1/N [ sum xi/σi^2 ] / [ sum 1/σi^2 ]

Question 26

The appropriate prior for a location parameter is a constant in the logarithm of the parameter in the allowed range.

Accepted Answer

False

Question 27

What distribution should one use for a scale parameter?

Accepted Answer

log P(X) = constant

Question 28

Which requirements is NOT necessary for a least-squares fit to be appropriate?

Accepted Answer

Nr of parameters > nr of data samples

Question 29

Compared to the linear correlation coefficient, Spearman's rank-order correlation coefficient is more robust against out

Accepted Answer

True

Question 30

Given L(X), a log PDF, how does one estimate the most probable value X0 for a variable X?

Accepted Answer

Solve X0 in dL/dX = 0

Question 31

For a uniform distribution, the cumulative distribution function and the probability density function are the same

Accepted Answer

False

Question 32

In some scenario, the accuracy of X increases as more data are added. What is the deviation in a single datum called?

Accepted Answer

Random uncertainties

Question 33

What is the most probable estimate of a parameter?

Accepted Answer

The maximum of likelihood x prior

Question 34

What about Jeffrey's prior is true?

Accepted Answer

It is used for scale parameters

Question 35

Select the binomial distribution

Accepted Answer

P(x) = n!/[(n-k)! k!] pk (1-p)n-k

Question 36

Given a function F(a,b) for which F(F(a,b),c) = F(a,F(b,c)), what form could F have?

Accepted Answer

F(a, b) = z-1 (z(a) + z(b))

Question 37

What distribution models a coastline of receptors and a random, uniformly flashing lighthouse?

Accepted Answer

Cauchy distribution

Question 38

You should always use least-squares to fit a straight line to data

Accepted Answer

False

Question 39

What is true about Bayesian model comparison?

Accepted Answer

It requires sensible priors of the estimated parameters

Question 40

Select the Chi2 distribution

Accepted Answer

P(x) = ( xν/2-1 e-x/2 ) / ( 2ν/2 Γ(ν/2) )

Question 41

A binomial distribution is an appropriate likelihood function for binned data when you know both the expected value

Accepted Answer

False

Question 42

Given 3 values that are from the same uniform distribution with zero mean, the sum of squared values is chi2 distributed

Accepted Answer

False

Question 43

When fitting y=a+bx and x=a'+b'x and calculating r = √bb' , what have I calculated?

Accepted Answer

Linear correlation coefficient

Statistics for Astronomy 2020

Questions 43

Statistics for Astronomy 2020

Questions 43