MS-DS Master of Data science FREE MS-DS Master of Data science Statistical and Probabilistic Analysis Questions and Answers 3

Question 1

What does the Markov chain Monte Carlo (MCMC) method primarily accomplish in statistical analysis?

Accepted Answer

It samples from complex posterior distributions that are difficult to compute analytically

Answer

MCMC methods generate samples from a target posterior distribution by constructing a Markov chain whose stationary distribution matches the desired posterior.

Question 2

In the context of hypothesis testing, what does statistical power represent?

Accepted Answer

The probability of correctly rejecting H₀ when H₁ is true

Answer

Statistical power is the probability of correctly detecting a true effect by rejecting the null hypothesis when the alternative hypothesis is actually true.

Question 3

Which condition is required for the Gauss-Markov theorem to guarantee that OLS estimators are BLUE?

Accepted Answer

Errors must have constant variance and zero mean with no autocorrelation

Answer

The Gauss-Markov theorem requires that errors have zero mean, constant variance (homoscedasticity), and are uncorrelated, but does not require normality.

Question 4

What is the primary purpose of the Expectation-Maximization (EM) algorithm?

Accepted Answer

To find maximum likelihood estimates when data has missing or latent variables

Answer

The EM algorithm iterates between computing expected values of latent variables (E-step) and maximizing the likelihood given those expectations (M-step) to find MLEs with incomplete data.

Question 5

For a multivariate normal distribution, what does a zero covariance between two variables imply?

Accepted Answer

The variables are both uncorrelated and independent

Answer

For multivariate normal distributions specifically, zero covariance implies independence, which is a stronger result than for general distributions.

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Practice Test

MS-DS Master of Data science FREE MS-DS Master of Data science Statistical and Probabilistic Analysis Questions and Answers 3