Statistical Inference Concepts Flashcards
7 cards from real MS-DS Master of Data science practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Statistical Inference Concepts flashcards as text
The Kolmogorov-Smirnov test is used to:
Answer: Test whether a sample comes from a specified distribution or compare two samples
The KS test compares the empirical CDF against a theoretical CDF (one-sample) or between two empirical CDFs (two-sample) to detect distributional differences.
In maximum likelihood estimation, the score function is defined as:
Answer: The gradient of the log-likelihood with respect to the parameter
The score is ∂ℓ(θ)/∂θ, the first derivative of the log-likelihood; at the MLE it equals zero.
When using the Wilcoxon signed-rank test instead of a paired t-test, the primary reason is:
Answer: The Wilcoxon test does not assume normality and is more robust to outliers
The Wilcoxon signed-rank test is a non-parametric alternative that only assumes symmetry of differences, making it robust when normality is violated.
In the context of regression, what does the term 'heteroscedasticity' refer to?
Answer: Error variance that changes across levels of the predictors
Heteroscedasticity means the variance of the regression errors is not constant (σᵢ² varies with X), violating the homoscedasticity assumption of OLS.
Which of the following is the correct formula for the standard error of a proportion p̂ estimated from n observations?
Answer: √(p̂(1−p̂)/n)
For a binomial proportion, SE(p̂) = √[p̂(1−p̂)/n], derived from the variance of the Bernoulli distribution divided by n.
A likelihood ratio test statistic −2ln(Λ) follows approximately which distribution under H₀ for large samples?
Answer: Chi-square distribution with degrees of freedom equal to the number of constrained parameters
By Wilks' theorem, −2ln(Λ) is asymptotically χ²(k) where k is the number of parameters constrained under H₀.
Which statement best describes the concept of a conjugate prior in Bayesian inference?
Answer: A prior from the same distributional family as the posterior, simplifying analytical computation
A conjugate prior yields a posterior in the same parametric family, making closed-form Bayesian updating possible (e.g., Beta prior with Binomial likelihood gives a Beta posterior).