MAP Estimation and Priors Quiz

Answers and explanations appear as you take the quiz.

1. Which quantity does MAP maximize?
   • The posterior density given the observed data
   • The likelihood alone, regardless of the prior
   • The prior density alone, regardless of observed data
   • The marginal likelihood integrated over all parameter values
2. What does MLE maximize compared with MAP?
   • The posterior including a prior
   • The likelihood
   • The prior density only
   • The posterior interval width
3. Which prior commonly yields an L2-style coefficient penalty in MAP?
   • A Laplace prior, whose log density gives an absolute-value penalty
   • A uniform prior, which is constant within its support
   • A zero-centered Gaussian prior, whose negative log density gives a squared penalty
   • A point mass at zero, which fixes every coefficient to zero
4. Which prior commonly yields an L1-style penalty?
   • A Gaussian prior, which gives a squared-magnitude penalty
   • A uniform prior, which gives no penalty within its support
   • A point mass at zero, which fixes the parameter
   • A Laplace prior, whose negative log density gives an absolute-value penalty
5. Why can MAP differ from MLE with limited data?
   • MAP discards the likelihood when data are limited
   • The prior can pull the estimate toward values it favors
   • MLE always returns a zero estimate with small samples
   • MAP selects the single observation with the largest value
6. What does a MAP point estimate provide by itself?
   • A point estimate that also specifies a credible interval
   • The full posterior distribution over all parameter values
   • The posterior mode, without a full uncertainty summary
   • A guarantee that the assumed prior is correct
7. Why can prior sensitivity analysis be informative?
   • It guarantees that posterior and prior distributions are identical
   • It proves that a likelihood is misspecified whenever the MAP changes
   • It removes the need to inspect observed data
   • It shows whether conclusions change under plausible prior choices
8. Why may a posterior mode change under reparameterization?
   • A density changes with the coordinate system, so its mode need not map invariantly
   • The likelihood stops depending on observations after transformation
   • A posterior mode is invariant by definition for every nonlinear map
   • Reparameterization converts a continuous parameter into a class label