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Quiz Łańcuch Markowa Monte Carlo

Przetestuj akceptację Metropolis-Hastings, aktualizacje warunkowe Gibbs i znaczenie autokorelacji i diagnostyki wielu łańcuchów.

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Pytanie 1 z 8

Why are MCMC draws usually not equivalent to the same number of independent samples?

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  1. Why are MCMC draws usually not equivalent to the same number of independent samples?
    • Successive states are dependent and often autocorrelated
    • The target distribution has no probabilities
    • Every proposal is always rejected
    • Only one parameter can be sampled
  2. For an asymmetric Metropolis-Hastings proposal, what additional ratio term is needed?
    • The number of parameters squared
    • The reverse proposal probability divided by the forward proposal probability
    • The sample mean of the target
    • The posterior interval width
  3. What does Gibbs sampling draw at each coordinate update?
    • A proposal that is always rejected
    • An independent draw from the joint posterior by definition
    • A value from that variable's full conditional given current other variables
    • A point with maximum likelihood
  4. Why run chains from dispersed starting values?
    • To estimate the data likelihood without a model
    • To make all posterior values equal
    • To guarantee each chain has independent draws
    • To reveal whether separate runs explore compatible target regions
  5. What does effective sample size estimate?
    • The total number of rows saved regardless of correlation
    • The independent-draw equivalent for a quantity after accounting for dependence
    • The number of parameters in the posterior
    • The probability that the model is correct
  6. What does R-hat compare across chains?
    • Prediction accuracy with training error
    • The prior density with the likelihood only
    • Within-chain and between-chain behavior
    • The number of parameters with observations
  7. Why does discarding warmup not guarantee convergence?
    • All chains become independent afterward
    • Warmup contains the exact posterior by definition
    • The target distribution changes after warmup
    • No fixed finite discard proves all relevant quantities have been explored
  8. A chain has many saved draws but low ESS for a tail probability. What follows?
    • The tail estimate may still have substantial Monte Carlo uncertainty
    • The tail probability is exactly zero
    • The posterior mean must be biased
    • The model is necessarily misspecified