Math Questions
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6. In classical Bayes approach, the prior density can be chosen or adapted by looking at the data.A. TrueB. False
1. Reverend T. Bayes' seminal results were published posthumously inA. 1563B. 1663C. 1763D. 1863
14. In Bayesian estimation, the MAP is:A. The value of the parameter that maximizes the priorB. The value of the parameter that maximizes the posteriorC. The maximum of the posteriorD. The maximum of the prior
2. Another renowned mathematician popularized and clarified Bayes's results, also estimating Saturn's mass and providing uncertainty on this mass. He was :A. JeffreyB. LagrangeC. Laplace
23. In Bayesian estimation, a 95% credible interval has 95% chance to contain the true value of the parameter.A. TrueB. False
11. Call x the data, m the parameter, l the likelihood, k the prior and f the marginal law of x. The posterior p writes:A. p(m|x) = l(x|m) * k(m) / f(x)B. p(m) = l(x|m) * f(x) / k(m)C. p(x|m) = l(m)*f(x|m)/k(m)
12. Using a non informative prior in Bayes estimationA. Is meaningless since the essence of Bayes' approach is to inject prior information in the inference processB. Allows to use all information provided by the posterior, like point estimates and credible intervals
17. The MAP is the same as the MLEA. If the prior is uniform, whatever the likelihoodB. If the likelihood is symmetric, whatever the prior C. Never
7. For the same problem, choosing different prior densities in the Bayesian approach will in general lead to different posterior laws, and hence to different parameter estimates.A. TrueB. False
18. The posterior can have several maxima.A. TrueB. False
4. ML estimation can be interpreted both in frequentist and Bayesian settingsA. TrueB. False
16. The definition of the posterior median isA. The value that separates the posterior density in two equal partsB. The same as the MAP if the posterior is symmetricC. The same as the posterior mean if the posterior is symmetric
15. In Bayes inference:A. It is in general better to consider the MAP than the posterior mean or than the posterior medianB. The MAP is computed a posteriori but the mean is computed a prioriC. MAP, posterior mean and posterior median are usually provided by the posterior law
9. Credible intervals are computed on:A. The likelihoodB. The prior densityC. The posterior densityD. The marginal density of the data
5. The influence of the prior density is to introduce a bias toward values of the parameters that are likely according to previous knowledge.A. TrueB. False
13. Improper priors can be used in Bayesian estimation.A. NeverB. If the marginal law of the data existsC. Provided their pdf does not diverge
8. Although the essence of Bayes' approach is to inject prior density reflecting prior knowledge, many works have tried to inject priors that are as much uninformative as possible.A. TrueB False
24. Uncertainties about the estimated parameters can be produced in the Bayesian setting but not in the frequentist setting.A. TrueB. False
La standardisation directe est idéale pour les populations avec un petit effectif.
Le dénominateur du taux d'incidence s'exprime en personnes-temps