i) [2 marks] In the rejection sampler discussed in the course, let c be the upper bound on the ratio of f(x)/9(x) over x, where f(x) is the function we wish to obtain samples from and g(x) is a trial density from which we can easily sample from. A. The algorithm is more efficient if c is small B. The algorithm is more efficient if c is large C. The algorithm's efficiency does not depend on c D. The algorithm can be used to sample continuous distributions ii) [2 marks] The inverse transform (IT) method was discussed in the course, for sampling from probability distribution f, say, A. IT can be used if the inverse CDF can be computed B. IT cannot be extended to multivariate distributions C. IT can be extended to multivariate distributions, however the inverse CDF is difficult to compute D. The IT can only sample from discrete distributions iii) [2 marks] Which of the following statements are correct? A. Both Bayesian and Frequentist inference requires a specification of a prior B. Bayesian inference is subjective, depending on the prior C. Most Frequentist inference can be made in terms of making proba- bility statements D. A conjugate prior is where the prior and the posterior comes from the same family of distributions E. Most Bayesian analysis do not require Monte Carlo computation iv) [2 marks] A natural cubic spline A. has first and second derivatives B. is a polynomial of order p = 3 C. is linear beyond the first and last knot points. D. All of the above v) [2 marks] Additive models A. beat the curse of dimensionality B. cannot capture interaction between covariates well C. in 2 dimensions, additive models perform better than a two dimen- sional loess smooths (assuming sufficient data) D. are better used for prediction than model interpretation