ST407 - Monte Carlo Methods & Gibbs Sampling, Blocking & Variance Reduction - Mathematics Assignment Help

Assignment Task -

b) What is the variance of ˆIn,β? (Express your answer in terms of the variance and covariance of ?(X) and ψ(X) with respect to f.) 

(c) What value of β would you choose, if you knew the values of the terms in (b)? What would the resulting variance be, and when would this technique be useful? 

(d) In practice, how might you make use of this technique to improve the estimates obtained from an MCMC algorithm which targets f? Explain how you might choose the values of any param eters which you would need to specify and comment upon the strengths and weaknesses of this approach. 

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