There is need to calculate R a+1 a f(x)dx, where f(x) has the Pareto distribution f(x)...

 

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There is need to calculate R a+1 a f(x)dx, where f(x) has the Pareto distribution f(x) = 2a 2 x3, a<x<∞. A student suggests using a Metropolis-Hastings algorithm with candidate (jumping) density e-x, 0<x<*>. (a) Write out this algorithm in detail, showing exactly how to calculate the integral. (b) Another student suggests using the Cauchy as a candidate (jumping) density: f(x) = 1 (1+x2), -∞<x<∞. Briefly discuss some pros and cons of this. (c) Can you suggest a way of calculating the integral that is better than those in parts (a) and (b). You do not have to provide anything, but you should define your choice There is need to calculate R a+1 a f(x)dx, where f(x) has the Pareto distribution f(x) = 2a 2 x3, a<x<∞. A student suggests using a Metropolis-Hastings algorithm with candidate (jumping) density e-x, 0<x<*>. (a) Write out this algorithm in detail, showing exactly how to calculate the integral. (b) Another student suggests using the Cauchy as a candidate (jumping) density: f(x) = 1 (1+x2), -∞<x<∞. Briefly discuss some pros and cons of this. (c) Can you suggest a way of calculating the integral that is better than those in parts (a) and (b). You do not have to provide anything, but you should define your choice

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a Write out this algorithm in detail showing exactly how to calculate the integral ANS WER The Met r... View the full answer