5. The inputs to a Metropolis-Hastings (MH) sampler are the target pdf f(x) and a transition...

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5. The inputs to a Metropolis-Hastings (MH) sampler are the target pdf f(x) and a transition density q(y |x). A key quantity is the acceptance probability S f(y)q(x|y) f(x) q(y|x)' a(x, y) = min (a) Formulate the general MH algorithm. (b) Suppose f (x) is a 2-dimensional pdf, and the proposal state is of the form Y = x+ Z/10, where Z is a 2-dimensional standard normal vector Z and x is the current state. What is q(y|x) in this case? How does a(x, y) simplify? 5. The inputs to a Metropolis-Hastings (MH) sampler are the target pdf f(x) and a transition density q(y |x). A key quantity is the acceptance probability S f(y)q(x|y) f(x) q(y|x)' a(x, y) = min (a) Formulate the general MH algorithm. (b) Suppose f (x) is a 2-dimensional pdf, and the proposal state is of the form Y = x+ Z/10, where Z is a 2-dimensional standard normal vector Z and x is the current state. What is q(y|x) in this case? How does a(x, y) simplify?

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The MH algorithm for sampling from a target distribution using transition kernel QQ consists of the ... View the full answer