Explore the use of the Metroplis-Hastings algorithm in higher dimensions. Generate 1000 samples for a trivariate normal distribution centered at the origin and covariance equal to the identity matrix....


Explore the use of the Metroplis-Hastings algorithm in higher dimensions. Generate 1000 samples for a trivariate normal distribution centered at the origin and covariance equal to the identity matrix. Thus, each coordinate direction should be a univariate standard normal distribution. Use a trivariate normal distribution with covariance matrix
 (i.e., 9’s are along the diagonal and 0’s everywhere else) and mean given by the current value of the chain
 as the starting point of the chain. Plot the sequential output for each coordinate. Construct a histogram for the first coordinate direction. Does it look like a standard normal? What value did you use for the burn-in period [Gentle, 1998]?



Dec 02, 2021
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