problem6_21 - Damaris Santana-Morant STA 6934 Problem...

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Damaris Santana-Morant STA 6934 Problem 6.21(a) (i) Figure 1 (left) shows that σ = .7 with acceptance rate .73. (ii) Figure 1 (right) shows that σ = 5.9. with mean squared error .89. Simulations using values of σ greater than 6 showed sometimes smaller mean squared error, but still with fluctuations. The R code used is shown below. Figure 1 σ versus acceptance rate (left) and σ versus mean squared error (right)
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#Problem 6.21 #target is a normal(0,1) dtarget <- function(a)dnorm(a,0,1) #define working variables and arrays nsim <- 10000 nparms <- 60 sigma <- array(0,dim=c(nparms,1)) accrate <- array(0,dim=c(nparms,1)) mserror <- array(0,dim=c(nparms,1)) s <- 0 #generate rvs from candidate Cauchy(0,1) #they will be reused as Cauchy(0,sigma) by multipliying by sigma
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