Consider an Accept-Reject method for the target density f based on the instrumental distribu- tion g....

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Consider an Accept-Reject method for the target density f based on the instrumental distribu- tion g. (a) Show that the Accept-Reject sample (X1, X2, ..., Xn) can be associated with two i.i.d. sam- ples, (U1, U2, ..., UN) and (Y, Y2, ..., YN), with corresponding distributions U [0,1] and g; N is the stopping time associated with the acceptance of n variables Yj. (b) Deduce that the corresponding estimator of E, [h(X)] based on (X1, X2, ..., Xn) can be written as n = (x) = n i=1 N 17 W h(Y;)IU,wj (4) with wi = f(Y) Mg(Y)* Consider an Accept-Reject method for the target density f based on the instrumental distribu- tion g. (a) Show that the Accept-Reject sample (X1, X2, ..., Xn) can be associated with two i.i.d. sam- ples, (U1, U2, ..., UN) and (Y, Y2, ..., YN), with corresponding distributions U [0,1] and g; N is the stopping time associated with the acceptance of n variables Yj. (b) Deduce that the corresponding estimator of E, [h(X)] based on (X1, X2, ..., Xn) can be written as n = (x) = n i=1 N 17 W h(Y;)IU,wj (4) with wi = f(Y) Mg(Y)*