MHKERNEL AEPOFHEPOAHEG Given that Xt+1 = :{ Xcand with proability p(Xt, Xcand) Xt with probability 1 - p(Xt, Xcand) The conditional probability density of X++1 given Xcand and Xt is thus f(X++1|Xcand, X+) = 8(Xcand - X++1) P(Xt, Xcand) + 8 (Xt X++1) (1 p (Xt, Xcand)), where 1 8(2) = 0 z=0 otherwise The transition kernel just wants the conditional probability of X++1 given Xt, and to obtain this, the distribution of the candidate value has to be integrated out. It is thus the case that K(X1, X++1) = K(X++1|X+) = (Xt+1|Xcand | = Xcand, X+)(Xcand = cand|X+)dcand- It can be shown that this is equal to R p(Xt, Xt+1)g(Xt+1|Xt) + 8(Xt+1 Xt) (1 r(Xt)), where r(X+) = p(x+, Xcand = Teand)9(Xcand = Teand|X+)dreand- Given the calculated the Kernel of the Metropolis-Hastings algorithm. Above claims it was p(Xt, Xt+1) g(Xt+1|Xt) + 8(Xt+1 Xt) (1 r(Xt)). - . Show the calculations that led to this.