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2. Suppose that the Bernstein-von Mises holds for the one-dimensional parameter 6, with Fisher information 2 equal to I(0) = —Eg{2z((0;z)} = 1. Define the sets 6 _ foods zalyi) it8, <0 "on — za/ v0) 8,20 where z, is the standard normal (1 — a) quantile (i.e., ov (right) tail cutoff). show that 2a. [2pts] (cr | x1,...,x,) = 1 — a, as n — oo (posterior probability of § € ch). 2b. [2pts] p(0 € c, | 6 =0) = 1—2a as n — oo (coverage probability, i.e., probability w.r.t. xy,...,x,, that the random interval c,, covers the true 6 = 0). hint: what is the tail probability of a truncated normal? conclude that not every credible set is a confidence set of the same asymptotic level. "on="" —="" za/="" v0)="" 8,20="" where="" z,="" is="" the="" standard="" normal="" (1="" —="" a)="" quantile="" (i.e.,="" ov="" (right)="" tail="" cutoff).="" show="" that="" 2a.="" [2pts]="" (cr="" |="" x1,...,x,)="1" —="" a,="" as="" n="" —="" oo="" (posterior="" probability="" of="" §="" €="" ch).="" 2b.="" [2pts]="" p(0="" €="" c,="" |="" 6="0)" =="" 1—2a="" as="" n="" —="" oo="" (coverage="" probability,="" i.e.,="" probability="" w.r.t.="" xy,...,x,,="" that="" the="" random="" interval="" c,,="" covers="" the="" true="" 6="0)." hint:="" what="" is="" the="" tail="" probability="" of="" a="" truncated="" normal?="" conclude="" that="" not="" every="" credible="" set="" is="" a="" confidence="" set="" of="" the="" same="" asymptotic="">