Suppose that1X\µ ~ Bernoulli(1+e-(u+2)and a standard normal N(0, 1) prior is specified for u. In a trial, the valuex = 1 is observed.(a) Show that the posterior for u when X is observed to be r = 1 isf(4x = 1) x (1+e¯(u+2)-le¬w²/2 on R.This posterior distribution cannot be sampled from directly. Suppose thatthe Metropolis-Hastings algorithm is to be used to simulate samples fromthe target posterior density f(H|r = 1).In order to simulate samples from the posterior distribution of parameter u,consider the sequence of random variables u1, #2, - such that µt is thevariable for iteration t of the Metropolis-Hastings algorithm. Let be itssimulated value. Suppose that the proposal distribution for +1H = Hewhich has density denoted by q(H+1\44), is N(µ,2).%3D

The random variable which has an integer value is called a discrete random variable. The Bernoulli…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that 1 1+e-(+2) Xu Bernoulli ( and a standard normal N(0, 1) prior is specified for u. In a trial, the value x= 1 is observed. (a) Show that the posterior for when X is observed to be r= 1 is ƒ(μ\x= 1) x (1 + e-(μ+2))-¹-²/2 on R.