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The observed data y = {yij, i = 1,...,n, j= 1,...,m} are the average results in an exam for school j within county i. The following hierarchical model is considered reasonable: Yij ~ Normal (ui, o), j = 1,...,m¡ µ¡ ~ Normal (µc,o²), i = 1,..., n. where μc, σs and oc are unknown parameters which are each assigned a prior distribution. Suppose that we have generated a sample of size M from the joint posterior distribution Pμc,os,oc,1,. 1,..., Mn | y). Explain how to use the posterior sample to estimate the following: the posterior mean for uc;

The observed data y = {yij, i = 1,...,n, j= 1,...,m} are the average results in an exam for school j within county i. The following hierarchical model is considered reasonable: Yij ~ Normal (ui, o), j = 1,...,m¡ µ¡ ~ Normal (µc,o²), i = 1,..., n. where μc, σs and oc are unknown parameters which are each assigned a prior distribution. Suppose that we have generated a sample of size M from the joint posterior distribution Pμc,os,oc,1,. 1,..., Mn | y). Explain how to use the posterior sample to estimate the following: the posterior mean for uc;

MATLAB: An Introduction with Applications
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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The observed data y = {yij, i = 1, ..., n, j = 1,...,m;} are the average results in an exam for school j within county i. The following hierarchical model is considered reasonable: Yij ~ Normal (u₁, o), j = 1,...,m; μ¡~ Normal (μc,o), i = 1,...,n. where µc, σs and σc are unknown parameters which are each assigned a prior distribution. Suppose that we have generated a sample of size M from the joint posterior distribution p(µc,os, oc, μ₁,..., Mn | y). Explain how to use the posterior sample to estimate the following: the posterior mean for uc; a 95% credible interval for os /oc; the posterior probability that μ₁ <μ2.
Transcribed Image Text:The observed data y = {yij, i = 1, ..., n, j = 1,...,m;} are the average results in an exam for school j within county i. The following hierarchical model is considered reasonable: Yij ~ Normal (u₁, o), j = 1,...,m; μ¡~ Normal (μc,o), i = 1,...,n. where µc, σs and σc are unknown parameters which are each assigned a prior distribution. Suppose that we have generated a sample of size M from the joint posterior distribution p(µc,os, oc, μ₁,..., Mn | y). Explain how to use the posterior sample to estimate the following: the posterior mean for uc; a 95% credible interval for os /oc; the posterior probability that μ₁ <μ2.
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