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;
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F340eecf6-2dbe-4964-aead-4c55d9744b59%2F9f24ebf7-3081-463c-88dc-912d50797634%2Fwq3qdk7_processed.jpeg&w=3840&q=75)
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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