For input data use the first column in the dataset, labelled x. Suppose that the observed data ₁,...,n follow a normal distribution N(u, o2), where o is assumed to be known and equal to 2. (a) Let the last two digits of your ID number be BC. As a prior distribution for u, take a normal distribution N(o, o). We want the prior mean to be B + 15 and the prior probability P(u ≤ C) to be 0.1. Find the prior parameters po and of that satisfy this. (b) Using this prior distribution, find the posterior distribution for μ. (You may use the formulas) (c) Calculate the posterior probability P(µ ≤ 2). (d) Calculate a 95% equal-tail credible interval for u. (e) Calculate a 95% HDP credible interval for μ X Y 14 43 O55 2.256 13 1.83 2.061 1.108 1.287 1.696 15 7 10 15 1.518 2 0.984 13 0.868 13 1.387 11 10 13 5 13 9 12 9 12 8 7 W 331
For input data use the first column in the dataset, labelled x. Suppose that the observed data ₁,...,n follow a normal distribution N(u, o2), where o is assumed to be known and equal to 2. (a) Let the last two digits of your ID number be BC. As a prior distribution for u, take a normal distribution N(o, o). We want the prior mean to be B + 15 and the prior probability P(u ≤ C) to be 0.1. Find the prior parameters po and of that satisfy this. (b) Using this prior distribution, find the posterior distribution for μ. (You may use the formulas) (c) Calculate the posterior probability P(µ ≤ 2). (d) Calculate a 95% equal-tail credible interval for u. (e) Calculate a 95% HDP credible interval for μ X Y 14 43 O55 2.256 13 1.83 2.061 1.108 1.287 1.696 15 7 10 15 1.518 2 0.984 13 0.868 13 1.387 11 10 13 5 13 9 12 9 12 8 7 W 331
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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for part a please show the method using example values for B and C
Transcribed Image Text:For input data use the first column in the dataset, labelled x. Suppose
that the observed data ₁,...,n follow a normal distribution N(μ, o2), where o is
assumed to be known and equal to 2.
(a) Let the last two digits of your ID number be BC.
As a prior distribution for µ, take a normal distribution N(o, o). We want the
prior mean to be B + 15 and the prior probability P(μ ≤ C) to be 0.1. Find the
prior parameters po and of that satisfy this.
(b) Using this prior distribution, find the posterior distribution for u. (You may use
the formulas)
(c) Calculate the posterior probability P(μ ≤ 2).
(d) Calculate a 95% equal-tail credible interval for μ.
(e) Calculate a 95% HDP credible interval for
X
у
2.256
14
1.83
13
2.061 7
1.108 10
1.287 15
15
1.696
1.518 2
0.984 13
0.868
13
1.387
055
WOHW w
11
10
13
SHOHOHON
5
13
9
12
9
12
8
7
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VIEWStep 2: Determine the prior parameters satisfying the conditions.
VIEWStep 3: Determine the posterior distribution for u using the prior distribution.
VIEWStep 4: Determine the posterior probability.
VIEWStep 5: Determine the 95% equal tail credible interval for u.
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