We would like to choose the gamma prior distribution parameters such that the prior mean is (B+10)/100, where B is the second-to-last digit of your ID number, and the prior coefficient of variation (standard deviation divided by the mean) is 0.5. Find the values of a and 3 that are needed. The data are y = (2,7,5, 3,C +1), where C is the last digit of your ID number, with n = 5. Set k = 2. (i) What is the MLEA? (ii) Using the prior distribution from part (c), what are the parameters of the posterior distribution for n? (iii) What are the posterior mean and standard deviation for n?
We would like to choose the gamma prior distribution parameters such that the prior mean is (B+10)/100, where B is the second-to-last digit of your ID number, and the prior coefficient of variation (standard deviation divided by the mean) is 0.5. Find the values of a and 3 that are needed. The data are y = (2,7,5, 3,C +1), where C is the last digit of your ID number, with n = 5. Set k = 2. (i) What is the MLEA? (ii) Using the prior distribution from part (c), what are the parameters of the posterior distribution for n? (iii) What are the posterior mean and standard deviation for n?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
parts c) & d)
Transcribed Image Text:Question 1
Suppose that we have data y = (y₁,..., yn). Each data-point y; is assumed to be generated by a
distribution with the following probability density function:
P(vin) = kny¹e, y₁ ≥ 0.
The unknown parameter is ŋ, with K assumed to be known, and ŋ, k > 0.
(a) Write down the likelihood for n given y. Find an expression for the maximum
likelihood estimate (MLE) n.
(b) A Gamma(a,ß) distribution is chosen as the prior distribution for n. Show that the
posterior distribution is also a gamma distribution with parameters that you should
determine.
We would like to choose the gamma prior distribution parameters such that the prior
mean is (B+10)/100, where B is the second-to-last digit of your ID number, and the
prior coefficient of variation (standard deviation divided by the mean) is 0.5. Find the
values of a and 3 that are needed.
The data are y = (2,7,5,3,C+1), where C is the last digit of your ID number, with
n = 5. Set K = 2.
(i) What is the MLE ?
(ii) Using the prior distribution from part (c), what are the parameters of the posterior
distribution for n?
(iii) What are the posterior mean and standard deviation for n?
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