Question 2 Suppose that we have data y = (v₁.....yn). Each data-point y, is assumed to be generated by a distribution with the following probability density function: 0² p(y₁|0) = - = exp(-)₁ 3₁ ² , y ≥ 0. The unknown parameter is 0, with > 0. (a) Write down the likelihood for 8 given y. Find an expression for the maximum likelihood estimate (MLE) 8. (b) A Gamma(a, 3) distribution is chosen as the prior distribution for 8. Derive the resulting posterior distribution for 8 given y. (c) We would like to choose the gamma prior distribution parameters so that a = 1, and P(0> 50+B) 0.05, B=2 Find the value of 3 that is needed. (d) The data are y =(4,4,8,8,4, C+3), C in the last Jigit olyan Inshas with n = 6. C = 3 (i) What is the MLE ? (ii) Using the prior distribution from part (c), what are the parameters of the posterior distribution for ? (iii) What are the posterior mean and standard deviation for A?
Question 2 Suppose that we have data y = (v₁.....yn). Each data-point y, is assumed to be generated by a distribution with the following probability density function: 0² p(y₁|0) = - = exp(-)₁ 3₁ ² , y ≥ 0. The unknown parameter is 0, with > 0. (a) Write down the likelihood for 8 given y. Find an expression for the maximum likelihood estimate (MLE) 8. (b) A Gamma(a, 3) distribution is chosen as the prior distribution for 8. Derive the resulting posterior distribution for 8 given y. (c) We would like to choose the gamma prior distribution parameters so that a = 1, and P(0> 50+B) 0.05, B=2 Find the value of 3 that is needed. (d) The data are y =(4,4,8,8,4, C+3), C in the last Jigit olyan Inshas with n = 6. C = 3 (i) What is the MLE ? (ii) Using the prior distribution from part (c), what are the parameters of the posterior distribution for ? (iii) What are the posterior mean and standard deviation for A?
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
100%
please c) and d) parts

Transcribed Image Text:Question 2
Suppose that we have data y = (v₁,...,yn). Each data-point y; is assumed to be generated by a
distribution with the following probability density function:
>= 1 / XP(-21).
«(-9). Vi
exp
p(yi|0) =
Yi ≥ 0.
The unknown parameter is 0, with 0 > 0.
(a) Write down the likelihood for given y. Find an expression for the maximum likelihood
estimate (MLE) Ô.
(b) A Gamma(a, 3) distribution is chosen as the prior distribution for 8. Derive the resulting
posterior distribution for 8 given y.
(c) We would like to choose the gamma prior distribution parameters so that a = 1, and
P(0> 50+B) = 0.05,
B = 2
Find the value of 3 that is needed.
(d) The data are y = (4,4,8,8,4, C+3), Gia the last digit of you. In aber, with
n = 6.
C = 3
(i) What is the MLE
(ii) Using the prior distribution from part (c), what are the parameters of the posterior
distribution for ?
(iii) What are the posterior mean and standard deviation for A?
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 51 images

Recommended textbooks for you

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON

The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman

Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman