a negative binomial distribution with parameters q and r. q is unkno vn. serve n weeks' worth of data, and the number of cases each week was y₁,
a negative binomial distribution with parameters q and r. q is unkno vn. serve n weeks' worth of data, and the number of cases each week was y₁,
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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![Suppose that the number of new casesolla medical condition each week can be modelled
using a negative binomial distribution with parameters q and r. q is unknown, while r
is known.
We observen weeks' worth of data. and the number of cases each week was y1,..,yn-
Yn.
(a) Show that a beta distribution provides a conjugate prior distribution for q, and
find the posterior distribution with such a prior.
Y1, ..., Yn. Assume that r is equal to 3.
(b) With a uniform prior distribution for q on the interval [0, 1], what is the posterior
distribution for q (including the numerical value of the parameters)?
(c) What is the posterior mean?
(d) Use R to find the posterior median and a 95% credible interval for q.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0fecb44-186c-4eaa-9f9b-a4318f02d1a0%2Fe00187d1-f245-46a6-baed-a725d484989e%2Fxgkkc0g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that the number of new casesolla medical condition each week can be modelled
using a negative binomial distribution with parameters q and r. q is unknown, while r
is known.
We observen weeks' worth of data. and the number of cases each week was y1,..,yn-
Yn.
(a) Show that a beta distribution provides a conjugate prior distribution for q, and
find the posterior distribution with such a prior.
Y1, ..., Yn. Assume that r is equal to 3.
(b) With a uniform prior distribution for q on the interval [0, 1], what is the posterior
distribution for q (including the numerical value of the parameters)?
(c) What is the posterior mean?
(d) Use R to find the posterior median and a 95% credible interval for q.
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