Suppose that the number of new cases of a medical condition observed each week can be modelled using a negative binomial distribution with parameters q and r. q is unknown, while r is known. We observe n weeks’ worth of data, and the number of cases each week was y1, . . . , yn. Show that a beta distribution provides a conjugate prior distribution for q, and find the posterior distribution with such a prior.
Suppose that the number of new cases of a medical condition observed each week can be modelled using a negative binomial distribution with parameters q and r. q is unknown, while r is known. We observe n weeks’ worth of data, and the number of cases each week was y1, . . . , yn. Show that a beta distribution provides a conjugate prior distribution for q, and find the posterior distribution with such a prior.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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Suppose that the number of new cases of a medical condition observed each week can be modelled using a negative binomial distribution with parameters q and r. q is unknown, while r is known.
We observe n weeks’ worth of data, and the number of cases each week was y1, . . . , yn.
Show that a beta distribution provides a conjugate prior distribution for q, and
find the posterior distribution with such a prior.
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