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Let X; E {1,2, 3,...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid X1, X2, ..., X, fxp(x |p) = (1 – p)"-'p for 0 < p <1 defined on r E {1,2, 3, ...} and 0 elsewhere. Here, p is the risk of relapse on each day. 1. Using a p~ Beta(a, B) prior, derive the posterior density of p, fpix, (p | Xn).

Let X; E {1,2, 3,...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid X1, X2, ..., X, fxp(x |p) = (1 – p)"-'p for 0 < p <1 defined on r E {1,2, 3, ...} and 0 elsewhere. Here, p is the risk of relapse on each day. 1. Using a p~ Beta(a, B) prior, derive the posterior density of p, fpix, (p | Xn).

MATLAB: An Introduction with Applications
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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Let X; € {1,2,3, ...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid fxp(x | p) (1 – p)*-'p x-1 X1, X2 - for 0 < p <1 defined on x E {1,2, 3, . ..} and 0 elsewhere. Here, p is the risk of relapse on each day. 1. Using a p~ Beta(a, ß) prior, derive the posterior density of p, fp|X, (p | Xn). 2. Find the posterior mean of p. Find the MLE of p - you do not need to verify that it is a max.
Transcribed Image Text:Let X; € {1,2,3, ...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid fxp(x | p) (1 – p)*-'p x-1 X1, X2 - for 0 < p <1 defined on x E {1,2, 3, . ..} and 0 elsewhere. Here, p is the risk of relapse on each day. 1. Using a p~ Beta(a, ß) prior, derive the posterior density of p, fp|X, (p | Xn). 2. Find the posterior mean of p. Find the MLE of p - you do not need to verify that it is a max.
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