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Suppose that several people try to quantify their belief about the unknown probability parameter p, 0

Suppose that several people try to quantify their belief about the unknown probability parameter p, 0

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 8E: Suppose the probability of incorrectly transmitting a single bit is . Compute the probability of...
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Suppose that several people try to quantify their belief about the unknown probability parameter p, 0 <p < 1, of the geometric distribution with pmf f(x\p) = (1 – p)²-'p on r= 1,2, 3, ... . (a) The first person is not an expert and has no particular opinions on the value of p. What is a suitable non-informative prior for this person to use? (b) Two experts, A and B, suggest two priors based on their knowledge of the likely values for p: Expert A's suggested prior is Beta(5, 5), while Expert B's is Beta(4, 10). By calculating the variance of each prior, explain which expert has the stronger prior, and hence who is more certain about their opinion. (c) Give a single reason why a gamma or a normal prior would not be suitable to use for p in this situation.
Transcribed Image Text:Suppose that several people try to quantify their belief about the unknown probability parameter p, 0 <p < 1, of the geometric distribution with pmf f(x\p) = (1 – p)²-'p on r= 1,2, 3, ... . (a) The first person is not an expert and has no particular opinions on the value of p. What is a suitable non-informative prior for this person to use? (b) Two experts, A and B, suggest two priors based on their knowledge of the likely values for p: Expert A's suggested prior is Beta(5, 5), while Expert B's is Beta(4, 10). By calculating the variance of each prior, explain which expert has the stronger prior, and hence who is more certain about their opinion. (c) Give a single reason why a gamma or a normal prior would not be suitable to use for p in this situation.
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