(a) Suppose that you can observe data that are independently and identically distributed as N(μ, 1). Your prior distribution for μ is N(m, v). After observing n₁ data with sample mean ₁, find your posterior distribution for μ. You now observe a second sample of size n2 and with mean 2. Derive your new posterior i. by sequentially using the new data to update the posterior you obtained from the first sample, and ii. by using all the data to update your original prior. Confirm that these two approaches yield the same answer.
(a) Suppose that you can observe data that are independently and identically distributed as N(μ, 1). Your prior distribution for μ is N(m, v). After observing n₁ data with sample mean ₁, find your posterior distribution for μ. You now observe a second sample of size n2 and with mean 2. Derive your new posterior i. by sequentially using the new data to update the posterior you obtained from the first sample, and ii. by using all the data to update your original prior. Confirm that these two approaches yield the same answer.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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