For the binomial model, with success probability q and observed data k successes out of n trials, assume a Beta(α,β) prior distribution for q. Show that the posterior mean for q is always in between the prior mean for q and the maximum likelihood estimator qˆ. Show that if the prior is uniform, then the posterior variance for q is always less than the prior variance. Find an example of α,β,k and n where the posterior variance is greater than the prior variance.
For the binomial model, with success probability q and observed data k successes out of n trials, assume a Beta(α,β) prior distribution for q. Show that the posterior mean for q is always in between the prior mean for q and the maximum likelihood estimator qˆ. Show that if the prior is uniform, then the posterior variance for q is always less than the prior variance. Find an example of α,β,k and n where the posterior variance is greater than the prior variance.
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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For the binomial model, with success
Show that if the prior is uniform, then the posterior variance for q is always less than the prior variance. Find an example of α,β,k and n where the posterior variance is greater than the prior variance.
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