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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

1994 • Question 9

Question

Math 6010 • Linear Models 1994 • Question 9

Suppose \(X\sim \operatorname {POISS}(\theta )\). Put a \(\operatorname {GAMMA}(\alpha ,\beta )\) prior on \(\theta \) and suppose we have the following loss function: \[ \ell (\theta ,a)=\frac {(a-\theta )^2}{\theta }. \] Find the Bayes’ estimator of \(\theta \).

Raw LaTeX

Suppose \(X\sim \operatorname{POISS}(\theta)\). Put a \(\operatorname{GAMMA}(\alpha,\beta)\) prior on \(\theta\) and suppose we have the following loss function:
\[
\ell(\theta,a)=\frac{(a-\theta)^2}{\theta}.
\]
Find the Bayes' estimator of \(\theta\).

Topic Tags

Bayesian Testing and Decision Theory Estimator Distributions Measure-Theoretic Probability Uniform Integrability and Truncation Methods