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

Raw LaTeX

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

Topic Tags

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