The prior distribution for $\theta$ is Gamma($\alpha,\beta$) and $(y|\theta)$ is exponentially with rate $\theta$.

  • For the first case A, we observe that $y\geq 10$, but we don't observe the exact number.
  • For the second case B, we observe that $y=10$.

I know the posterior distributions for these two case.

  • For case A, posterior distribution is Gamma($\alpha,\beta+10$)
  • For case B, posterior distribution is Gamma($\alpha+1,\beta+10$)

According to the formula for the Gamma distribution we know that the posterior variance of A is smaller.

However, is there an intuitive or simple reason for the case A will have a smaller posterior variance without calculating their variance by formula?

New contributor
Xuanming is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.

Your Answer

Xuanming is a new contributor. Be nice, and check out our Code of Conduct.

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.