-   When it comes to estimating $\gamma$, the uniform prior outperforms the other methods regardless of the nominal value of $\Delta$.

-   In general, Jeffreys’ prior and the reference prior tend to give similar results regardless of the nominal value of $\Delta$.

![Graphs of the 81 empirical MSEs for $\Delta$ generated from the case $\Delta=0$.](890f01)

![Graphs of the 81 of empirical MSEs for $\Delta$ generated from case $\Delta=0.8$.](890f02)

![Graph of the 81 empirical lengths of 90% HPD intervals generated from the case $\Delta=0.0$.](890f03)

![Graph of the 81 empirical lengths of 90% HPD intervals generated from the case $\Delta=0.0, 0.5, 0.8$.](890f04)

A summary of the findings for the MSE criterion is given as follows.

-   Jeffreys’ prior and the reference prior perform similarly regardless of the nominal value of $\Delta$. The MSEs for $\Delta$ are scattered around the line $y=x$, with increasing deviations as $n$ gets smaller. As $\Delta$ increases, the deviations from the 45 degree line also increase with a slim advantage of Jeffreys’ prior when $\Delta>0.5$. See Figures 1 and 2. The same pattern is observed with the global measure of MSE obtained by adding the MSEs for $\gamma, \lambda_0$ and $\lambda_1$.

-   Jeffreys’ prior and the uniform prior 