Comparison analysis of Bayesian D-error and fixed D-error

[Yuchenj]

Dear Dr Bilemer,
I'm using Ngene to generate the SP survey design first time, and I created a Bayesian efficent model to complete the design. In the end, I found the Bayesian mean D-error was larger than fixed D-error. The results are as follows.

Fixed Bayesian mean
D error 0.186766 0.355442
A error 6.613701 18.16263
B estimate 77.2706 0.38612
S estimate 359.009045 3525.984452
My question is that I found some papers said the Bayesian efficient esimation is better than D-efficient method, but why my result is opposite?

Thank you so much for your help and time.

[Michiel Bliemer]

There is no such thing as "Bayesian efficient model" or "Bayesian efficient estimation". An experimental design is Bayesian efficient if the design has a low Bayesian D-error.

A Bayesian D-error is the average D-error over a range of draws from a distribution of prior values instead of a specific fixed prior value. This average D-error is expected to be larger than the D-error when optimising only for a fixed value.

Using a Bayesian efficient design is usually considered better than a local D-efficient design because it is more robust to prior misspecification.

Michiel