Prior parameter variance

[#1]

Hi,

I am trying to understand the Prior Parameter Variance option for the Bayesian D-optimal design. JMP help says: "The value that you enter is the square root of the reciprocal of the prior variance. A larger value represents a smaller variance and therefore more prior information that the effect is not active."

I am a bit confused, since I thought that if I enter larger value, that would inform the algorithm that I have more prior knowledge that the effect is important. However, the Help statement says that larger value means the effect is not active. Can someone clarify this for me please?

Thanks

[#2 · Accepted solution]

"The value that you enter is the square root of the reciprocal of the prior variance." This refers to how prior uncertainty about model parameters is represented numerically. Specifically: This is the reciprocal of the standard deviation, also known as the precision of the prior.

"A larger value represents a smaller variance and therefore more prior information that the effect is not active."

This tells you how to interpret the number:

• A larger value (i.e., higher precision or smaller variance) suggests that you strongly believe the effect is close to zero — that it is not active.
• A smaller value (i.e., lower precision or larger variance) means you're more uncertain — you're more open to the possibility that the effect could be nonzero.

Why does this matter for Bayesian D-optimal design?

Bayesian D-optimal designs use prior information to determine which experimental runs will give you the most information given what you already believe.

• If you strongly believe certain effects are negligible (i.e., inactive), you give them tight priors (small variances → large values in JMP).
• If you’re unsure about some effects, you use weak priors (large variances → small values in JMP).

This helps the design focus on estimating the most informative or uncertain parts of the model.

[#3]

Many thanks statman,

That also explains why the Variance prediction profiler in the Evaluate design shows much smaller variance across the parameter space for the factors which are inactive, since those effects are close to zero.