A-Optimal Design

A-Optimal Design is an optimal experimental design that minimizes the average variance of the estimated model parameters — minimizing the trace of the inverse information matrix $(X^TX)^{-1}$, focusing on the average precision across all parameters equally.

A-Optimal vs. D-Optimal

• D-Optimal: Minimizes the volume of the confidence ellipsoid (determinant criterion).
• A-Optimal: Minimizes the average axis length of the confidence ellipsoid (trace criterion).
• Difference: A-optimal weights all parameters equally; D-optimal can be dominated by a few well-estimated parameters.
• Choice: Use A-optimal when all parameters are equally important; D-optimal for overall model quality.

Why It Matters

• Equal Parameter Importance: When every model parameter matters equally, A-optimal is the right criterion.
• Complementary: A-optimal and D-optimal often produce similar designs but can differ when some parameters are harder to estimate.
• Less Common: D-optimal is more widely used in practice, but A-optimal provides a useful alternative perspective.

A-Optimal Design is equal-opportunity precision — designing experiments that minimize the average parameter estimation error across all model coefficients.