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.