optimal design of experiments

**Optimal Design of Experiments** is the **construction of experimental designs that optimize a specific statistical criterion** — using mathematical optimization to find the best possible set of experiments for a given model, constraints, and design size, rather than relying on classical factorial templates. **Key Optimality Criteria** - **D-Optimal**: Maximizes the determinant of $X^TX$ — minimizes the volume of the parameter confidence ellipsoid. - **A-Optimal**: Minimizes the average variance of parameter estimates. - **I-Optimal**: Minimizes the average prediction variance across the design space. - **G-Optimal**: Minimizes the maximum prediction variance. **Why It Matters** - **Irregular Regions**: Works for constrained, non-rectangular parameter spaces where classical designs don't fit. - **Custom Models**: Can design experiments for any specified model (non-standard terms, mixture models). - **Fewer Runs**: Often achieves the same statistical power with fewer experiments than classical designs. **Optimal DOE** is **custom-tailored experiments** — using math to design the statistically best possible experiment for your specific situation.