d-optimal design

**D-Optimal Design** is the **most widely used optimal experimental design criterion** — selecting the set of experimental runs that maximizes the determinant of the information matrix ($X^TX$), resulting in the smallest possible confidence region for the estimated model parameters. **How D-Optimal Design Works** - **Candidate Set**: Generate a large set of candidate design points within the factor space. - **Algorithm**: Exchange algorithms (Fedorov, coordinate exchange) iteratively swap candidate points to maximize $|X^TX|$. - **Model**: Specify the regression model (linear, quadratic, interaction terms) that will be fit. - **Output**: The selected subset of candidate points forms the D-optimal design. **Why It Matters** - **Most Precise Estimates**: D-optimal designs provide the most statistically precise parameter estimates. - **Flexible**: Works with any number of factors, levels, and model terms — no preset templates needed. - **Constraints**: Handles factor constraints, mixture constraints, and irregular design regions naturally. **D-Optimal Design** is **the most informative experiment** — choosing experimental runs to maximize the precision of the estimated model coefficients.