of the information matrix. This criterion results in minimizing the average variance of the estimates of the regression coefficients. C-optimality This criterion minimizes the variance of a best linear unbiased estimator of a predetermined linear combination of model parameters. D-optimality (determinant) A popular criterion is D-optimality, which seeks to minimize |(X'X)−1|, or equivalently maximize the determinant of the information matrix X'X of the design. This criterion results in maximizing the differential Shannon information content of the parameter estimates. E-optimality (eigenvalue) Another design is E-optimality, which maximizes the minimum eigenvalue of the information matrix. S-optimality This criterion maximizes a quantity measuring the mutual column orthogonality of X and the determinant of the information matrix. T-optimality This criterion maximizes the discrepancy between two proposed models at the design locations. Other optimality-criteria are concerned with the variance of predictions: G-optimality A popular criterion is G-optimality, which seeks to minimize the maximum entry in the diagonal of the hat matrix X(X'X)−1X'. This has the effect of minimizing the maximum variance of the predicted values. I-optimality (integrated) A second criterion on prediction variance is I-optimality, which seeks to minimize the average prediction variance over the design space. V-optimality (variance) A third criterion on prediction variance is V-optimality, which seeks to minimize the average prediction variance over a set of m specific points. Contrasts In many applications, the statistician is most concerned with a "parameter of interest" rather than with "nuisance parameters". More generally, statisticians consider linear combinations of parameters, which are estimated via linear combinations of treatment-means in the design of experiments and in the analysis of variance; such linear combinations are called contrasts. Statisticians can use appropriate optimality-criteria for such parameters of interest and for contrasts. Implementation Catalogs of optimal designs occur in books and in software libraries. In addition, major statistical systems like SAS and R have procedures for optimizing a design according to a user's specification. The experimenter must specify a model for the design and an optimality-criterion before the method can compute an optimal design. Practical considerations Some advanced topics in optimal design require more statistical theory and practical knowledge in designing experiments. Model dependence and robustness Since the optimality criterion of most optimal designs is based on some function of the information matrix, the 'optimality' of a given design is model dependent: While an optimal design is best for that model, its performance may deteriorate on other models. On other