Agnes M. Herzberg’s scientific contributions

... One important omission is the rich literature on "optimal experimental design," or "optimal design" for short, that draws from the literature of linear algebra, optimization, and statistics. We only discuss the optimal experimental design literature when it overlaps with experimental design for causal inference in Section 5. We refer to Atkinson et al. (2007), Fedorov (2013), Pukelsheim (2006), Silvey (2013) for textbooks and Atkinson and Fedorov (1975), Card and Krueger (1993), Titterington (1975) for papers on optimal experimental design. A related omission is the literature on "optimal Bayesian design." ...

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Experimental Design For Causal Inference Through An Optimization Lens

... It will be noted that our a corresponds to the block size in the simple block model and that the condition of Theorem 1 always holds in that model for proper block designs. The condition in Theorem 1 is easier to achieve than the one in Herzberg and Wynn (1982). They were concerned with the question of when the estimator for given g2 can be written as a linear combination of the estimators for 02=0 and for fixed effects. ...

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Information matrices for mixed effects models with applications to the optimality of repeated measurements designs

... In selecting designs for balancing dose groups by cage position, our priorities are a) Latin square balance: dose groups are balanced with respect to the "rows" (i.e., horizontal position) and "columns" (i.e., vertical position) within a rack, with each dose group appearing the same number oftimes in each row and column; b) nearest neighbor balance: cages to the north, south, east, west ofeach cage are balanced by dose group (14); and c) front-back balance: dose groups are balanced with respect to pairs of cages in the front and back of racks, referred to as orthogonality. It is usually not possible to achieve perfect balance according to these criteria; therefore, one attempts to use designs that come as close as possible. ...

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Cage allocation designs for rodent carcinogenicity experiments