Planning for Parameter Estimation

The current parameter estimates are obtained from the posterior density function, which we approximated in Section 6.6 by expansion via the matrix Aee or its inverse. Expected values of these matrices after additional observations are computable from simulations of those augmented data sets. The preferred candidate for the next event can then be selected according to the desired criterion of estimation. 

The full determinant strategy was introduced by Box and Lucas (1959) and applied sequentially by Box and Hunter (1965) the subset strategy was introduced by Michael Box (1971). Experimental designs of these types are called D-optimal [St. John and Draper (1975)] the literature on them is extensive. 

Two shape criteria for the HPD region have been proposed for planning experiments for parameter estimation. Hosten (1974) advocated selection to maximize the smallest eigenvalue of A, thus giving the HPD region a rounder shape. Pritchard and Bacon (1975) selected the next experiment to reduce the interdependence of the parameter estimates. Reparameterization can give such results more easily, as shown by Agarwal and Brisk (1985) and by Ratkowsky (1985). 

A trace criterion for precise estimation was introduced by Pinto, Lobao, and Monteiro (1990). Here one selects the next experiment to minimize A , the trace of the inverse matrix A . This quantity is the sum of the eigenvalues of A and is proportional to the sum of the variances 

The determinant criterion and the trace criterion are well regarded, and both are provided as options in GREGPLUS. Example C.l applies the full determinant criterion to a three-parameter model. 

---