Designs for nonlinear regression with a prior on the parameters
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Abstract
This thesis deals with finding design points for nonlinear regression models with the possibility that the fitted model is incorrect. The information matrix depends on the parameter in nonlinear situations. We have assumed a range of values of the parameter and have specified a prior on the parameter space. A loss function has been developed and then a minimax approach has been adopted to achieve our goal. We have found an explicit expression for the maximized loss and a numerical minimization of it has been done by a genetic algorithm (GA). The whole approach has been implemented by considering some well-known nonlinear functions. We see that changing the values of the parameter of the prior density have effect on design points. However, changing the tuning constants of GA does not alter the design points noticeably. This indicates that we have obtained the minimizing design.