Approximate simulation model for analysis and optimization in engineering system design

Computational support of the engineering design process routinely requires mathematical models of behavior to inform designers of the system response to external stimuli. However, designers also need to know the effect of the changes in design variable values on the system behavior. For large engineering systems, the conventional way of evaluating these effects by repetitive simulation of behavior for perturbed variables is impractical because of excessive cost and inadequate accuracy. An alternative is described based on recently developed system sensitivity analysis that is combined with extrapolation to form a model of design. This design model is complementary to the model of behavior and capable of direct simulation of the effects of design variable changes

A generalized Fellner-Schall method for smoothing parameter estimation with application to Tweedie location, scale and shape models

We consider the estimation of smoothing parameters and variance components in models with a regular log likelihood subject to quadratic penalization of the model coefficients, via a generalization of the method of Fellner (1986) and Schall (1991). In particular: (i) we generalize the original method to the case of penalties that are linear in several smoothing parameters, thereby covering the important cases of tensor product and adaptive smoothers; (ii) we show why the method's steps increase the restricted marginal likelihood of the model, that it tends to converge faster than the EM algorithm, or obvious accelerations of this, and investigate its relation to Newton optimization; (iii) we generalize the method to any Fisher regular likelihood. The method represents a considerable simplification over existing methods of estimating smoothing parameters in the context of regular likelihoods, without sacrificing generality: for example, it is only necessary to compute with the same first and second derivatives of the log-likelihood required for coefficient estimation, and not with the third or fourth order derivatives required by alternative approaches. Examples are provided which would have been impossible or impractical with pre-existing Fellner-Schall methods, along with an example of a Tweedie location, scale and shape model which would be a challenge for alternative methods