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Multivariate output sensitivity analysis has gained much attention when the output of the computational model is a vector. A preferable strategy to deal with the multivariate output issue is the covariance decomposition approach based on the polynomial chaos expansion (PCE) metamodel. However, since the PCE construction depends on the quality of experimental design to some extent, the selection of design points is significant in determining the accuracy of the sensitivity estimator. In this article, a PCE-based sequential experimental design is proposed to estimate the multivariate output sensitivity index. In this method, the optimal design point is sequentially selected to minimize the determinant of covariance matrix of the sensitivity estimator. To validate the performance of the proposed method, several numerical examples are presented, which show that the sequential design approach performs better than other prevalent methods in terms of accuracy and robustness. [ABSTRACT FROM AUTHOR]

This paper studies the parameter estimation algorithms of multivariate pseudo-linear autoregressive systems. A decomposition-based recursive generalised least squares algorithm is deduced for estimating the system parameters by decomposing the multivariate pseudo-linear autoregressive system into two subsystems. In order to further improve the parameter accuracy, a decomposition based multi-innovation recursive generalised least squares algorithm is developed by means of the multi-innovation theory. The simulation results confirm that these two algorithms are effective. [ABSTRACT FROM AUTHOR]

The current parameterization and algorithm used to fit a smoothing spline analysis of variance (SSANOVA) model are computationally expensive, making a generalized additive model (GAM) the preferred method for multivariate smoothing. In this article, we propose an efficient reparameterization of the smoothing parameters in SSANOVA models, and a scalable algorithm for estimating multiple smoothing parameters in SSANOVAs. To validate our approach, we present two simulation studies comparing our reparameterization and algorithm to implementations of SSANOVAs and GAMs that are currently available in R. Our simulation results demonstrate that (a) our scalable SSANOVA algorithm outperforms the currently used SSANOVA algorithm, and (b) SSANOVAs can be a fast and reliable alternative to GAMs. We also provide an example with oceanographic data that demonstrates the practical advantage of our SSANOVA framework. Supplementary materials that are available online can be used to replicate the analyses in this article. [ABSTRACT FROM PUBLISHER]

Generalized linear mixed-effect models are widely used for the analysis of correlated non-Gaussian data such as those found in longitudinal studies. In this article, we consider extensions with nonparametric fixed effects and parametric random effects. The estimation is through the penalized likelihood method, and our focus is on the efficient computation and the effective smoothing parameter selection. To assist efficient computation, the joint likelihood of the observations and the latent variables of the random effects is used instead of the marginal likelihood of the observations. For the selection of smoothing parameters and correlation parameters, direct cross-validation techniques are employed; the effectiveness of cross-validation with respect to a few loss functions are evaluated through simulation studies. Real data examples are presented to illustrate potential applications of the methodology. Open-source R code is demonstrated in the Appendix. [ABSTRACT FROM AUTHOR]