This chapter is concered with how to calibrate a computer model to observational data when the model produces multivariate output and is temporally expensive to run. The significance of considering models with long run times is that they can only be run at a limited number of different inputs, ruling out a brute-force Monte Carlo approach. Consequently, all inference must be done with a limited...

1. Methods to be considered for multivariate calibration Many methods for multivariate calibration have been proposed. It turns out that many of the methods perform similarly. To avoid confusion due to use of many different methods, it is suggested that only the following should be considered: Multiple linear regression (MLR) Principal component regression (PCR) Partial least squares (PLS) Neur...

Traditionally multivariate calibration models have been developed using regression based techniques including principal component regression and partial least squares and their non-linear counterparts. This paper proposes the application of Gaussian process regression as an alternative method for the development of a calibration model. By formulating the regression problem in a probabilistic fr...

We present a hybrid multivariate calibration method, constrained regularization (CR), and demonstrate its utility via numerical simulations and experimental Raman spectra. In this new method, multivariate calibration is treated as an inverse problem in which an optimal balance between model complexity and noise rejection is achieved with the inclusion of prior information in the form of a spect...

• y(u) aims at reproducing some real phenomenon which we denote by y 1.2 Validation of computer models •Question of interest: Does the computer model adequately represent reality? •Obtain field data yi that results from observing reality in a physical experiment yFi = y +εi , εi ∼ Np(0,Σ F ), ,Σ = Λ R Λ, Λ = diag(σ i ) •Combine model and field data with a statistical model y = y(u) + b (Kennedy...

In the multivariate calibration framework we revisit and investigate the prediction performance of three high-dimensional modeling strategies: partial least squares, principal component regression and P-spline signal regression. Specifically we are interested in comparing the stability and robustness of prediction under differing conditions, e.g. training the model under one temperature and usi...

In multivariate calibrations usually a minimal residual error in the model’s predictions is aimed at, while generally less attention is paid to the robustness of the model with respect to changes in instrumentation, laboratory conditions, or sample composition. In this paper, we propose a strategy for selecting a multivariate calibration model which possesses a small prediction error and, simul...

Article history: In general, linearity is assum Received 16 November 2008 Received in revised form 20 January 2009 Accepted 3 February 2009 Available online 12 February 2009