Tesi di LAUREA SPECIALISTICA Titolo Bayesian Hierarchical Gaussian Process Model: an Application to Multi-Resolution Metrology Data Data 2011-03-31 Autore/i Dolci, Lucia Relatore Colosimo, B. M. Full text non disponibile Abstract In the present work we discuss and extend an existing Bayesian Hierarchical Gaussian Process Model (BHGP) used to integrate data with different accuracies. The low-accuracy data are the deterministic output of a computer experiment and the high-accuracy data come from a more precise computer simulation or a physical experiment. A Gaussian process model is used to fit the low-accuracy data. Then the high-accuracy data are linked to the low-accuracy data using a flexible adjustment model where two further Gaussian processes perform scale and location adjustments. An empirical Bayesian approach is chosen and a Monte Carlo Markov Chain (MCMC) algorithm is used to approximate the predictive distribution at new input sites. The existing BHGP model is then extended in order to model the more general situation where also the low accuracy data come from a physical experiment. A measurement error term needs to be included in the model for the low-accuracy data and the MCMC prediction method is accordingly adjusted. The BHGP model is implemented in Matlab and a validation study is performed to verify the developed code and to evaluate the predictive performance of the model. The extended BHGP model is then applied to a set multi-sensor metrology data in order to model the surface of an object. The low-accuracy data are measured with an innovative optical-based Mobile Spatial Coordinate Measuring System II (MScMS-II), developed at Politecnico di Torino, Italy, and the high-resolution data are acquired with a Coordinate-Measuring Machine (CMM). Comparing the BHGP model with other existing methods allows us to conclude that significative improvements (by 11% − 22%) in terms of prediction error are achieved when low-resolution and high-resolution data are combined using an appropriate adjustment model.