New methods for modelling and data analysis in gas chromatography: a Bayesian view

Along this thesis were presented several application of Bayesian statistics in gas-chromatographic data analysis. Although complex in understanding for the public used with the frequentist data analysis, Bayesian statistics proved to be useful, robust and objective tool for chromatographic data treatment.
The present work proves, in each chapter, the benefits of Bayesian statistics and encourages to use and to combine various methods from machine learning, image processing, information theory, psychometrics etc. As a successful example of such a combination of metrics is the 4^th chapter of this thesis, where Jansen-Shannon divergence, coming from information theory, was combined with Bayesian hypothesis testing. The 3^rd chapter can also be regarded as an image processing approach (i.e. scaling the GCxGC- FID tiles are similar to scaling tiles of images) combined with Bayesian statistics.
One of the concerns in using Bayesian, is the speed of computations. This concern is rooted in the Bayes rule, more specifically in the cases where an integration of the likelihood is required to explore all space of the parameters in case of the parameter selection. One solution is the use of MCMC algorithm for sampling from the posterior distribution which can be extremely time consuming when dealing with large number of parameters (i.e. high dimensional space). However, in some cases as it was presented in the 5^th chapter, an approximation – Laplace approximation – may be used to evaluate the likelihood in the optimal values of the parameters. The speed of computation presented in the discussions and conclusions of the 3^rd, 4^th and 5^th chapters proves the efficiency of the algorithms with the objectivity of the answer provided.