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 4th chapter of this thesis, where Jansen-Shannon divergence, coming from information theory, was combined with Bayesian hypothesis testing. The 3rd 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 5th 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 3rd, 4th and 5th chapters proves the efficiency of the algorithms with the objectivity of the answer provided

Use of Bayesian Statistics for Pairwise Comparison of Megavariate Data Sets: Extracting Meaningful Differences between GCxGC-MS Chromatograms Using Jensen-Shannon Divergence

A new method for comparison of GCxGC-MS is proposed. The method is aimed at spotting the differences between two GCxGC-MS injections, in order to highlight the differences between two samples, in order to flag differences in composition, or to spot compounds only present in one of the samples. The method is based on application of the Jensen-Shannon divergence (JS) analysis combined with Bayesian hypothesis testing. In order to make the method robust against misalignment in both time dimensions, a moving-window approach is proposed. Using a Bayesian framework, we provide a probabilistic visual map (i.e., log likelihood ratio map) of the significant differences between two data sets consequently excluding the deterministic (i.e., "yes" or "no") decision. We proved this approach to be a versatile tool in GCxGC-MS data analysis, especially when the differences are embedded inside a complex matrix. We tested the approach to spot contamination of diesel samples

Bayesian peak tracking: A novel probabilistic approach to match GCxGC chromatograms

A novel peak tracking method based on Bayesian statistics is proposed. The method consists of assigning (i.e. tracking) peaks from two GCxGC-FID data sets of the same sample taken in different conditions. Opposed to traditional (i.e. deterministic) peak tracking algorithms, in which the assignment problem is solved with a unique solution, the proposed algorithm is probabilistic. In other words, we quantify the uncertainty of matching two peaks without excluding other possible candidates, ranking the possible peak assignments regarding their posterior probability. This represents a significant advantage over existing deterministic methods. Two algorithms are presented: the blind peak tracking algorithm (BPTA) and peak table matching algorithm (PTMA). PTMA method was able to assign correctly 78% of a selection of peaks in a GCxGC-FID chromatogram of a diesel sample and proved to be extremely fast

Retention time prediction in temperature-​programmed, comprehensive two-​dimensional gas chromatography: Modeling and error assessment

In this paper we present a model relating exptl. factors (column lengths, diams. and thickness, modulation times, pressures and temp. programs) with retention times. Unfortunately, an anal. soln. to calc. the retention in temp. programmed GC×GC is impossible, making thus necessary to perform a numerical integration. In this paper we present a computational phys. model of GC×GC, capable of predicting with a high accuracy retention times in both dimensions.Once fitted (e.g., calibrated)​, the model is used to make predictions, which are always subject to error. In this way, the prediction can result rather in a probability distribution of (predicted) retention times than in a fixed (most likely) value. One of the most common problems that can occur when fitting unknown parameters using exptl. data is overfitting. In order to detect overfitting situations and assess the error, the K-​fold cross-​validation technique was applied. Another technique of error assessment proposed in this article is the use of error propagation using Jacobians. This method is based on estn. of the accuracy of the model by the partial derivs. of the retention time prediction with respect to the fitted parameters (in this case entropy and enthalpy for each component) in a set of given conditions. By treating the predictions of the model in terms of intervals rather than as precise values, it is possible to considerably increase the robustness of any optimization algorithm

Determination of multiple mycotoxins in Qatari population serum samples by LC-MS/MS

Human exposure to mycotoxins is almost inevitable as mycotoxins are naturally occurring contaminants of large portion of food and feed. Depending on the type of mycotoxins, inter-individual mycotoxin adsorption, bioaccumulation, distribution, metabolism and excretion, can cause serious adverse health effects. Therefore, continuous biomonitoring studies of population exposure to mycotoxins are needed. Here we describe a multi-analyte approach for the detection and quantification of 20 mycotoxins in human serum using ultra-performance liquid chromatography-electrospray/tandem mass spectrometry operated in targeted multiple reaction monitoring mode. The validated method was used to assess occurrence of mycotoxins in serum samples of 46 residents of Qatar. Mycotoxins that were detected with high incidence were HT-2 toxin (13.0%), sterigmatocystin (10.9%) and 3-acetyldeoxynivalenol (6.5%). Also, co-exposure to several mycotoxins was noticed in the analysed samples. Our results show that strict food quality control is needed to remove mycotoxin contaminated food from the market in order to minimise human exposure to mycotoxins