Bayesian Modelling of Ion-Selective Electrode Sensor Arrays

Abstract

<p>Non-linear multivariate calibration methods are increasingly used to extract information from different types of sensors. As the complexity of the data increases, new methods are required to estimate parameters and to provide realistic estimates of uncertainty. Particularly, the quantification of uncertainty for the measurands, or for a sensor’s figures of merit (e.g. limit of detection (LOD), the lowest non-zero concentration of an analyte that can be reliably distinguished from a blank), is not well understood nor is it common practice. This thesis is largely focused on the study of establishing a meaningful limit of detection for sensors and sensor arrays with non-linear response, as well as developing advanced calibration techniques and estimators. Throughout, we use ion selective electrodes (ISEs) as a model system of specific interest. However, the techniques we employ could easily be adopted for other non-linear sensors governed by a physico-chemical model.</p> <p>Although The International Union of Pure and Applied Chemistry (IUPAC) has recommended a probabilistic approach to determining LOD, the current LOD definition for ISEs conflicts with that recommendation. Here, a new LOD definition for ISEs and a Bayesian approach for LOD estimation for non-linear sensors is demonstrated. The method also provides estimates of LOD uncertainty that is currently missing from other LOD estimation procedures. The study shows that the proposed method has substantially less bias than the current official definition for ISEs.</p> <p>Next, a Bayesian algorithm was developed to construct the LOD distribution for a non-linear sensor array. This algorithm accommodates the multivariate signal that arises when multiple individual sensors are incorporated into a sensor array. By combining sensors into an array, the overall LOD is reduced compared to LOD from individual sensors. In some cases, this means that low-quality sensors that may not individually meet the needs of a challenging application may provide sufficient quality estimates when combined into an array.</p> <p>A comprehensive study of modularisation in sensors and sensor arrays is conducted. This is motivated by practical limitations of the “cut” function in Bayesian graphical models as implemented by BUGS (Bayesian inference Using Gibbs Sampling) statistical language, where the desired posterior distribution may not be returned. Alternative algorithms, based on Approximate Bayesian computation (ABC), for sensors and sensor arrays are proposed and evaluated.</p> <p>Finally, my collaborators and I introduce an experimental protocol and a Bayesian model for the collection and analysis of complex data produced by potentiometer sensors, motivated by data produced by ‘electronic tongues’. This approach leads to better characterisation of the instrument and better estimates of experimental samples compared to common approaches currently in use.</p>