A bootstrapping-based statistical procedure for multivariate calibration of sensor arrays

Abstract

One of the major challenges of calibrating a sensor array lies in the typically large samples required to estimate a high-quality multivariate calibration (MC) model, which functionally relates the array responses to the target analyte concentrations. For the efficient calibration of sensor arrays, this work develops a multi-stage procedure to guide the sampling in a sequential manner: Preliminary experiments are performed in the initial stage to collect some data; in each subsequent stage, information is derived from all the data collected from the previous stages and is employed to obtain the optimal design of the current-stage experiments. The design optimization at each stage seeks to optimize the quality of the MC model with a given sample size, and is performed based on the new statistical inference method, which quantifies the dependence of the MC model quality (the uncertainty/variability of the model estimates) upon the design of experiments. The proposed statistical inference takes advantages of both forward and inverse calibration modeling in the literature, is able to accommodate nonlinear sensor arrays, and utilizes the bootstrapping resampling method to handle the statistical inference issues that cannot be adequately addressed by existing methods. Substantial simulation studies have been performed to demonstrate the efficiency of the multi-stage procedure over the traditional once-and-for-all sampling.