The multivariate regression model is considered with p regressors. A latent vector with p binary entries serves to identify one of two types of regression coef®cients: those close to 0 and those not. Specializing our general distributional setting to the linear model with Gaussian errors and using natural conjugate prior distributions, we derive the marginal posterior distribution of the binary latent vector. Fast algorithms aid its direct computation, and in high dimensions these are supplemented by a Markov chain Monte Carlo approach to sampling from the known posterior distribution. Problems with hundreds of regressor variables become quite feasible. We give a simple method of assigning the hyperparameters of the prior distribution. The posterior predictive distribution is derived and the approach illustrated on compositional analysis of data involving three sugars with 160 near infra-red absorbances as regressors.

No abstract

Transferring calibrations between near infrared instruments is not always straightforward, even when the instruments are nominally the same. Problems can include both wavelength shifts and differences in absorbance response between instruments. This review describes a number of chemometric methods that have been developed to aid calibration transfer. The approaches are classified under three headings: making robust calibrations, adjusting calibrations and adjusting spectra. Calibrations can be made more robust, and more transferable, by the appropriate use of spectral pre-treatments that reduce between-instrument variability. Robust calibrations can also be made by pooling data from several instruments when calibrating. Calibrations can be adjusted using skew and bias corrections estimated from a modest number of samples with known reference values. Under the third heading, adjusting spectra, come methods such as piecewise direct standardisation and the patented method of Shenk and Westerhaus that use spectral information from samples measured on two instruments to match the spectral response of the instruments.

The potential of near-infrared spectroscopy to measure fat, total protein, and lactose contents of unhomogenized milk was studied for use in dairy management, as a new tool for on-line milk analysis in the process of milking. Influence of the spectral region, sample thickness, and spectral data treatment on the accuracy of determination was investigated. Transmittance spectra of 258 milk samples, collected at different stages of the milking process, were obtained with a spectrophotometer (NIRSystems 6500; FOSS-NIRSystems, Silver Spring, MD) in the wavelength range from 400 to 2500 nm with sample thicknesses of 1 mm, 4 mm, and 10 mm. The spectral region and sample thickness were found to be significant factors for milk fat and total protein determination but not the lactose determination. The best accuracy was obtained with the 1100 to 2400 nm region, 1-mm sample thickness, and the first derivative data transformation. For the spectral region from 700 to 1100 nm, close accuracy was obtained for fat with a 10-mm sample and for total protein with a 1-mm sample thickness. The sample thickness did not change significantly the accuracy of lactose determination. Different treatments of spectral data did not improve the calibrations for fat and protein. For the region from 700 to 1100 nm, where inexpensive on-line sensors could be used, the highest positive coefficients for fat were at 930, 968, 990, 1026, 1076, and 1092 nm; for lactose were at 734, 750, 786, 812, 908, 974, 982, and 1064 nm; and for total protein were at 776, 880, 902, 952, and 1034 nm.

In this study, we investigate the use of convolutional neural networks (CNN) for near infrared (NIR) calibration. We propose a unified CNN structure that can be used for general multivariate regression purpose. The comparison between the CNN method and the partial least squares regression (PLSR) method was done on three different NIR datasets of spectra and lab reference values. Datasets are from different sources and contain 6998, 1000 and 415 training and 618, 597 and 108 validation samples, respectively. Results indicated that compared to the PLSR models, the CNN models are more accurate and less noisy. The convolutional layer in the CNN model can automatically find the suitable spectral preprocessing filter on the dataset, which significantly saves efforts in training the model.