Orthogonal Bayesian calibration of XRF data for geological applications João M.F. Lopes, Daljeet S. Gahle, Alessandro Migliori, Kalliopi Kanaki Chemometrics and Intelligent Laboratory Systems, 2026 X-ray fluorescence (XRF) calibration for quantitative analysis is typically performed using certified reference materials (CRMs), where the relationship between the concentration of an element and the net area of its peak in the spectrum is assumed, after properly applying corrections for possible matrix effects, to be linear. The calibration is often obtained by Ordinary Least Squares (OLS) by minimizing the vertical distance between regression line and data points taking into account the experimental uncertainty. However, uncertainties in CRM-certified concentrations are often neglected, potentially leading to underestimated errors in the calibration model. In this work, a Bayesian approach is employed to obtain calibration curves by minimizing the orthogonal distance, taking into account both experimental and certified uncertainties. Twenty-four geological, soil, and sediment CRMs were analyzed using an energy-dispersive XRF spectrometer, and the resulting spectra were employed for constructed calibration curves for eight oxides and seven elements. The model parameters were estimated via maximum a posteriori (MAP) optimization and the posterior was evaluated by a Gibbs sampling algorithm in an orthogonal parameter space. A principal components analysis (PCA) was implemented for this coordinate transformation to remove the linear correlation. Validation against independent samples shows that the Bayesian approach demonstrates that the ordinary least-squares regression calibration curve deviates from the orthogonal Bayesian MAP curve by up to one standard deviation, particularly for elements with higher reference material variability and lower concentrations. Mean absolute errors and root mean squared errors indicate improved predictive performance for major oxides, while trace elements exhibit variable agreement due to instrumental and sample-specific factors. The results demonstrate that orthogonal Bayesian XRF calibration can enhance both accuracy and uncertainty quantification in multi-elemental analyses. • Novel Bayesian calibration for XRF accounts for uncertainties in both net peak area and CRM-certified concentrations. • Significant discrepancies between Bayesian and OLS regressions are observed where CRM uncertainties are high. • MCMC sampling provides full posterior distributions for parameters, enabling credible intervals and LOD estimates.
Archaeometric study of archaeological pottery from the Ventarron-Collud Archaeological Complex-Lambayeque, Peru: A multi-technique approach using EDXRF, FTIR, XRD, gamma … CSA Desanti, CR Appoloni, RA Ikeoka, MMA Suner, M Fagundes, ... RADIATION PHYSICS AND CHEMISTRY 246 , 2026 2026.0
Orthogonal Bayesian calibration of XRF data for geological applications JMF Lopes, DS Gahle, A Migliori, K Kanaki Chemometrics and Intelligent Laboratory Systems 272, 105662 , 2026 2026.0
Archaeometric study of archaeological pottery from the Ventarrón-Collud Complex–Lambayeque, Peru: A multi-technique approach using EDXRF, FTIR, XRD, Gamma Spectrometry, and … CSA Desanti, CR Appoloni, RA Ikeoka, MMA Suñer, M Fagundes, ... Radiation Physics and Chemistry, 113926 , 2026 2026.0
Be-7 measurement in an urban area using a low-resolution gamma spectrometer AZ Neto, RO Bastos, BW Borsoi, RA Ikeoka, FL Melquiades, JMF Lopes, ... Applied Radiation and Isotopes, 112529 , 2026 2026.0
Calibration transfer from HPGe to NaI (Tl) detectors for radionuclides quantification JMF Lopes, FL Melquiades, RO Bastos, AZ Neto, AC Andrello Journal of Environmental Radioactivity 293, 107885 , 2026 2026.0 Citations: 1
7Be measurements in agricultural soil using a low resolution NaI (Tl) detector BW Borsoi, RO Bastos, AZ Neto, DG Rodríguez, JMF Lopes, AC Andrello, ... Radiation Measurements, 107591 , 2025 2025.0 Citations: 1
Analysis of the first rain after a prolonged drought in southern Brazil using TXRF LM Birelo, AM de França, JMF Lopes, AC Andrello, EI Jussiani Radiation Physics and Chemistry 237, 113117 , 2025 2025.0 Citations: 1
XRF and gamma-ray data fusion for predicting key soil fertility attributes JV Ribeiro, JMF Lopes, AC Andrello, JF de Oliveira, GMC Barbosa, ... Radiation Physics and Chemistry 234, 112750 , 2025 2025.0 Citations: 3
Spectral deconvolution approach for beryllium-7 detection: Evaluating soil redistribution with nai (tl) detectors JMF Lopes, FL Melquiades, RO Bastos, JF de Oliveira, GMC Barbosa, ... Radiation Physics and Chemistry 225, 112153 , 2024 2024.0 Citations: 6
Gamma-rays and X-rays spectrometries applied to evaluate soil redistribution JMF Lopes, JV Ribeiro, AC Andrello, FL Melquiades Journal of Environmental Radioactivity 278, 107479 , 2024 2024.0 Citations: 1
Análise elementar por TXRF de amostras de saliva de pacientes com peri-implantite JMF Lopes 2024.0
Espectroscopia de Impedância: Uma Visão Elétrica e Mecânica TC de Curso Universidade Estadual de Maringá , 2020 2020.0
7Be measurements in agricultural soil using a low resolution detector BW Borsoi, RO Bastos, AZ Neto, DG Rodríguez, JM Lopes, AC Andrello, ... Available at SSRN 5231021 , 0
Elemental analysis of saliva samples affected by peri-implant diseases using X-ray fluorescence JMF Lopes, AC Andrello, IJV Netto
Análise Exploratória de Solo por Espectrometria Gama para Identificaçao de Berılio-7 JMF Lopes, AC Andrello, FL Melquiades
PIÕES, SPINERS E GIROSCÓPIOS, BRINQUEDOS E APLICAÇÕES FÍSICAS JMF Lopes–UEM, LM Azevedo–UEM, LF Demétrio–UEM, ...
CÂMARA DE NUVENS: UMA PROPOSTA EXPERIMENTAL DIDÁTICA LM da Silva, PH Pinto, JMF Lopes, LF Demétrio, FT Karia
MOST CITED SCHOLAR PUBLICATIONS
Spectral deconvolution approach for beryllium-7 detection: Evaluating soil redistribution with nai (tl) detectors JMF Lopes, FL Melquiades, RO Bastos, JF de Oliveira, GMC Barbosa, ... Radiation Physics and Chemistry 225, 112153 , 2024 2024.0 Citations: 6
XRF and gamma-ray data fusion for predicting key soil fertility attributes JV Ribeiro, JMF Lopes, AC Andrello, JF de Oliveira, GMC Barbosa, ... Radiation Physics and Chemistry 234, 112750 , 2025 2025.0 Citations: 3
Calibration transfer from HPGe to NaI (Tl) detectors for radionuclides quantification JMF Lopes, FL Melquiades, RO Bastos, AZ Neto, AC Andrello Journal of Environmental Radioactivity 293, 107885 , 2026 2026.0 Citations: 1
7Be measurements in agricultural soil using a low resolution NaI (Tl) detector BW Borsoi, RO Bastos, AZ Neto, DG Rodríguez, JMF Lopes, AC Andrello, ... Radiation Measurements, 107591 , 2025 2025.0 Citations: 1
Analysis of the first rain after a prolonged drought in southern Brazil using TXRF LM Birelo, AM de França, JMF Lopes, AC Andrello, EI Jussiani Radiation Physics and Chemistry 237, 113117 , 2025 2025.0 Citations: 1
Gamma-rays and X-rays spectrometries applied to evaluate soil redistribution JMF Lopes, JV Ribeiro, AC Andrello, FL Melquiades Journal of Environmental Radioactivity 278, 107479 , 2024 2024.0 Citations: 1
Archaeometric study of archaeological pottery from the Ventarron-Collud Archaeological Complex-Lambayeque, Peru: A multi-technique approach using EDXRF, FTIR, XRD, gamma … CSA Desanti, CR Appoloni, RA Ikeoka, MMA Suner, M Fagundes, ... RADIATION PHYSICS AND CHEMISTRY 246 , 2026 2026.0
Orthogonal Bayesian calibration of XRF data for geological applications JMF Lopes, DS Gahle, A Migliori, K Kanaki Chemometrics and Intelligent Laboratory Systems 272, 105662 , 2026 2026.0
Archaeometric study of archaeological pottery from the Ventarrón-Collud Complex–Lambayeque, Peru: A multi-technique approach using EDXRF, FTIR, XRD, Gamma Spectrometry, and … CSA Desanti, CR Appoloni, RA Ikeoka, MMA Suñer, M Fagundes, ... Radiation Physics and Chemistry, 113926 , 2026 2026.0
Be-7 measurement in an urban area using a low-resolution gamma spectrometer AZ Neto, RO Bastos, BW Borsoi, RA Ikeoka, FL Melquiades, JMF Lopes, ... Applied Radiation and Isotopes, 112529 , 2026 2026.0
Análise elementar por TXRF de amostras de saliva de pacientes com peri-implantite JMF Lopes 2024.0
Espectroscopia de Impedância: Uma Visão Elétrica e Mecânica TC de Curso Universidade Estadual de Maringá , 2020 2020.0
7Be measurements in agricultural soil using a low resolution detector BW Borsoi, RO Bastos, AZ Neto, DG Rodríguez, JM Lopes, AC Andrello, ... Available at SSRN 5231021 , 0
Elemental analysis of saliva samples affected by peri-implant diseases using X-ray fluorescence JMF Lopes, AC Andrello, IJV Netto
Análise Exploratória de Solo por Espectrometria Gama para Identificaçao de Berılio-7 JMF Lopes, AC Andrello, FL Melquiades
PIÕES, SPINERS E GIROSCÓPIOS, BRINQUEDOS E APLICAÇÕES FÍSICAS JMF Lopes–UEM, LM Azevedo–UEM, LF Demétrio–UEM, ...
CÂMARA DE NUVENS: UMA PROPOSTA EXPERIMENTAL DIDÁTICA LM da Silva, PH Pinto, JMF Lopes, LF Demétrio, FT Karia
