An ad-hoc modified Likelihood Function Applied to Optimization of Data Analysis in Atomic Spectroscopy

TL;DR

This paper introduces a modified likelihood function tailored for atomic spectroscopy data analysis, improving accuracy and precision over traditional least squares methods through a new statistical approach evaluated via simulations.

Contribution

It presents a novel ad-hoc likelihood function modification that accounts for specific statistical properties of spectral data, enhancing analysis accuracy.

Findings

Improved accuracy and precision over least squares methods.

Achieved an order of magnitude better parameter estimation.

Potential for better detection and quantitation limits in spectral analysis.

Abstract

In this paper we propose an ad-hoc construction of the Likelihood Function, in order to develop a data analysis procedure, to be applied in atomic and nuclear spectral analysis. The classical Likelihood Function was modified taking into account the underlying statistics of the phenomena studied, by the inspection of the residues of the fitting, which should behave with specific statistical properties. This new formulation was analytically developed, but the sought parameter should be evaluated numerically, since it cannot be obtained as a function of each one of the independent variables. For this simple numerical evaluation, along with the acquired data, we also should process many sets of external data, with specific properties - This new data should be uncorrelated with the acquired signal. The developed statistical method was evaluated using computer simulated spectra. The numerical estimations of the calculated parameter applying this method, indicate an improvement over accuracy and precision, being one order of magnitude better than those produced by least squares approaches. We still have to evaluate the improvement produced by this method over Detection and Quantitation Limits, in TXRF spectral analysis.