Exploratory analysis of elements in incineration bottom ash with numerous values below the detection limit using selected substitution methods

Abstract

This study investigates the influence of substitution methods for left-censored values on exploratory data analysis (EDA) of the incineration bottom ash (IBA). IBA, a by-product of municipal solid waste incineration, contains a wide range of economically valuable elements, many of which are frequently reported below detection limits due to analytical constraints. The study aims to evaluate the impact of different substitution methods on descriptive statistics, correlation analysis, and regression modeling outcomes.Four widely used substitution approaches were compared: (i) replacement with half of the detection limit, (ii) random values from a uniform distribution, (iii) robust regression on order statistics (ROS), and (iv) tobit regression (applied in both small and large variants). Five trace elements with different proportions of censored values (13–67%) were analyzed using a dataset of 52 weekly samples collected throughout 2021 at the Krakow Thermal Waste Treatment Plant. The impact of each method was assessed using descriptive statistics, Pearson correlation matrices, and multiple linear regression models. Additional analyses incorporated 11 auxiliary elements to enhance correlation and regression model robustness. The results show that substitution methods significantly affect data distributions, particularly for elements with high censoring rates. ROS and tobit regression produced more stable statistical outputs and narrower histograms compared to simpler methods. Furthermore, regression model performance improved with substitution compared to raw data, with tobit methods demonstrating the highest accuracy for elements with strong inter-element correlations. The findings provide methodological guidance for reliable data handling in IBA analysis and recovery assessments.