## 1 Introduction  
The limit of detection (_LOD_) of a given element/compound is a key parameter in analytical chemistry, representing the lower concentration of a given element that an analytical technique can detect with a reasonable certainty. The limit of detection depends on the matrix in which the analyte is present but also on the specific experimental setup used for the analysis. For this reason, the _LOD_ is often used to compare the performances of different techniques, or variations of the same technique, in terms of their analytical capability. In this paper, we will discuss the issues related to the calculation of the _LOD_s in applications of the Laser-Induced Breakdown Spectroscopy (_LIBS_) technique [1]. _LIBS_ is a powerful spectroscopic technique which is based on the analysis of the light emitted by a laser-induced plasma (LIP). One of its most interesting features is its ability to work on untreated samples, which makes it particularly suited for in situ analysis [2; 3; 4; 5]. In the laboratory applications of _LIBS_, the possibility of working without solvents or gases is also appreciated, as well as the short time needed for the analysis and the simplicity of the experimental apparatus [6; 7; 8; 9; 10]. However, the same characteristics above described make sometimes problematic the building of _LIBS_ calibration curves of good quality. _LIBS_'s unique feature of not needing to prepare a sample has as a counterpart the occurrence of strong matrix effects (the signal of the analyte depends on the composition of the sample) [11], which may negatively affect its sensitivity, as well as the trueness of the _LIBS_ analytical results. According to the current narrative, _LIBS_ is characterized by high _LOD_s for many of the elements of interest (typically in the range of parts per million or higher). The _LOD_ of a given analyte is usually derived from a calibration curve, which reports the measured signal as a function of the analyte concentration in suitable samples of known composition (standards) [12; 13]. To reduce matrix effects, it is necessary to build calibration curves using standards of known composition, having the same matrix as the samples to be analyzed. Depending on the application, the availability of suitable matrix-matched standards may be limited. It is not uncommon to see _LIBS_ calibration curves built with less than 10 samples, sometimes characterized by concentrations of the analyte that are very different from the concentrations of the unknown sample. In some cases, the change in the concentration of the analyte among the standards may produce non-linearities in the calibration curve [14]. Finding suitable blanks (reference samples where the analyte is absent) with the same matrix of the samples to be analyzed can be problematic, too. Besides that, it must be stressed that the growing use of multivariate analytical tools [15] for the quantitative determination of samples' composition calls for a reconsideration of the formulas traditionally used for the calculation of the _LOD_s [16]. A similar effort is needed for extending the calculation of _LOD_s in the framework of standardised/calibration-free analytical approaches [17; 18]. Despite the abundant literature on the topic [14; 16; 19; 20; 21; 22; 23; 24], _LOD_s in Laser-Induced Breakdown Spectroscopy (_LIBS_) are often miscalculated [1], leading to over-optimistic estimations of the analytic capabilities of the technique. Moreover, as already mentioned, the calculation of the _LOD_ is usually limited to the case of univariate analysis, after the construction of a suitable calibration curve [14]. At the best of our knowledge, the problem of calculating the elemental _LOD_s in multivariate analysis has not been previously discussed within the framework of _LIBS_ analysis. The issues associated with the building of a calibration curve in _LIBS_ have been extensively discussed in the past [14; 25; 26]; as we have seen, the number of available standards is usually small, and sometimes, it can be hard to obtain a suitable blank.