## 1 Introduction  
One fundamental task of physical anthropologists is that of reconstructing the biological identity of human remains from the incomplete information provided by the skeleton or parts of it [1]. Available methods to establish the sex from the skeleton include protocols based on the visual inspection of morphological traits differing between males and females or quantitative methods often relying on linear measurements used to discriminate between sexes by means of specific algorithms. Such methods have been successfully applied to attribute sex from several different elements within the human skeleton (i.e., femur [2], humerus [3], pelvis [4], teeth [5], talus and calcaneus [6], upper limb [7], and the metacarpal bones [8]). To achieve the highest accuracy, the analysis of the most dimorphic skeletal regions is desirable, such as the coxal bone and other post-cranial elements [9]; when these are not available, another useful source of information is found in the cranium [1, 10]. Some important sources of information regarding sexual dimorphism in the human cranium reside in the occipital protuberance, the mastoid process, and the glabellar region [11, 12], among others. To provide a standardised approach, potentially less prone to individual bias, it is essential to refine the quantitative methodologies currently available, defining their limitations and establishing the expected performance achievable. In traditional anthropology, a common procedure for estimating sex from the cranium uses a scoring system of morphological traits evaluated visually [11; 13]. Despite being a straightforward and practical method, the success of these traditional approaches depends directly on the experience of the observer, and errors due to subjectivity tend to be higher than in quantitative methods [14; 15]. To overcome such obstacles, the use of quantitative measurements and algorithm-based methods have received considerable attention in the last decades. Previous studies have highlighted the challenges of extrapolating sex information from cranial morphology and variability. The cranium, by its own nature, is a sum of multivariate factors, such as ontogeny, ageing, diet, genetics, epigenetics, and pathologies [16], and it is, therefore, difficult to isolate sex-related information from those confounding factors. Another great challenge comes from the relationship between morphology and ancestry. For example, some studies define small and gracile skulls as females, while the attributes of a large size and robust appearance are associated with males [12; 17; 18]. These differences cannot be applied to humans _tout court_ because the association between the robust/gracile appearance is never perfectly binary: depending on the population, it is possible to find small males and robust females and overlapping morphological variability between sexes is common in modern humans [16], as it is the general overlapping among populations [19]. These circumstances led several authors to focus their studies on individual populations [20; 21; 22; 23; 24], which produce results that can hardly be extrapolated to the whole human variability. The last few decades have witnessed a remarkable development in quantitative methods such as geometric morphometrics and machine learning, which have been successfully applied to Biological and Forensic Anthropology [25; 26; 27]. Those methods have triggered a tremendous growth in the search for new quantitative solutions to the problem of estimating sex from the human skeleton [19; 28; 29; 30; 31]. In particular, machine learning (ML) provides a flexible approach to estimating attributes such as sex from skeletal measurements--an approach adopted more and more in the field [25; 26; 27; 28; 29; 30; 31; 32]. All too often, though, algorithm-based studies addressing sex estimation from the human cranium suffer from a lack of \"generalisability\" and the absence of a solid testing framework.