Inferring Alignments I: Exploring the Accuracy and Precision of Two Statistical Approaches

Abstract

Using computer simulations, this paper explores and quantifies the accuracy and precision of two approaches to the statistical inference of the most-likely targets of a set of structural orientations. It discusses the curvigram method of wide currency in archaeoastronomy (also known as Kernel Density Estimation or Summed Probability Densities), and introduces the largely unused maximum likelihood method, that is quite popular in other fields. The analysis of their accuracy and precision is done for a scenario with a single target, from which resulted equations that can be used to estimate the minimum number of surveyed structures to ensure a high-precision statistical inference. Two fundamental observations are also made: that, although both approaches are quite accurate, the maximum likelihood approach is considerably more precise than the curvigram approach; and that underestimating measurement uncertainty severely undermines the precision of the curvigram method. Finally, the implications of these observations for past, present and future archaeoastronomical research, is discussed.