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 (also known as kernel density estimation or summed probability distribution) in wide currency in archaeoastronomy, and introduces the largely unutilised maximum likelihood (ML) method, which has popularity in other academic fields. An analysis of both methods’ accuracy and precision is done, using a scenario with a single target, and the resulting equations can be used to estimate the minimum number of surveyed structures required to ensure a high-precision statistical inference. Two fundamental observations emerge: firstly, that although both approaches are quite accurate, the ML approach is considerably more precise than the curvigram approach; and secondly, 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 are discussed.