POINT-PATTERN MATCHING AND PROBABILITY IN ARCHAEOASTRONOMY

Archaeologists and archaeoastronomers are often faced with the problem of deciding whether a specific archaeological artifact is an intentional representation of an asterism on the sky or rather if such a resemblance is purely coincidental. Sorting out this kind of problems is difficult also because of the lack of a statistical evaluation of the probability of the alleged similarity, and, although in the literature one can find a few attempts in this direction, there is no general consensus about a procedure with a rigorous statistical background. The aim of this work is to propose one possible rigorous approach, built on the principles of the Point-Pattern Matching (PPM) technique used in astronomy and in other fields of science, and at the same time on those of the axiomatic theory of probability. We first analyze the similarities and the differences between the PPM in astronomy and archaeoastronomy, showing that a simple least-squares fit can be used to find the best matching between the asterism and the artifact. Then we discuss the interpretation of the residuals of such a fit in other approaches found in the literature, and we propose a different use of these residuals to estimate the matching probability by means of a Monte Carlo simulation. We test our procedure on the well-known case of the three Giza pyramids and their alleged resemblance with the stars of the Orion Belt, and we use the results to stress that the probability found in this way represents just the matching probability that a single random extraction can match a single asterism, while the final probability has to take into account the matching probability with different asterisms by the complete population of similar artifacts. This requires to give a reliable estimation of the number of eligible asterisms <italic>n</italic>_{<italic>A</italic>} and of that of the artifacts <italic>n</italic>_{<italic>G</italic>}. It is in general very difficult to obtain a precise estimation of <italic>n</italic>_{<italic>A</italic>} and <italic>n</italic>_{<italic>G</italic>}, and although one can finally obtain a reasonable conclusion for the case of the Giza pyramids, each case makes a story on its own and it has to be studied individually, with no guarantee of reaching a conclusive result. We therefore conclude that the proposed method is certainly based on a solid statistical background and that it gives a reliable estimation of the matching probability for a single extraction. The definition of the overall probability for any asterism and the complete population of artifacts is also straightforward in case of independent extractions, but the difficulty of providing a reliable estimation of <italic>n</italic>_{<italic>A</italic>} and <italic>n</italic>_{<italic>G</italic>} can hamper the chances of deciding on the issue of intentionality solely on the basis of a probabilistic approach. However, it is likely that this analysis can provide useful results that can be used together with other pieces of evidence.