Journal of Skyscape Archaeology, Vol 3, No 1 (2017)

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

Fabio Silva

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.

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DOI: 10.1558/jsa.31958

References


Aveni, A. F., ed., 1982. Archaeoastronomy in the New World: American Primitive Astronomy. Cambridge: Cambridge University Press.


Barcelo, J. A. and I. Bogdanovic, eds, 2015. Mathematics and Archaeology. New York: CRC Press.


Belmonte Avilés, J. A., 2006. “De la arqueoastronomía a la astronomía cultural”. Boletín de la SEA 15: 23–40.


Bevan, A. and M. Lake, eds, 2013. Computational Approaches to Archaeological Spaces. Walnut Creek, CA: Left Coast Press.


Clapham, C. and J. Nicholson, 2014. The Concise Oxford Dictionary of Mathematics (5th edition). Oxford: Oxford University Press.


Cummings, V., A. Jones and A. Watson, 2002. “Divided Places: Phenomenology and Asymmetry in the Monuments of the Black Mountains, Southeast Wales”. Cambridge Archaeological Journal 12 (1): 57–70. https://doi.org/10.1017/S0959774302000033


Edwards, A. W. F., 1992. Likelihood (expanded edition). Baltimore: The Johns Hopkins University Press.


Fisher, R. A., 1922. “On the Mathematical Foundations of Theoretical Statistics”. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 222: 309–368. https://doi.org/10.1098/rsta.1922.0009


Fishman, G. S., 1995. Monte Carlo: Concepts, Algorithms, and Applications. New York: Springer.


Freeman, P. R. and W. Elmore, 1979. “Test for the Significance of Astronomical Alignments”. Archaeoastronomy 1 (Supplement to the Journal for the History for Astronomy 10): S86–S96.


González-García, A. C. and I. Šprajc, 2016. “Astronomical Significance of Architectural Orientations in the Maya Lowlands: A Statistical Approach”. Journal of Archaeological Science: Reports 9: 191–202. https://doi.org/10.1016/j.jasrep.2016.07.020


Heggie, D. C., 1982. Archaeoastronomy in the Old World. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511898310


Henty, L., 2014. “The Archaeoastronomy of Tomnaverie Recumbent Stone Circle: A Comparison of Methodologies”. Papers from the Institute of Archaeology 24 (1): Art. 15 [online]. https://doi.org/10.5334/pia.464


Hoare, P. G. and C. S. Sweet, 2000. “The Orientation of Early Medieval Churches in England”. Journal of Historical Geography 26(2): 162–173. https://doi.org/10.1006/jhge.2000.0210


Hoskin, M., 2001. Tombs, Temples and Their Orientations: A New Perspective on Mediterranean Prehistory. Bognor Regis, UK: Ocarina Books.


Hoskin, M., 2002. “Studies in Iberian Archaeoastronomy: (9) An Overview”. Archaeoastronomy 27 (supplement to Journal for the History of Astronomy 33): S75–S82.


Lake, M. W., 2014. “Trends in Archaeological Simulation”. Journal of Archaeological Method and Theory 21 (2): 258–287. https://doi.org/10.1007/s10816-013-9188-1


Magli, G., 2016. Archaeoastronomy: Introduction to the Science of Stars and Stones. New York and London: Springer. https://doi.org/10.1007/978-3-319-22882-2


McLachlan, G. J. and D. Peel, 2000. Finite Mixture Models. New York: John Wiley & Sons. https://doi.org/10.1002/0471721182


Pimenta, F., L. Tirapicos and A. Smith, 2009. “A Bayesian Approach to the Orientations of Central Alentejo Megalithic Enclosures”. Archaeoastronomy 22: 1–20.


Pimenta, F., N. Ribeiro, A. Smith, A. Joaquinito, S. Pereira and L. Tirapicos, 2015. “Open Air Rock Art between Alva and Ceira Rivers: A Voyage through Mining, Trading, Transhumance Routes and the Orientation in the Landscape”. In SEAC 2011: Stars and Stones: Vogages in Archaeoastronomy and Cultural Astronomy, edited by F. Pimenta, N. Ribeiro, F. Silva, N. Campion, A. Joaquinito and L. Tirapicos. British Archaeological Reports, International Series 2720: 220–230. Oxford: Archaeopress.


Prendergast, F., 2011. Linked Landscapes: Spatial, Archaeoastronomical and Social Network Analysis of the Irish Passage Tomb Tradition. PhD Diss., University College Dublin.


R Project. 2016. “The R Project for Statistical Computing.” [online]. Accessed October 2016, https://www.R-project.org


Ruggles, C. L. N., 1981. “A Critical Examination of the Megalithic Lunar Observatories”. In Astronomy and Society in Britain during the Period 4000–1500 BC, edited by C. L. N. Ruggles and A. W. R. Whittle, 153–209. British Archaeological Reports, British Series 88. Oxford: British Archaeological Reports.


Ruggles, C. L. N., 1999. Astronomy in Prehistoric Britain and Ireland. New Haven, CT: Yale University Press.


Ruggles C. L. N., ed., 2015. The Handbook of Archaeoastronomy and Ethnoastronomy, 3 vols. New York: Springer.


Shennan, S., S. S. Downey, A. Timpson, K. Edinborough, S. Colledge, T. Kerig, K. Manning and M. G. Thomas, 2013. “Regional Population Collapse Followed Initial Agriculture Booms in Mid-Holocene Europe”. Nature Communications 4: 2486. https://doi.org/10.1038/ncomms3486


Silva, F., 2015. “The View from Within: A ‘Time-Space-Action’ Approach to Megalithism
in Central Portugal”. In Skyscapes: The Role and Importance of the Sky in Archaeology, edited by F. Silva and N. Campion, 120–139. Oxford: Oxbow Books.


Silva, F. and F. Pimenta, 2012. “The Crossover of the Sun and the Moon”. Journal for the History of Astronomy 43 (2): 191–208. https://doi.org/10.1177/002182861204300204


Silva, F., C. J. Stevens, A. Weisskopf, C. Castillo, L. Qin, A. Bevan and D. Q. Fuller, 2015. “Modelling the Geographical Origin of Rice Cultivation in Asia Using the Rice Archaeological Database”. PLoS ONE 10 (9): e0137024. https://doi.org/10.1371/journal.pone.0137024


Silverman, B. W., 1986. Density Estimation for Statistics and Data Analysis. London: Chapman & Hall / CRC. https://doi.org/10.1007/978-1-4899-3324-9


Sims, L., 2009. “Entering, and Returning From, the Underworld: Reconstituting Silbury Hill by Combining a Quantified Landscape Phenomenology with Archaeoastronomy”. Journal of the Royal Anthropological Institute 15 (2): 386–408. https://doi.org/10.1111/j.1467-9655.2009.01559.x


Šprajc, I., 2015. “Astronomical Correlates of Architecture and Landscape in Mesoamerica”. In The Handbook of Archaeoastronomy and Ethnoastronomy, edited by C. L. N. Ruggles, 1: 715–728. New York: Springer. https://doi.org/10.1007/978-1-4614-6141-8_56


Stevens, C. J. and D. Q. Fuller, 2012. “Did Neolithic Farming Fail? The Case for a Bronze Age Agricultural Revolution in the British Isles”. Antiquity 86 (333): 707–722. https://doi.org/10.1017/S0003598X00047864


Taylor, J. R., 1997. An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. Sausalito, CA: University Science Books.


Thom, A., 1955. Megalithic sites in Britain. Oxford: Oxford University Press.


Thom, A., 1967. Megalithic Lunar Observatories. Oxford: Oxford University Press.


Tilley, C., 1997. A Phenomenology of Landscape: Places, Paths and Monuments. London: Bloomsbury Academic.


Williams, A., 2012. “The Use of Summed Radiocarbon Probability Distributions in Archaeology: A Review of Methods”. Journal of Archaeological Science 39: 578–589. https://doi.org/10.1016/j.jas.2011.07.014


Zahid, H. J., E. Robinson and R. L. Kelly, 2015. “Agriculture, Population Growth, and Statistical Analysis of the Radiocarbon Record”. Proceedings of the National Academy of Sciences 113 (4): 931–935. https://doi.org/10.1073/pnas.1517650112


Zar, J. H., 1984. Biostatistical Analysis. Englewood Cliffs, NJ: Prentice Hall.


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