Regression analysis with partially labelled regressors: carbon dating of the Shroud of Turin

Abstract

The twelve results from the 1988 radio carbon dating of the Shroud of Turin show surprising heterogeneity. We try to explain this lack of homogeneity by regression on spatial coordinates. However, although the locations of the samples sent to the three laboratories involved are known, the locations of the 12 subsamples within these samples are not. We consider all 387,072 plausible spatial allocations and analyse the resulting distributions of statistics. Plots of robust regression residuals from the forward search indicate that some sets of allocations are implausible. We establish the existence of a trend in the results and suggest how better experimental design would have enabled stronger conclusions to have been drawn from this multi-centre experiment

Monte Carlo method applied to the mechanical dating of the Turin Shroud

“…The mechanical dating method has been applied to single flax fibers coming from the backside of the TS, picked up during the 1978 campaign in correspondence of the buttocks area [11,12] in order to obtain an age of the Relic, alternative to that furnished by the 1988 radiocarbon dating [4] that showed a questionable result [8].…”

“…In 1988 the TS has been radiocarbon dated in medieval age [4]. The result has been widely criticized for many reasons [5,6,7,8], but no alternative dating has been proposed. For this, alternative dating methods have recently been suggested [9] both of chemical (based on Raman and FT-IT spectrometry) and of mechanical type [10].…”

Introductory Paper: Scientific Results on the Turin Shroud Coming from a Paduan University Research Project

“…In 1988, the TS was radiocarbon-dated to 1260-1390 A.D. [4], but the results are questionable [5,6]. As the process that formed the body image is still unknown, the dating method cannot be rigorously applied because the environment in which the object under analysis was conserved must be known from a contamination point of view.…”

“…In 1988 the TS has been radiocarbon dated [4] to 1260-1390 A.D. at 95% confidence level with evident statistical errors [6] that made this result doubtful. Perhaps the most evident demonstration that these results are not coherent with the assigned uncertainty of ±65 years at 95% confidence level is the following: the twelve published results are in a much wider range of 204 years (1155-1359 A.D.).…”

“…Once ascertained that the 1988-radiocarbon result is not reliable, at least from a statistical point of view [6,29,330], alternative dating methods are necessary to give information on the age of the TS fabric. Two chemical methods based on FT-IR and Raman spectrometry have been proposed to date the TS [51] and the results of these methods are here presented by P. Baraldi and A. Tinti in this issue.…”