This is the conclusion from an eighteen-page paper, “Carbon Dating of the Shroud of Turin: Partially Labelled Regressors and the Design of Experiments,” co-authored by Marco Riani, Anthony C. Atkinson, Giulio Fanti and Fabio Crosilla and recently published on the website of the London School of Economics:

Due to the heterogeneity of the data and the evidence of a strong linear trend the twelve measurements of the age of the TS [=Turin Shroud] cannot be considered as repeated measurements of a single unknown quantity. The statement of Damon, Donahue, Gore, and eighteen others (1989) that “The results provide conclusive evidence that the linen of the Shroud of Turin is mediaeval” needs to be reconsidered in the light of the evidence produced by our use of robust statistical techniques.

This is a big deal. Robust statistical techniques are a big deal. This is completely consistent with the evidence of mending proposed by Joe Marino and Sue Benford about ten years after the carbon dating in 1988. Ray Rogers, a chemist at the Los Alamos National Laboratory, who accepted the carbon dating, sought to disprove what he considered to be Marino’s and Benford’s crazy explanation from what he called the “lunatic fringe.” What Rogers discovered was that the crazy idea seemed to be right. He concluded that the sample used for carbon dating was not representative of the cloth. It was chemically different. Moreover, one of the chemical differences, the amount of vanillin, provided a new clue about the cloth’s age. Samples from the main part of the cloth, unlike the
carbon 14 sample area, did not contain any vanillin. If the shroud was only as old as the radiocarbon date, it would have plentiful vanillin.  The Shroud was at least twice as old. In fact, it might be 2000 years old. After a lengthy peer review process, his findings that the carbon dating was wholly invalid were published in the scientific journal Thermochimica
Acta.

Rogers’ published work showing that the carbon dating is invalid has been confirmed by John L Brown, a forensic materials specialist at Georgia Tech in Atlanta, Georgia and by Robert Villarreal and a team of nine scientists at the Los Alamos National Laboratory in New Mexico.

This statistical analysis is completely consistent, it seems.