Dental development has been used to assess whether an individual may be below or above an age that serves as a legal threshold. This study used development of the first and second mandibular molars from a large sample of individuals (N = 2,676) to examine the age threshold for minimum age of criminal responsibility. A bivariate ordered probit model was applied to dental scores following the Moorrees et al. (1963) system, with the addition of a crypt-absent/present stage. Then a 10-fold cross-validation within each of the sexes showed that the bivariate models produce unbiased estimates of age but are heteroskedastic (with increasing spread of the estimates against actual age). To address the age threshold problem, a normal prior centered on the threshold is assumed, and the product of the prior and the likelihood is integrated up to the age threshold and again starting at the age threshold. The ratio of these two integrals is a Bayes factor, which because the prior is symmetric around the threshold, can also be interpreted as the posterior odds that an individual is over versus under the age threshold. It was necessary to assume an unreasonably high standard deviation of age in the prior to achieve posterior odds that were well above "evens." These results indicate that dental developmental evidence from the first and second molars is of limited use in examining the question of whether an individual is below or over the minimum age of criminal responsibility. As the third molar is more variable in its development than the first two molars, the question of dental evidence regarding the age of majority (generally 18 years) remains problematic.

中文翻译：

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先验概率和年龄阈值问题：第一和第二磨牙发育。

牙齿发育已被用来评估一个人是否可能低于或高于作为法定门槛的年龄。本研究使用来自大量个体（N = 2,676）的第一和第二下颌磨牙的发育来检查最低刑事责任年龄的年龄阈值。Moorrees 等人将双变量有序概率模型应用于牙科评分。（1963）系统，增加了一个无地穴/现阶段。然后在每个性别中进行 10 倍的交叉验证表明，双变量模型产生了无偏的年龄估计，但是是异方差的（估计与实际年龄的分布越来越大）。为了解决年龄阈值问题，假设以阈值为中心的正常先验，并且先验和似然的乘积被整合到年龄阈值并再次从年龄阈值开始。这两个积分的比率是贝叶斯因子，因为先验在阈值周围对称，也可以解释为个体超过年龄阈值与低于年龄阈值的后验几率。有必要假设之前的年龄标准偏差不合理，以实现远高于“偶数”的后验赔率。这些结果表明，来自第一和第二磨牙的牙齿发育证据在检查个人是否低于或超过最低刑事责任年龄的问题时用途有限。由于第三磨牙的发育比前两磨牙更易变化，