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Brief communication A probabilistic approach to age estimation from infracranial sequences of maturation.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 142:655–664 (2010)
Brief Communication: A Probabilistic Approach to Age
Estimation From Infracranial Sequences of Maturation
Hélène Coqueugniot,1,2 Timothy D. Weaver,2,3* and Francis Houët1
1
UMR 5199—PACEA, Laboratoire d’Anthropologie des Populations du Passé, Université Bordeaux 1,
avenue des Facultés, 33405 Talence cedex, France
2
Department of Human Evolution, Max Planck Institute for Evolutionary Anthropology, Deutscher Platz 6,
D-04103 Leipzig, Germany
3
Department of Anthropology, University of California, Davis, CA 95616
KEY WORDS
Bayesian statistics; osteological collections; postcranium; skeletal maturation
ABSTRACT
Infracranial sequences of maturation are
commonly used to estimate the age at death of nonadult
specimens found in archaeological, paleoanthropological,
or forensic contexts. Typically, an age assessment is made
by comparing the degree of long-bone epiphyseal fusion in
the target specimen to the age ranges for different stages
of fusion in a reference skeletal collection. While useful as
a first approximation, this approach has a number of
shortcomings, including the potential for ‘‘age mimicry,’’
being highly dependent on the sample size of the reference
sample and outliers, not using the entire fusion distribution, and lacking a straightforward quantitative way of
combining age estimates from multiple sites of fusion.
Here we present an alternative probabilistic approach
based on data collected on 137 individuals, ranging in age
from 7- to 29-years old, from a documented skeletal collection from Coimbra, Portugal. We then use cross validation
to evaluate the accuracy of age estimation from epiphyseal
fusion. While point estimates of age can, at least in some
circumstances, be both accurate and precise based on the
entire skeleton, or many sites of fusion, there will often be
substantial error in these estimates when they derive
from one or only a few sites. Because a probabilistic
approach to age estimation from epiphyseal fusion is computationally intensive, we make available a series of
spreadsheets or computer programs that implement the
approach presented here. Am J Phys Anthropol 142:655–
664, 2010. V 2010 Wiley-Liss, Inc.
Age estimation is crucial in forensic contexts for identity determination, and it is required in archaeological or
paleoanthropological contexts for further analysis of
growth and development, pathology, or paleodemography. Infracranial sequences of maturation are commonly
used to estimate the age at death of nonadult individuals
found in archaeological, paleoanthropological, or forensic
contexts, particularly when the dentition is not available
or too few teeth are preserved for an accurate age
assessment. Typically, an age assessment is made by
comparing the degree of long-bone epiphyseal fusion in
the target specimen to the age ranges for different
stages of fusion in a reference skeletal collection (e.g.,
charts in Steele and Bramblett, 1988; Buikstra and
Ubelaker, 1994; Bass, 1995; Mays, 1998; White and Folkens, 2000; Byers, 2002; Baker et al., 2005). While useful
as a first approximation, this approach has a number of
shortcomings. The age assessment may be subject to
‘‘age mimicry,’’ whereby the estimated age of the target
specimen is inappropriately influenced by the composition of the reference sample (Bocquet-Appel and Masset,
1982; Love and Müller, 2002). For example, in the reference sample we use in this study there are no 13-yearold individuals, which means that the fusion range of an
epiphyses can never begin or end at age 13. Additionally,
the range is a statistic that is highly dependent on the
sample size of the reference sample and outliers, and it
conveys limited information about the fusion distribution
of the reference sample. A method that considers the
entire distribution would be expected to produce more
precise age estimates. There is also no straightforward
quantitative way of combining age estimates from multiple sites of fusion into a single composite age estimate.
Range charts (e.g., Byers, 2002) can be helpful in this
regard, but it is still unclear how to weigh the different
sites of fusion in the composite age estimate. A final,
nonmethodological, issue is that commonly used standards for epiphyseal fusion are based on a limited number
of documented skeletal collections (Coqueugniot and
Weaver, 2007; Schaefer, 2008).
This study has two primary objectives: first, to present
a probabilistic approach to age estimation from epiphyseal fusion that overcomes the methodological shortcomings outlined above, and second, to evaluate the accuracy
of age assessment from epiphyseal fusion. This article
follows on our earlier paper documenting the ages of
epiphyseal fusion in the documented skeletal collection
from Coimbra, Portugal (Coqueugniot and Weaver,
2007).
C 2010
V
WILEY-LISS, INC.
C
MATERIALS AND METHODS
Sample and dataset
Our analyses are based on data collected by HC and
TDW on a documented skeletal collection from Coimbra,
Portugal, that is housed in the Department of AnthropolFrancis Houët: Deceased.
*Correspondence to: Timothy D. Weaver, Department of Anthropology, University of California, One Shields Avenue, Davis, CA
95616. E-mail: tdweaver@ucdavis.edu
Received 6 November 2009; accepted 24 February 2010
DOI 10.1002/ajpa.21312
Published online 28 April 2010 in Wiley InterScience
(www.interscience.wiley.com).
656
H. COQUEUGNIOT ET AL.
TABLE 1. List of fusion sites and abbreviations used
Fig. 1. Age and sex composition of the skeletal sample used
for this study.
ogy, Coimbra University (Coqueugniot and Weaver,
2007). This collection was assembled in the first half of
the 20th century by Professor E. Tamagnini (BocquetAppel, 1984; Rocha, 1995; Coqueugniot and Weaver,
2007). The majority of the skeletons in the collection
were excavated from the Cemiterio da Conchada, the
largest cemetery in the city of Coimbra. The individuals
were born between 1826 and 1922 and died between
1904 and 1938. The entire collection consists of 505 skeletons from both adults and subadults, with the ages at
death ranging from 7- to 96-years old. Documentation
for all the individuals is available in the Anthropology
Department, Coimbra University, and it includes biographical information such as name, parents’ names,
sex, marital status, occupation, birthplace, location and
cause of death, age at death, and date of death. For this
study, we used the 137 individuals from this collection
aged between 7 and 29 years (69 females and 68 males,
Fig. 1). None of these individuals showed any obvious signs
of pathology that could have significantly disrupted growth
and development, and based on the documentation, none of
them were known to have died of tuberculosis.
For each skeleton, the degree of fusion was recorded
for the spheno-occipital synchondrosis and 63 infracranial sites of fusion on the sacrum and the left and right
os coxae, scapulae, clavicles, humeri, radii, ulnae, femora, tibiae, and calcanae (Table 1). Fusion at each site
was coded in three stages, ‘‘a,’’ ‘‘b,’’ and ‘‘c,’’ corresponding to open (no fusion), partial union, and complete
union, respectively. More details on the scoring protocol,
any difficulties in scoring, and interobserver error are
given in Coqueugniot and Weaver (2007).
Age estimation approach
The objective of our age estimation approach is to produce a distribution of probabilities that an unknown
individual is a given age. These probabilities can then be
used to produce either a single age estimate (point estimate) or a range of age estimates that span the ages
with high probabilities (interval estimate). The first step
is to use the reference dataset to estimate likelihoods,
which are probabilities of observing a particular stage
American Journal of Physical Anthropology
Fusion site
Abbreviation
Ilium pubis
Upper ischium pubis
Lower ischium pubis
Ischium ilium
Iliac crest
Ischial tuberosity
Anterior inferior iliac spine
Medial sacral segments 1–2
Lateral sacral segments 1–2
Posterior sacral segments 1–2
Medial sacral segments 2–3
Lateral sacral segments 2–3
Posterior sacral segments 2–3
Medial sacral segments 3–4
Lateral sacral segments 3–4
Posterior sacral segments 3–4
Medial sacral segments 4–5
Lateral sacral segments 4–5
Posterior sacral segments 4–5
Coracoid
Acromion
Sternal end
Humerus head
Humerus medial epicondyle
Humerus distal end
Radius proximal end
Radius distal end
Ulna proximal end
Ulna distal end
Femur head
Femur greater trochanter
Femur lesser trochanter
Femur distal end
Tibia proximal end
Tibia distal end
Fibula proximal end
Fibula distal end
Calcaneus posterior end
Spheno-occipital synchondrosis
Il_Pu
U_Is_Pu
L_Is_Pu
Is_Il
Ic
It
Aiis
M_SS_1_2
L_SS_1_2
P_SS_1_2
M_SS_2_3
L_SS_2_3
P_SS_2_3
M_SS_3_4
L_SS_3_4
P_SS_3_4
M_SS_4_5
L_SS_4_5
P_SS_4_5
Crd
Acm
Ster
Hum_Hd
Hum_Me
Hum_De
Rad_Pe
Rad_De
Uln_Pe
Uln_De
Fem_Hd
Fem_Gt
Fem_Lt
Fem_De
Tib_Pe
Tib_De
Fib_Pe
Fib_De
Clc_Pe
SOS
(‘‘a,’’ ‘‘b,’’ or ‘‘c’’) at a particular fusion site (e.g., iliac
crest) if an individual is a particular age (e.g., 10-years
old). Following Love and Müller (2002), we use kernel
smoothing, a nonparametric regression procedure, to
produce likelihood distributions for each site and age.
Love and Müller (2002) call these likelihood distributions
‘‘weight functions,’’ because they can be thought of as
functions describing the relationship between age and
the probability of showing a particular stage of fusion. If
we had an extremely large reference sample for which
every age was represented by many individuals, then for
each fusion site we could simply use the relative frequencies of the different fusion stages for individuals of
a particular age as an estimate of likelihood distribution
for that site and age. However, many reference samples,
including the one we use here, are only on the order of
100 individuals, and the coverage is uneven across ages,
making this approach problematic. For example, because
there are no 13-year-old individuals in this study’s reference sample, simply using the relative frequencies as
likelihoods results in an estimated likelihood of zero of
showing any stage at any site for a 13-year-old individual. The weight functions alleviate this problem by
expanding the data used to calculate the likelihood for a
given age to adjacent age classes. Specifically, for each
site, the likelihood distribution for a particular age is
AGE ESTIMATION FROM INFRACRANIAL MATURATION
657
Fig. 2. Example of an asymmetrical posterior probability distribution.
estimated from the frequencies of each of the stages for
the age, as well as the frequencies for adjacent ages.
Here we use information from a 2-year window in each
direction of an age (including 2 years younger and
2 years older), so for example, the likelihoods for age
13 would be based on information from ages 11 to 15. In
the kernel estimation equations this window size corresponds to a bandwidth of 3 years, which is 12% of the
range of ages in the reference sample. This percentage is
close to the 10% recommended by Love and Müller
(2002).
To produce a distribution of probabilities that an
unknown individual is a given age (posterior probabilities) we need to know not only the likelihoods but also
the prior probabilities for each age (priors). Bayes’ Rule
can then be used to calculate the posterior probabilities
from the priors and likelihoods (Berry, 1996). The priors
are based on contextual information (e.g., the unknown
individual was a soldier) that makes certain ages more
probable than others in advance of collecting data on the
skeleton. When there is no such information, equal prior
probabilities are assigned to all ages (uniform or uninformative priors). We discuss priors in more detail below in
the context of evaluating the accuracy of age estimation
from epiphyseal fusion.
The last step is to combine information from multiple
sites of fusion. To do this, we assume that an unknown
skeleton’s stages of fusion at different sites are independent of each other given age (conditional independence). For instance, individuals showing Stage ‘‘a’’ at site
no. 1 may be more likely to show Stage ‘‘a’’ at site no. 2,
but if the conditional independence assumption is true,
then the tendency for cooccurrence of Stage ‘‘a’’ at the
two sites is only because the degree of fusion at both
sites is correlated with age rather than because of specific genetic or developmental links between the two
sites. By assuming conditional independence, we can calculate the posterior probabilities for a set of fusion sites
by sequentially applying Bayes’ rule, so the posterior
probabilities based on the 1st site become the prior probabilities for the 2nd site, the posterior probabilities based
on the 2nd site become the prior probabilities for the 3rd
site, and so on. The final posterior probability is the
same regardless of the order of the sites in the sequence.
Evaluating accuracy
Ideally, we would have a large reference sample to
use for estimating likelihoods and multiple large target
samples to use for evaluating the accuracy of age estimation, but we only have data from a single sample.
We could divide the sample in half and use one half as
the reference sample and the other half as the target
sample, but this procedure will tend to bias the results
in the direction of poor performance, because the likelihoods are estimated from a very small sample. Additionally, the test of accuracy is based on a single target
sample, which by chance may happen to be classified
more or less accurately than a typical target sample.
Instead, we use cross validation, which allows us to
mimic using both a large reference sample and multiple
target samples. The basic idea is to hold out a small
subset of the sample (target sample), classify these individuals based on likelihoods estimated from the remaining portion of the sample (reference sample), and then
repeat the procedure many times holding out a different target sample each time (Krzanowski, 2000; Roff,
2006). Importantly, for each iteration, the individuals in
the target sample are different from those in the reference sample, so the results are not biased in the direction of good performance. There is some question as to
the optimal number of individuals to hold out each
time (Roff, 2006), so we performed the cross validation
test twice: either leaving out 1 or 20 individuals. The
results are extremely similar, so we present only the
hold-out-20 results.
To evaluate accuracy, we focus on point estimation
rather than interval estimation, because otherwise it is
difficult to separate accuracy from precision. Essentially,
the larger the interval is, the lower the precision and
the higher the accuracy, with the extreme case of an
interval from 7- to 29-years old resulting in 100% accuracy. For each individual, we define the point estimate
as the age with the highest posterior probability (a posterior mode point estimate). Sometimes, particularly for
estimates based on a single fusion site, there is a block
of ages with the same posterior probability. In this case,
we define the point estimate as the average of the oldest
and youngest ages with this probability. We could have
defined the point estimate as the weighted average of all
the ages where the weights are the posterior probabilities for each age (a posterior mean point estimate), but
this approach biases the age estimates to be too old for
very young individuals and too young for very old individuals. This bias results from the posterior probability
distribution being asymmetrical when the mode is close
to 7- or 29-years old, because the distribution is truncated below 7- and above 29-years old. For example,
American Journal of Physical Anthropology
658
H. COQUEUGNIOT ET AL.
Fig. 3. (See legend page 659.)
Figure 2 shows an asymmetrical posterior probability
distribution for which the weighted average point estimate is 9-years old and the mode point estimate is
American Journal of Physical Anthropology
7-years old. The mode point estimate seems more reasonable based on the overall shape of the posterior probability distribution.
AGE ESTIMATION FROM INFRACRANIAL MATURATION
659
Fig. 3. Example of os coxae posterior probabilities for different stages of fusion without kernel smoothing. The distribution is
based on uniform initial priors. Stages ‘‘a,’’ ‘‘b,’’ and ‘‘c’’ correspond to open, partial union, and complete union, respectively. The
abbreviations used for the fusion sites (Il_Pu, U_Is_Pu, L_Is_Pu, Is_Il, Ic, It, and Aiis) are explained in Table 1. In Panel A, all
seven os coxae fusion sites are open and the posterior probabilities for an age at death of 7-, 9-, 10-, and 12-years old are 0.383,
0.287, 0.255, and 0.076, respectively. The other panels give results for other combinations of maturation stages.
The initial prior probabilities are the final pieces of information that we need to calculate the posterior probabilities. We chose two different sets of prior probabilities
to derive the point estimates for accuracy evaluation.
First, we used the relative frequencies of different ages
in the Coimbra sample as the initial priors (Coimbra priors), because these relative frequencies are representative of the distribution of ages of the ‘‘unknown’’ individuals in the target sample. However, because prior knowledge is never this informative (i.e., Coimbra priors are
only representative of the distribution of ages in the
Coimbra sample), point estimates derived this way will
tend to overestimate the accuracy of age estimation in
real applications. So, second, we used uniform priors (on
the interval from 7- to 29-years old). Using uniform priors evaluates the accuracy of estimating the age of an
isolated individual when the demographic structure of
the unknown population from which the individual
derives is unknown (Bocquet-Appel and Masset, 1996).
RESULTS
The panels of Figure 3 show posterior probability distributions for different states of os coxae fusion when the
likelihoods are estimated without kernel smoothing.
Figure 4 gives distributions for the same fusion states
with kernel smoothing. When the states of fusion are
Il_Pu 5 a, U_Is_Pu 5 a, L_Is_Pu 5 a, Is_Il 5 b, Ic 5 a,
It 5 a, and Aiis 5 a, the posterior probabilities are undefined without kernel smoothing (see Fig. 3B), because for
every age at least one of the site-stage combinations has
an estimated likelihood of zero. In contrast, with kernel
smoothing, ages 9- though 14-years old have nonzero
posterior probabilities, with 11-years old being the most
probable age (see Fig. 4B). The most striking contrast
between Figures 3 and 4 is for the ‘‘B’’ panels (posterior
probabilities are undefined without kernel smoothing),
but the other panels illustrate other, albeit less extreme,
problems with the posterior probability distributions
without kernel smoothing. As we discuss in the introduction, with extremely large samples from all ages, kernel
smoothing is unnecessary, but with smaller or unevenly
distributed samples it leads to more reasonable posterior
probability distributions that are less subject to ‘‘age
mimicry.’’
Tables 2 and 3 summarize the results of the cross validation test of accuracy with the two different choices of
priors. In these tables, we present results for individual
sites and combinations of sites. Many other combinations
are possible, and in any particular application, the exact
combination will depend on which skeletal elements are
present and how they are preserved. Rather than being
comprehensive Tables 2 and 3 are meant to be representative of the types of site combinations that would occur
in practice. We categorized age estimates into those that
are within 15% and within 30% (double the error) of the
actual age.
We chose 15% as the first cut-off because this percentage corresponds to an absolute error of 1 year in
either direction for our youngest age category (7-years
American Journal of Physical Anthropology
660
H. COQUEUGNIOT ET AL.
Fig. 4. (See legend page 661.)
old), and confusing a 7-year old for a 6- or 8-year old
seems to be an acceptable margin of error for most purposes. The absolute error for the oldest individuals,
American Journal of Physical Anthropology
who are 29-years old, is 4 years in either direction.
These error ranges are comparable to, if not better
than, those typically given for age estimates based on
AGE ESTIMATION FROM INFRACRANIAL MATURATION
661
Fig. 4. Example of os coxae probabilities for different stages of fusion with kernel smoothing. The distribution is based on uniform initial priors. Stages ‘‘a,’’ ‘‘b,’’ and ‘‘c’’ correspond to open, partial union, and complete union, respectively. The ordering of the
panels is the same as in Figure 3.
dental development. For example, Ubelaker’s (1978)
classic chart of tooth formation and eruption stages
gives error ranges of 2 years in either direction for 7year-old individuals and 3 years in either direction 15year-old individuals, which would correspond to 29%
and 20 errors, respectively. Alternatively, the percentage errors can be thought of as levels of precision,
which for 15% errors corresponds to levels of precision
ranging from 3- to 9-year intervals for the youngest to
oldest age classes, respectively. In practice, the errors
for 7-year-old individuals will always be in the direction
of being too old, and the errors for 29-year-old individuals will always be in the direction of being too young,
because point estimates will never be younger than
7-years old or older than 29-years old (see Materials
and Methods).
Tables 2 and 3 show that while point estimates of
age can be quite accurate based on the entire skeleton
(82% within 15% error for both sets of priors) or when
many sites of fusion are used (e.g., 79 and 77% within
15% error for the entire pelvis with Coimbra and uniform priors, respectively), there can be substantial
errors in these estimates when they derive from one or
only a few sites, particularly when good prior information is not available (ranging from 41 to 67% within
15% error for single sites with uniform priors). The age
estimates tend to be more accurate with the Coimbra
priors, but there can still be substantial errors for estimates from single sites (ranging from 49 to 78% within
15% error). The frequent poor performance of single
sites is not unexpected given that with our coding
scheme individuals can only group into three age cate-
gories, based on whether the epiphysis is open, partially fused, or completely fused. The percentage of
individuals who are correctly classified approaches or
surpasses 90% for many individual bones for both
Coimbra and uniform priors when the percent error is
increased to 30%. However, with this amount of error
the precision ranges from 5 to 17 years for the youngest to oldest age classes respectively, which for many
applications would be an unacceptably low.
Age estimates for females tended to be biased in the
direction of being too old for most loci, whereas for males
they were often in the direction of being too young. This
pattern is the result of pooling of the sexes in the reference sample, because bone maturation tends to be faster
in females than in males in the Coimbra sample
(Coqueugniot and Weaver, 2007).
DISCUSSION AND CONCLUSIONS
A significant shortcoming of the reference sample that
we use here is the absence of individuals \7-years old. To
overcome this problem and other sample deficiencies, in
the future, we would like to expand the reference sample
to include numerous individuals from all subadult and
young adult ages. Given that there appears to be interpopulational variability in epiphyseal fusion (compare, for
example, Stevenson, 1924; McKern and Stewart, 1957;
Veschi and Facchini, 2002; Coqueugniot and Weaver,
2007; Cardoso, 2008a,b; Schaefer, 2008) that may be
related to ancestry or environmental factors such as socioeconomic status (Meijerman et al., 2007; Schaefer, 2008),
these additional samples would ideally be geographically,
American Journal of Physical Anthropology
662
H. COQUEUGNIOT ET AL.
TABLE 2. Accuracy of age estimation by fusion site and groups of sites with priors based on the Coimbra sample
Percentage error
Site
Site group
615 (%)
630 (%)
615 (%)
630 (%)
615 (%)
630 (%)
615 (%)
630 (%)
Il_Pu
U_Is_Pu
L_Is_Pu
Is_Il
Ic
It
Aiis
M_SS_1_2
L_SS_1_2
P_SS_1_2
M_SS_2_3
L_SS_2_3
P_SS_2_3
M_SS_3_4
L_SS_3_4
P_SS_3_4
M_SS_4_5
L_SS_4_5
P_SS_4_5
Crd
Acm
Ster
Hum_Hd
Hum_Me
Hum_De
Rad_Pe
Rad_De
Uln_Pe
Uln_De
Fem_Hd
Fem_Gt
Fem_Lt
Fem_De
Tib_Pe
Tib_De
Fib_Pe
Fib_De
Clc_Pe
SOS
Os Coxae
62
58
49
59
69
78
59
52
73
62
68
76
57
74
70
59
73
55
59
58
66
67
68
56
56
60
68
56
63
73
64
63
64
73
63
66
72
58
67
80
79
70
80
79
91
81
71
89
82
89
91
80
90
88
81
91
74
79
80
85
85
83
79
78
80
82
79
79
89
84
83
84
87
85
87
88
80
88
84
93
79
91
82
95
74
91
74
92
82
93
67
79
85
95
85
96
78
93
75
93
75
91
80
93
76
91
76
91
58
67
80
88
67
88
Sacrum
Scapula
Clavicle
Humerus
Radius
Ulna
Femur
Tibia
Fibula
Calcaneus
Skull
Columns 3–10 give the percentage of age estimates that were within 15 or 30% of the actual age of the individual. The percentages in
columns 5–10 correspond to age estimates based on the group of sites from the row of percentage to the row above the next percentage.
temporally, and nutritionally similar to the Coimbra sample. However, it would also be worthwhile to build-up a
more diverse test sample for evaluating the accuracy, precision, and bias of age estimates when the unknown individuals come from a different population than the individuals in the reference sample. Given that interobserver
error for epiphyseal fusion should be much lower than age
indicators with more complicated patterns of changes,
such as the pubic symphysis, it may be possible to pool
together data collected by multiple researchers. In principle, data sharing along these lines could lead to a central
repository of epiphyseal fusion data, which could be made
generally available, leading to more accurate and consistent age estimates.
Our results indicate that infracranial sequences of
maturation, at least in some circumstances, can be used
as accurate age indicators for nonadults. Not surprisingly, the general pattern is the more sites of fusion that
are used for an age estimate, the more accurate the estimate (holding precision constant). However, this increase
in accuracy with number of sites is not linear; some twobone combinations are about as accurate as age estimates based on all 11 infracranial bones and the sphenooccipital synchondrosis (Tables 2 and 3). A nonlinear
American Journal of Physical Anthropology
increase in accuracy with number of sites suggests that
the assumption of conditional independence of site fusion
(see Materials and Methods) is not strictly correct, so
after a few sites, each additional site adds very little
new information about age. This assumption could be
tested with very large sample sizes.
Skeletal elements with more fusion sites, such as
the pelvis (os coxae and sacrum) and humerus, can
provide accurate age estimates across a wide range of
ages, while elements with only a single site, such as
the clavicle or calcaneus, will often be quite inaccurate
(Tables 2 and 3). Nevertheless, single sites that fuse
either particularly early or late, such as the clavicle
(Szilvássy, 1980; Webb and Suchey, 1985; Black and
Scheuer, 1996; Coqueugniot and Weaver, 2007), are
not useless, because they can indicate than an
unknown individual is older or younger than a particular age cut-off. This example about the clavicle illustrates the variety of uses of age estimation and the
need to evaluate accuracy within the context of a particular application. Consequently, the test of accuracy
we present here, depending on the objective, may or
may not be applicable. Comparing the Coimbra priors
results with those for uniform priors indicates that
663
AGE ESTIMATION FROM INFRACRANIAL MATURATION
TABLE 3. Accuracy of age estimation by fusion site and groups of sites with uniform priors
Percentage error
Site
Site group
615 (%)
630 (%)
615 (%)
630 (%)
615 (%)
630 (%)
615 (%)
630 (%)
Il_Pu
U_Is_Pu
L_Is_Pu
Is_Il
Ic
It
Aiis
M_SS_1_2
L_SS_1_2
P_SS_1_2
M_SS_2_3
L_SS_2_3
P_SS_2_3
M_SS_3_4
L_SS_3_4
P_SS_3_4
M_SS_4_5
L_SS_4_5
P_SS_4_5
Crd
Acm
Ster
Hum_Hd
Hum_Me
Hum_De
Rad_Pe
Rad_De
Uln_Pe
Uln_De
Fem_Hd
Fem_Gt
Fem_Lt
Fem_De
Tib_Pe
Tib_De
Fib_Pe
Fib_De
Clc_Pe
SOS
Os Coxae
41
52
47
56
60
67
56
50
55
43
55
67
52
70
56
54
60
51
45
49
63
52
65
54
57
54
64
54
59
62
62
55
61
65
59
62
67
52
62
69
80
73
86
76
90
83
73
83
68
78
84
80
91
83
79
86
67
65
74
81
64
78
81
88
81
80
81
75
85
86
81
80
85
87
82
84
80
78
70
94
77
93
82
97
73
89
62
88
75
93
52
72
64
91
76
93
67
91
65
91
62
86
64
89
66
89
69
88
52
62
80
78
62
78
Sacrum
Scapula
Clavicle
Humerus
Radius
Ulna
Femur
Tibia
Fibula
Calcaneus
Skull
Columns and rows are the same as in Table 2.
informative priors should be used when appropriate
information is available, but it is important to keep in
mind that prior information will never be as informative as in our test of accuracy with the Coimbra priors. Finally, age estimates based on sex-specific reference samples would be expected to be more accurate
than those based on pooled-sex samples, but in practice, it is often impossible to determine the sex of nonadult individuals.
In summary, although a probabilistic approach to age
estimation from epiphyseal fusion is more computationally intensive than the typical approach based on age
ranges, it has a number of advantages. Among these, it
uses more information from the reference sample,
allows data from multiple loci to be combined in
a straightforward way into a single, composite age
estimate, and generates an entire probability distribution that a researcher can then use to produce various
point or interval age estimates, depending on the purpose of the age estimate. For these reasons, we recommend that researchers use a probabilistic approach to
estimate the ages of nonadult skeletons from infracranial sequences of maturation. A series of Excel (Microsoft, Redmond, WA) spreadsheets or Matlab (Mathworks, Natick, MA) computer programs that implement
that approach presented here are available at either at
http://www.pacea.u-bordeaux1.fr or http://anthropology.ucdavis.edu. We will provide further guidance about
how to use the spreadsheets and programs upon
request.
ACKNOWLEDGMENTS
The authors thank Professors E. Cunha and N. Porto
for access and permissions; Professors O. Dutour and C.
Roseman for fruitful discussions; and Professor C. Ruff
and two anonymous referees for helpful comments.
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