=Paper=
{{Paper
|id=Vol-3834/paper13
|storemode=property
|title=Beyond the Register: Demographic Modeling of Arrest Patterns in 1879-1880 Brussels
|pdfUrl=https://ceur-ws.org/Vol-3834/paper13.pdf
|volume=Vol-3834
|authors=Folgert Karsdorp,Mike Kestemont,Margo de Koster
|dblpUrl=https://dblp.org/rec/conf/chr/KarsdorpKK24
}}
==Beyond the Register: Demographic Modeling of Arrest Patterns in 1879-1880 Brussels==
https://ceur-ws.org/Vol-3834/paper13.pdf
Beyond the Register: Demographic Modeling of
Arrest Patterns in 1879-1880 Brussels
Folgert Karsdorp1,∗ , Mike Kestemont2 and Margo de Koster3
1
KNAW Meertens Institute, Amsterdam, the Netherlands
2
University of Antwerp, Antwerp, Belgium
3
Ghent University, Ghent, Belgium
Abstract
Unseen species models from ecology have recently been applied to censored historical cultural datasets
to estimate unobserved populations. We extend this approach to historical criminology, analyzing the
police registers of Brussels’ Amigo prison (1879-1880) using the Generalized Chao estimator. Our study
aims to quantify the ‘dark number’ of unarrested perpetrators and model demographic biases in policing
efforts. We investigate how factors such as age, gender, and origin influence arrest vulnerability. While
all examined covariates contribute positively to our model, their small effect sizes limit the model’s
predictive performance. Our findings largely align with prior historical scholarship but suggest that
demographic factors alone may insufÏciently explain arrest patterns. The Generalized Chao estimator
modestly improves population size estimates compared to simpler models. However, our results indi-
cate that more refined models or additional data may be necessary for robust estimates in historical
criminological studies. This work contributes to the growing field of computational methods in hu-
manities research and offers insights into the challenges of quantifying hidden populations in historical
datasets.
Keywords
unseen species model, Generalized Chao, survivorship bias, police history, historical criminology
1. Introduction: dark numbers in history
‘Dark numbers’ are a well-established concept in criminology and sociology, referring to un-
observed or latent criminality not captured in ofÏcial crime statistics [21]. This concept has
gained traction in popular discourse, highlighting the gap between reported and actual crime
rates. Contemporary examples of phenomena with significant ‘dark numbers’ include drug
use in urban areas, undocumented migration, and domestic violence – all areas with strong ev-
idence of underreporting [13]. These examples underscore the challenges in accurately quan-
tifying certain types of criminal activity.
Researchers have developed various methods to estimate these undocumented numbers,
ranging from comparing self-reported arrests with ofÏcial statistics [19] to more sophisticated
CHR 2024: Computational Humanities Research Conference, December 4–6, 2024, Aarhus, Denmark
∗
Corresponding author.
£ folgert.karsdorp@meertens.knaw.nl (F. Karsdorp); mike.kestemont@uantwerpen.be (M. Kestemont);
margo.dekoster@ugent.be (M. d. Koster)
ç https://www.karsdorp.io (F. Karsdorp); http://mikekestemont.github.io/ (M. Kestemont)
ȉ 0000-0002-5958-0551 (F. Karsdorp); 0000-0003-3590-693X (M. Kestemont); 0000-0002-5566-9137 (M. d. Koster)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
265
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
statistical modeling approaches. While empirical validation of these estimates remains chal-
lenging, they provide valuable insights that can inform policy decisions and guide law enforce-
ment strategies. In recent years, criminology has increasingly turned to advanced quantitative
methods to address the negative bias in available data. Although these models have produced
valuable insights into contemporary crime patterns, their application to historical data remains
limited.
Our study aims to bridge this gap by applying one such modern technique, the Generalized
Chao method [5], to a historical case study: the register of the Amigo prison in Brussels for
the period 1879-1880. This unique source documents individuals imprisoned overnight in the
municipal police’s central detention institution. Given the complex nature of urban crime in a
major 19th-century city like Brussels, it is reasonable to assume that police arrest efforts were
imperfect, leaving a considerable amount of undetected crime. Our analysis aims to quantify
this ‘dark number’ by estimating a lower bound on undetected crime in late-nineteenth century
Brussels.
Furthermore, we leverage the demographic information available in the Amigo register to
construct a model that predicts crime detection rates across different social groups. This ap-
proach allows us to explore historical vulnerability to arrest, potentially revealing differential
treatment by the police and broader societal biases of the era. By applying contemporary sta-
tistical methods to historical data, we aim to provide new insights into the dynamics of crime
and law enforcement in 19th-century urban environments.1
Our research aligns with a growing scholarly interest in measuring the amount of under-
detection in historical data, known as Überlieferungschance [10]. This issue of under-sampling
is pervasive across disciplines studying the past, where available datasets often represent only
a fraction of the original historical population, be it artifacts or individuals. Imperfect registra-
tion and survival rates result in incomplete and potentially biased historical data, often skewed
towards categories with higher survival ratios due to their material nature (e.g., stone inscrip-
tions versus papyrus writings). This situation exemplifies ‘survivorship bias’, a concept that
has gained popular attention, partly due to Abraham Wald’s seminal work on R.A.F. bombers
during World War II [17, 20].2 Humanities scholars have long recognized this precarious situ-
ation but often lacked a rigorous framework to address it systematically.
Recent scholarship has turned to unseen species models from ecology as an innovative ap-
proach to estimating the extent of lost or forgotten data, particularly in cultural heritage stud-
ies [15]. In the Humanities, these models have found surprising applications across diverse
domains, including medieval literature, early modern collections of printed books, and studies
of Dutch sailors [24, 18, 16]. Our work contributes to this emerging trend by applying these
ecological models to historical criminology, offering new insights into the ‘dark numbers’ of
19th-century urban crime.
1
Reference to anonymized earlier conference presentation on which this paper is based.
2
On social media, the same visual representation of an airplane (with bullet holes in specific areas) tends to be
reproduced, but this is not a historic image: the origin of the image (the first version was created by around 2005)
is traced in a blog: https://web.archive.org/web/20240430093343/https://cameronmoll.com/journal/abraham-wal
d-red-bullet-holes-origin-story. To the best of our knowledge, no published sketches by Wald himself are known.
See e.g. [23, p. 58-60] but note that the illustration on p. 60 is also not historical.
266
2. Materials: the Amigo register of 1880
The primary source for our study is the Amigo register, a serial, handwritten source housed in
the City Archives Brussels, within the records of the Brussels municipal police.3 This unique
historical resource, illustrated in Fig. 1, takes a tabular form, with each row recording informa-
tion about an individual who spent the night in the Amigo prison.4 Unfortunately, like many
archival records of urban police forces, the Amigo register has suffered from poor conserva-
tion. For Brussels, only a few registers from the 1880s have survived. Our study focuses on
the register covering the period from October 31, 1879, to November 1, 1880, encompassing all
individuals detained in the Brussels police prison during this time.
2.1. Involuntary Arrests
A critical distinction in the Amigo register data is between two types of entries:
1. Involuntary detentions: Individuals forcefully arrested and detained by the police;
2. Voluntary stays (nuit sur demande or ‘night on request’): Individuals who voluntarily
sought shelter at the Amigo.
The latter category primarily comprised socially vulnerable people lacking financial means or
family support. These individuals requested to spend the night at the Amigo for shelter, rather
than being brought in through active law enforcement efforts. The voluntary nature of the nuit
sure demande entries contrasts sharply with the involuntary detentions, potentially impacting
our interpretation of arrest patterns and policing efforts in late 19th-century Brussels.
Our analysis primarily focuses on involuntary detentions, specifically individuals arrested
and locked up in the Amigo police prison on charges of ’vagrancy’. At the end of the 19th cen-
tury, the Belgian economy suffered a depression, which heightened concerns about the influx
of foreign ‘vagrants’ and other perceived undesirable newcomers. in response, urban munici-
pal authorities implemented stricter local ordinances targeting poor migrants. These included
entry regulations and passport requirements at the city gates, as well as mandatory report-
ing by landlords and innkeepers about their lodgers’ characteristics and previous settlements.
Concurrently, new anti-vagrancy legislation criminalized several conditions: (a) the inability
to prove stable attachment to a local community, (b) failure to register as required by law,
and (c) lack of a steady income. From 1866 onwards, a police arrest and judicial conviction
for vagrancy or begging resulted in forced internment in State Vagrancy Colonies (Rijkswel-
dadigheidskolonies). Before being transported to the vagrancy colonies, arrested vagrants were
held in the police prison of the city where the arrest was made: these were the individuals
who were registered as ‘vagrants’ or ‘beggars’ in the Amigo register, and who constitute our
research population [9].
3
City Archives Brussels (SAB), Records of the Brussels Municipal Police, Amigo, register “Vagabonds et Mendiants”
and register “Ivrognes, logés, prostituées”, 1880 (no series or piece number).
4
The historical building of the Amigo prison in Brussels still exists today and currently houses a luxury hotel,
centrally located, adjacent to the Grand-Place of Brussels. The name is a corruption of the older Dutch word
Vrunte, which meant ‘place of detention’, misinterpreted during the Spanish occupation as ‘friend’ (Dutch vriend),
hence the Spanish ‘amigo’.
267
Figure 1: Photographic reproduction of two representative pages in the Amigo register of 1880, City
Archives Brussels (SAB), fol. 95v–96r.
2.2. Recidivism
Recidivism is a prominent feature in our dataset, with many individuals experiencing multiple
arrests. Table 1 illustrates the distribution of arrest counts. In total, the data holds evidence
for 8,367 forceful arrests of 6,016 unique individuals. The mean number of nights an individual
was locked up in the Amigo is therefore ∼ 1.39. However, this average masks a highly un-
even distribution of arrests across perpetrators. While most individuals were registered only
once, repeat offenders were common, with one extreme case involving 35 arrests for public
intoxication within a single year.
Fig. 2 visualizes the temporal patterns of arrests for several individuals, revealing an interest-
ing phenomenon of ‘burstiness’ in the data. Arrest events involving the same individual often
form local temporal clusters. To investigate this pattern, we applied a simple Poisson model
to all individuals arrested at least twice. This model predicts the time lag (in days) between
an individual’s arrests based on their number of previous arrests. As illustrated in Fig. 3, the
time lag generally decreases as the number of previous arrests increases. One way to interpret
this is that the police gradually lost their patience with recidivists. Additionally, this suggests
that the policing effort in arrests was not entirely neutral or random, but was guided by certain
268
Table 1
The distribution of the frequency with which individuals were arrested in the Amigo prison (𝑓1 = number
of people arrested once, 𝑓2 = number of people arrested exactly twice, etc.), incl. the total number of
arrests (𝑁 ) in the data and the unique individuals (𝑆𝑜𝑏𝑠 ).
𝑓1 𝑓2 𝑓3 𝑓4 𝑓5 𝑓6 𝑓7 𝑓8 𝑓9 𝑓10 𝑓11 𝑓12 𝑓13 𝑓14 𝑓16 𝑓22 𝑓35 𝑁 𝑆𝑜𝑏𝑠
4704 851 244 100 44 26 18 11 2 5 3 2 1 2 1 1 1 8367 6016
Figure 2: Visualization of the moments in time (red vertical stripes) when three representative individu-
als were arrested throughout the chronological range covered by the data. (Arrests of other individuals
are shown as non-distinct gray vertical lines.) Note that these events are bursty and often cluster lo-
cally in time, indicating short time lapses between two consecutive arrests of the same perpetrator.
biases. The Amigo register holds information on the date of entry, but not on the release date:
historians assume that the typical imprisonment was typically restricted to a short time period
(i.e. a single night). The re-arrest data shows that individuals could indeed be re-registered af-
ter a short interval, which lends credibility to the assumption that incarceration was generally
short-lived.
269
Figure 3: Predictive plot from a Poisson model (94% HDI) for recidivists (individuals with ≥ 2 arrests),
showing how timelapse (i.e. the number of days after the previous arrest of an individual) varies as a
function of the arrest occasion index (i.e. the number times an individual has been previously arrested).
3. Research Hypotheses
There exist valid reasons to assume that these data do not cover all of the individuals which
theoretically could have been arrested by the police. One of these is the elevated number of
singletons and doubletons in this distribution: if so many individuals were only recorded once
or twice in the data, this renders it statistically quite likely that many perpetrators were never
captured at all and don’t appear in the register. The arrest data must therefore be considered
incomplete and, in all likelihood, severely underestimate the true number of perpetrators in
Brussels for the time period considered.
The methodology described below enables us to estimate a lower bound on these “dark num-
bers” in historical Brussels, i.e. the number of perpetrators who were criminally active in this time
period, but who were never formally registered by the police. While this estimand presents a valu-
able scholarly objective in itself, this paper is also interested in characterizing this unobserved
share of the criminal population in terms of demographics. Were men more likely to be ar-
rested than women? Was the police effort more heavily geared towards younger individuals?
Is there evidence of an active bias towards foreigners in comparison to local citizens? And,
are there any intersections in these biases? Answering these questions would shed more light
on the subjective drivers behind arrests and, thus, the historical vulnerability to arrest across
demographic groups. On a more abstract level, explaining the drivers of under-detection in
such historical datasets represents a major advance with respect to previous work in this area,
which could only estimate the mere size of the non-observed share of the population, but not
explain or characterize its composition.
Based on previous historical studies of the Amigo register [9], we formulated several hy-
270
potheses to guide our experimental design:
H.1 Impact of voluntary stays: We hypothesize that a previous confinement on request (nuit
sur demande) might have increased the visibility of socially fragile individuals to the local
police, thus increasing their vulnerability to future arrest. For example, Joseph Janssens,
a 25-year-old construction worker, was granted night shelter on March 20, 1880, but was
arrested for public drunkenness just days later on March 28.
H.2 Age-related arrest patterns: We expect that vulnerability to arrest generally increased
with an individual’s age. Prior work suggests that the police were more lenient towards
younger individuals, particularly children, although minors were surprisingly often incar-
cerated. Among recidivists, there is a high presence of elderly citizens, who were more
socially vulnerable due to a lack of suitable care institutions.
H.3 Gender disparities: While there appear to be fewer criminally active women in the city,
many women are among the recidivists. This suggests that the police effort may have
been negatively biased towards socially vulnerable women.
H.4 Migratory status: Contrary to older assumptions about discriminatory police biases
against migrants, recent work found no clear evidence for this in the register’s data. In
fact, the data suggest that local, sedentary citizens were much more vulnerable to arrest
than perpetrators born outside of Brussels.
H.5 Family-based biases: We hypothesize that there existed negative biases against mem-
bers of perceived ”criminal families.” The data shows frequent reappearance of the same
family names across different individuals, sometimes with family members co-arrested.
For instance, in autumn 1880, we find frequent arrests of 10 children (aged 8-10) from the
same migrant family from Naples, Italy, who were active as beggars in the city.
After preprocessing and manual disambiguation of individuals appearing in the dataset, the
following data was available for each individual:
𝛽.1 prior: Binary indicator (’prior’ (reference level) and ’no prior’) whether the individual was
granted at least one ”night on request” (nuit sur demande) prior to the date of their first
arrest;
𝛽.2 age: An individual’s mean age at the time of arrest, measured in years (scalar variable,
centered and standardised).
𝛽.3 sex: An individual’s biological sex (binary: ‘female’ or ‘male’ as reference level). We de-
liberately use the term ‘sex’ as the data contains no information on an individual’s gender
role.
𝛽.4 origin: Manually coded factor based on the individual’s place of birth (‘ABROAD’ for
individuals born outside of Belgium, ‘BE’ for those born in Belgium, and ‘BXL’ (reference
level) for locally born individuals from Brussels).
𝛽.5 family: Binary indicator (‘no family’ (reference level) and ‘family’) whether an individual
with the same family name occurs in the dataset. This variable aims to capture bias against
known ”criminal families” but should be interpreted cautiously, because we cannot rule out
the possibility that unrelated individuals shared the same last name.
271
4. Estimating dark numbers with unseen species models
In this paper, we apply a so-called unseen species model to the Amigo data, borrowed from the
biostatistical literature in ecology, to help solve the problem of estimating the number of unob-
served perpetrators. Capture-recapture surveys are important bioregistration instruments in
the field of ecology, used to monitor aspects of biodiversity, such as species richness (the num-
ber of unique species living in a certain area) [12]. During such campaigns, field workers use
a variety of trapping devices (e.g. cameras) to register animals, mark them and release them
again, so that they can be re-sighted at a later time. This process results in what is known
as “abundance data”: counts that record how often animal types have been observed, such as
singletons (𝑓1 or the number of species sighted exactly once), doubletons (𝑓2 or the number
of species sighted exactly twice), etc. Because of the imperfect observation process, however,
many animal types will not be observed during such campaigns, leading to an underestimation
of the true ecological diversity (“unseen species”). The resulting count data must therefore be
treated as censored, because it is zero-truncated: the number of relevant species which exist
in the area but which were never observed (𝑓0 ) are missing. Statistical methods are therefore
used to estimate 𝑓0 as 𝑓0̂ and correct for the observation bias, by adding 𝑓0̂ to 𝑆 (the number of
observed species) to obtain an estimate of the true population size 𝑆.̂ Chao1 [7], for instance,
is a widely used estimator that estimates a lower bound on 𝑓0 as follows: 𝑓0̂ ≥ 𝑓12 /2𝑓2 .
4.1. Unseen heterogeneity
For theoretical reasons, it is important to stress that Chao1 only estimates a lower bound on
the true 𝑓0 , i.e. it estimates the minimum number of unobserved criminals; 𝑓0 , in reality, could
in fact could have been larger than 𝑓0̂ . (Readers should take time to convince themselves of the
fact that, conversely, the detection ratio 𝑆/(𝑓0̂ + 𝑆) is an upper bound for that reason.) The fact
that Chao1 only offers a lower bound is related to the fact that it does not take into account any
heterogeneity in the data [4]: it is derived from the standard Poisson distribution, which as-
sumes homogeneity across the data points. And yet, it is clear that some individuals in our data
might have had higher detection rates, just like some species in ecology might be easier to ob-
serve in nature (because of their large size, bright color, loud vocalization, etc.) [8]. It has been
shown that ignoring the heterogeneity in a dataset, if any were present, will inevitably lead to
(lower bound) estimates for the true population size that are excessively conservative [5]. Con-
versely, if we can account for potential differences in detection probability, this conservative
bias in Chao1 can be reduced, and the population estimate is adjusted upwards, consequently
becoming less of a lower bound. To test whether there is indeed any such heterogeneity in
a dataset, Böhning and colleagues [2, 13] recommend the use of a so-called ratio plot for the
function:
(𝑥 + 1)𝑓𝑥+1
𝑟𝑥̂ = , (1)
𝑓𝑥
where 𝑓𝑥 refers to the number of items that occur exactly 𝑥 times [2]. If the data points are
homogeneous and do not violate the Poisson assumptions, the resulting points should present
as a constant, i.e. a horizontal line. If that is not the case, there is reason to assume that there
is unobserved heterogeneity. In Fig. 4, we present a ratio plot for the arrest data up to 𝑥 = 6
272
Figure 4: A ratio plot for the count statistics from the arrest data.
from the Amigo prison. It is clear that we are not dealing with a straight horizontal line. Thus,
we have reason to believe that there is heterogeneity in the data that is not accounted for by
the standard Chao1.
4.2. Generalized Chao
In this section, we discuss the Generalized Chao: a generalization of the Chao1 method that
can take into account statistical covariates and thus model heterogeneity across individual per-
petrators in a dataset. This estimator, originally proposed by Böhning et al., aims to model
heterogeneity in the data by modeling the detection probabilities as a regression problem. The
method is characterized by a similar focus on low-frequency species (𝑓1 and 𝑓2 ) as Chao1, cap-
turing the intuition that such uncommon species carry the most information about species
which were not observed at all. These data consisting of 𝑓1 and 𝑓2 counts can be said to arise
from a Poisson distribution, 𝑦𝑖 ∼ Poisson(𝜆), but a truncated one with 𝑦𝑖 ∈ 1, 2.
Böhning and colleagues show that by maximizing the binomial likelihood, we can obtain an
𝑝̂
estimate for 𝜆𝑖 using 𝜆̂ 𝑖 = 2 (1−𝑖𝑝̂ ) [5]. Here, 𝑝𝑖̂ refers to the estimated probability of species
𝑖
𝑖 to occur once or twice. To estimate 𝑝,̂ then, we fit a Generalized Linear Model assuming a
binomial distribution:
𝑦𝑖 ∼ Binomial(1, 𝑝𝑖 )
logit(𝑝𝑖 ) = 𝛼 + 𝛽𝑥 𝑥𝑖 + …
Here, 𝛼 represents the intercept and 𝛽𝑥 represents the coefÏcient for a predictor 𝑥𝑖 which is
available for the 𝑖-th species in the data; the outcome variable is binary with the negative class
representing species that occur once and the positive class those that occur twice. Given 𝑝𝑖̂ ,
the lower bound on the true population size can be estimated as follows:
𝑓1 +𝑓2
1
𝑆̂ = 𝑆 + ∑ (2)
𝑖=1 𝜆̂ 𝑖 + 𝜆̂ 𝑖2 /2
273
We employ Bayesian logistic regression models as implemented in the Python package
Bambi[6] as an interface to PyMC [1]. The ‘No U-Turn Sampler’ (NUTS) was used for sam-
pling [14], also known as the adaptive Hamiltonian Monte Carlo (HMC) algorithm. We use
weakly informative priors for all model terms. The convergence of all models was verified
through examination of their trace plots and the 𝑅̂ statistic [11]. As all 𝑅̂ values were well
below the 1.1 threshold, indicating convergence, we opted not to report individual values. To
assess and compare the performance of the regression models on unseen data, we employ ap-
proximate Leave-One-Out Cross Validation (LOO-CV) [22].
4.3. Estimating the probability of repeated occurrence
We fit a series of models for diverse (additive) combinations of the available covariates. No
interactions or random effects are considered. We include linear and quadratic terms for the
age predictor. We compare all models against an intercept-only model which, as it ignores
any heterogeneity in the data, should produce estimates equal to the Chao1 model, and can
thus be considered a baseline in these experiments. We compare the predictive performance
of the models using LOO-CV [22], and visualize the expected log pointwise predictive density
(ELPD) and error in the left panel of Fig. 5. The model ranking suggests that the inclusion of
predictors generally improves the predictive performance. Akaike model weights are reported
in the middle panel: these in turn suggest that the more complex, additive models offer added
value over simpler models, but caution is warranted as these weights are determined as point
estimates and do not account for uncertainty [20]. In fact, given the considerable overlap in
the errors of the ELPD estimates, no single model clearly outperforms the others and should
be unequivocally preferred.
In Fig. 6, we show a forest plot for the coefÏcients included in the highest ranked model,
which is also the most complex in terms of parameters. The predictor coefÏcients’ HDI val-
ues do not intersect with zero suggesting that they each contribute meaningfully to the model.
Given the strong class imbalance, however (cf. the intercept estimate), their effect sizes are
however small, which is both reflected in the non-distinctness of the model comparison above
and the marginal effect plots in Fig. 7. The coefÏcients show how this particular model as-
sesses the likelihood of an individual being a doubleton (as opposed to a singleton), i.e. 𝑝(𝑓2 ).
First of all, the arrest rates vary with gender: we see that female individuals were more likely
to be a doubleton than men. There appears to be a non-linear relationship with “age”, which
peaks around the age of 50. Doubletons are also slightly common in the local population from
Brussels, who suffered higher arrest rates than people born elsewhere in Belgium – the vul-
nerability to arrest of native Belgians appears comparable to individuals born outside of the
country. People who previously stayed the night in the Amigo at their own request also saw
a higher doubleton incidence than others. Finally, this model finds weak evidence for a bias
against individuals with a known last name, potentially indicating more police effort against
members from families perceived as “troublemakers”.
Given the lack of decisive arguments to conclusively prefer one model over the rest, we opt
for the common practice of (weighted) model averaging. This approach allows us to account
for model uncertainty by combining the predictions of multiple models, rather than relying
solely on a single ‘best’ model. Specifically, we employ the stacking of predictive distributions
274
Figure 5: Left panel: Visualization of the model comparison for the LOO information criterion (ELPD
= expected log pointwise predictive density), including the difference with the baseline intercept model
(𝑦 1). The intervals for the out-of-sample predictive fit overlap across nearly all models. Middle panel:
Akaike weights for each model. Right panel: Adjusted population size estimate using the Generalized
Chao. Only for the best performing additive models, we see that the lower end of the credible intervals
does not overlap with the point estimate for Chao1.
Figure 6: Forest plot visualization for the model coefficients of the best performing individual model,
excluding the intercept (with 89% HDIs). None of the shown ranges intersect with zero, although many
of the effects are relatively small. (Origin[B] refers to ‘BE’ in relation to the reference level ‘BXL’ and
Origin[C] to ‘ABROAD’.)
method [25], as implemented in PyMC. This technique generates a meta or ensemble model
by computing a weighted average of the posterior predictions from all considered models. The
weights assigned to each model are derived from the model weights in our previous model
comparison analysis (cf. the middle panel of Fig. 5).
275
Figure 7: Marginal effect plots contrasting the predictors ’sex’, ’age’, and ’origin’. Shown are the 50%
and 89% credible intervals. The top row displays the marginal effect of ‘sex’, with females showing a
higher effect than males. The middle row contrasts ‘age’ effects, revealing a non-linear relationship
peaking around age 50, with separate curves for males and females. The bottom row illustrates the
interaction between ‘sex’, ‘age’, and ‘origin’, where ‘BXL’ (Brussels), ‘BE’ (Belgium), and ‘ABROAD’
categories are compared.
4.4. Adjusted population estimates
The main results are presented in in Table 2, which is primarily insightful for the categorical
predictors. Here, the adjusted population size estimates are shown with 89% upper and lower
credible intervals, both for the highest ranked model and the ensemble model, together with the
observed counts and the original Chao1 estimate for each predictor level. Detection rates are
presented for each predictor. Asterisks in the table indicate that the lower end of the credible
interval for a level does not include the corresponding Chao1 estimate: this is of particular
interest, because these are instances where the novel estimators deviate meaningfully from the
baseline estimator, identifying demographic categories where the detection rate is potentially
underestimated by Chao1. Crucially, we see that the Generalized Chao estimates consistently
yield an upwards adjustment for the total population in comparison to Chao1: as the estimated
276
Table 2
Tabular overview of the Generalized Chao estimates (best performing model (𝑆,̂ and model averaging
̂ ) across the different demographic levels in the data, including per-level observed counts and the
𝑆MA
original Chao1. Asterisks in the table indicate that the lower end of the credible intervals for a level
does not include the corresponding Chao1 estimate.
𝑆𝑙̂ 𝑆𝑢̂ 𝑆 𝑆̂ ̂
𝑆MA Chao1 ratio
∗
Pop. total 17409 19505 5610 18414 18238 16937 0.305
BXL 7160 8202 2582 7660∗ 7690∗ 7148 0.337
origin BE 6940 8154 2275 7530 7457 7029 0.302
ABROAD 2759 3783 753 3223 3093 2982 0.234
male 15042 16993 4649 15969∗ 15779 14818 0.291
sex
female 2193 2730 961 2444 2460 2272 0.393
no 16364 18458 5100 17363∗ 17155 16299 0.294
prior
yes 942 1174 510 1050 1084 1007 0.486
no 10708 12407 3237 11536∗ 11312 10688 0.281
family
yes 6403 7401 2373 6877 6927 6409 0.345
population total went up from 16,937 to 18,414, our estimated detection rate dwindled down
from 33%, to 31%. While the adjustments can be limited in some instances, this suggests that
the Generalized Chao has successfully managed to capture at least some of the heterogeneity
across the demographic group in the data. As expected, the model averaging yields slightly
lower estimates than the single-model approach and presents a more cautious approach that
might be preferable in the case of ranking ties between models, like here.
When we compare the detection rates across the levels of specific factors, interesting trends
can be discerned. These insights are further supported by the marginal effects plots in Fig. 7.
The estimated number of female perpetrators is much lower than for male perpetrators, but
we see that women’s vulnerability to arrest was considerably higher. In the case of migratory
status, we see that local citizens form the largest group, but this time we see that the arrest ef-
forts clearly targeted this group more intensely than people born outside of the city or country.
Again, no bias against migrants is manifest in the data. A factor that considerably increased
detect rates was the stay of a prior night in the Amigo. Somewhat weaker is the effect of be-
longing to a family of perceived troublemakers: again, a smaller demographic group, but with
much more policing effort geared against them. Often, we see that the effects are strongest for
the smallest, most underrepresented subgroups in the criminalized population, such as women,
which are heavily outnumbered by men. This might help explain why even the best performing
model in the evaluation in the end does not clearly outperform the baseline model.
5. Discussion and model criticism
Our application of the Generalized Chao method to the Amigo prison register data has yielded
valuable insights into the ‘dark number’ of criminality in late 19th-century Brussels. By in-
277
corporating demographic covariates into our model, we’ve been able to estimate not only the
total number of unobserved perpetrators but also to characterize patterns of arrest vulnerabil-
ity across different social groups. Our finding suggests that the true criminal population was
likely much larger than can be observed in the register data, and that the Generalized Chao,
albeit slightly, adjust the population estimate relative to the Chao1 model.
However, it’s crucial to acknowledge the limitations of our approach. Our statistical models
primarily focus on relatively stable individual characteristics and do not incorporate event-
specific information such as the date, location, or reason for arrest. The inclusion of age as a
predictor, while informative, is only justified by the narrow one-year time frame of our dataset.
In ecological terms, our model considers species-level covariates but lacks observation-level
predictors. This constraint represents a significant limitation of the method and highlights an
area for future methodological development.
Despite these limitations, our rigorous model comparison revealed valuable insights. Distin-
guishing between singletons and doubletons proved to be a complex task, with considerable
model uncertainty. While our models incorporating demographic covariates didn’t markedly
outperform the baseline model in terms of out-of-sample predictive ability, this finding itself is
valuable. It underscores the complexity of historical criminality and arrest patterns, suggesting
that simple demographic factors alone may not fully explain arrest vulnerability.
While our model comparison revealed limitations in predictive power, it’s crucial to consider
additional factors that may influence our results. One such factor is the potential violation of
core assumptions underlying the Chao1 estimator and its generalizations, particularly the as-
sumption of a closed population during the observation period. In many applications, includ-
ing ecology, this assumption is often violated due to births and deaths within the population.
However, in our historical urban context, migration presents a more significant concern. Late
19th-century Brussels experienced extreme population turnover, with historians estimating an-
nual rates as high as 10% [9]. This dynamic population flux challenges the closed population
assumption inherent in our models. Furthermore, the specific nature of our data introduces
additional complexities. Some arrested vagrants were temporarily sent to vagrancy colonies
outside Brussels. While many of these individuals eventually returned to the city, they were
temporarily unobservable [9]. This periodic absence of individuals from the observable popu-
lation further complicates our modeling efforts.
These factors likely contributed to one-inflation in our data, an excess of singletons (indi-
viduals observed only once) compared to doubletons (individuals observed twice). This phe-
nomenon requires careful consideration, as standard models, including non-parametric lower
bound estimators, tend to overestimate the true population size in such cases [3]. Several
mechanisms can contribute to one-inflation in a population:
1. Behavioral change: Identified individuals may alter their behavior after initial detec-
tion. In our context, the experience of incarceration might have had a strong dissuasive
effect, reducing the likelihood of repeat offenses and contributing to one-inflation;
2. Mismatching: Individuals actually detected twice might be incorrectly recorded as sin-
gle detections, artificially inflating the singleton category. Given the nature of our his-
torical data, such mismatches are plausible. For instance, an intoxicated arrestee with
impaired speech might have been difÏcult for police to accurately identify and record.
278
Population turnover: As discussed earlier, the high rate of population flux in late 19th-
century Brussels could contribute to one-inflation by introducing many individuals who
were only briefly present in the city.
3. Temporary absences: The practice of sending some arrested vagrants to colonies out-
side Brussels, as previously mentioned, could also contribute to one-inflation by inter-
rupting the observability of these individuals.
The presence of one-inflation in our data may partially explain the limited improvement in
predictive power we observed when incorporating demographic covariates into our models.
It also underscores the importance of developing and applying methods that can account for
such data characteristics in historical criminology research.
Looking beyond the specific challenges of our study, this work has significant implications
for the broader field of computational humanities, particularly from the perspective of critical
data studies. A persistent challenge in historical scholarship is the under-representation of
marginalized groups in archival records. This systemic bias not only skews our understanding
of historical societies but also perpetuates the silencing of under-represented voices. Our work
with the Generalized Chao estimator offers a concrete, quantitative approach to addressing
this issue. By estimating the ‘dark numbers’ and characterizing demographic patterns in ar-
rest vulnerability, we provide a method for: (a) quantifying the extent of under-representation
in historical records, (b) identifying specific demographic groups that may be disproportion-
ately under-represented, and (c) adjusting historical narratives to account for these ‘invisible’
populations.
While our study focused on historical criminology, the methodology has potential appli-
cations across various domains of historical research. It could be adapted to estimate under-
representation in census data, literary corpora, or other historical datasets where certain groups
may be systematically excluded or under-reported. Clearly, statistical methods alone cannot
fully rectify historical biases. They must be used in conjunction with critical historical analysis,
interdisciplinary collaboration, and a commitment to amplifying marginalized voices. Future
research should explore how unseen species models can be integrated with other quantitative
and qualitative methods in the humanities to provide a more comprehensive and equitable view
of historical societies.
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A. Online Resources
The full code and data for replicating our analysis will be made available from the following
GitHub repository upon the publication of the paper: https://doi.org/10.5281/zenodo.13969373.
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