Mapping the uncertainty of 19th century West African slave origins using a Markov decision process model

Ashton Wiens; Eric Vance; Henry Lovejoy; Zachary Mullen

REVIEW 5 major objections 6 minor 13 references

Mapping the uncertainty of 19th century West African slave origins using a Markov decision process model

T0 review · 5 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A simulation combining conflict-intensity kriging and a Markov decision process maps likely inland origins of slaves departing West African ports between 1816 and 1836.

desk verdict A promising but unfinished preprint: the modeling pipeline is new, the validation is absent, and the central conflict-as-capture proxy is unproven. read the letter →

arxiv 1908.00431 v1 pith:WGWPX4FQ submitted 2019-08-01 stat.AP

Zachary Mullen , Ashton Wiens , Eric Vance , Henry Lovejoy This is my paper · ORCID

classification stat.AP

keywords slavequestionslavesafricaafricanapproachcapturecertain

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper addresses a historical question: if a person was sold into the trans-Atlantic slave trade from a port like Lagos or Ouidah between 1816 and 1836, where in the Oyo region of West Africa were they most likely captured? The authors build a two-stage computer model. First, they take a list of known conflict events such as battles and destroyed towns, each with a severity score, and use spatial kriging to turn those discrete points into a smooth annual map of conflict intensity. They then treat that map as a probability distribution for where slaves were captured. Second, they model the inland trade as a network of cities connected by routes. A Markov decision process chooses the best route for a slaver to move a captive to a coastal sale port, with route costs increased near conflicts and sale rewards drawn randomly for each simulated individual. Repeating this for 10,000 simulated slaves per year produces maps that color the likely origin region by the eventual port of departure. The paper also describes a web app, but the app is not yet available at a real address. The modeling is creative, but the preprint is incomplete. The data sources are not described or cited, several parameters are set by hand with no estimation procedure, and the only comparison to real data is a plot of estimated versus recorded ship departures without error bars or goodness-of-fit statistics. The authors state that the method has no mathematical optimization strategy and that validation against linguistic data is future work. Because the simulated capture locations come directly from the conflict map, the final origin maps may largely reflect the assumed relationship between conflict and capture rather than independent evidence.

Extended reading notes

Core claim

Abstract: 'we can use this two-step approach of providing capture locations to a historical trade network in a simulative fashion to generate and visualize the conditional probability of a slave coming from a certain spatial region given they were sold at a certain port.' Section 1: 'The goal is to provide a functional and descriptive model for the most likely inland origin locations of slaves given a known year and port of origin.' The load-bearing assertion is that the combination of a conflict-intensity kriging surface and an MDP over the trade network yields valid conditional origin maps.

Load-bearing premise

The annual conflict-intensity surface, after normalization, is treated as the probability density for slave capture locations. Section 3.1.3 states: 'we can also view the resulting surface as an implied probability density function, where the higher points of the ridge near conflict locations represent regions of increased probability of slave capture.' This premise is asserted without independent evidence that recorded conflict events are an unbiased spatial sample of slave capture intensity, and it is the direct source distribution for all simulated origins. If conflict records are biased or if captures occurred away from recorded battle sites, the entire posterior origin map is distorted.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Worth a look if you work on spatial models in digital humanities, but this is clearly a draft. The new thing here is the pipeline: kriged conflict intensity, simulated capture locations, a Markov decision process over a trade network, and port-conditional origin maps. I don't know of another paper that connects slave origins to departure ports through an explicit decision model, and the interactive app idea is a sensible output for historians. The writing is honest; Section 3.3.3 flatly says there is no mathematical optimization strategy, and Section 4 disclaims historical truth. That candor counts.

The soft spot is load-bearing. Simulated capture locations are drawn from the normalized conflict kriging surface (Section 3.1.3), and that surface is asserted to be an implied probability density of slave capture. There is no evidence that recorded battles and destroyed towns are an unbiased spatial sample of capture intensity. Raids and captures along marches could easily be off the documented battle sites. Because every simulated origin is drawn from this surface, any bias propagates into every port-conditional map. The port totals used for tuning constrain volumes, not spatial origins, so they cannot validate the source distribution. The paper itself flags the missing validation via linguistic data as future work, which is honest but does not fill the gap.

Other issues: parameters like the Matern range, smoothness, conflict cost multiplier C, and reward variance are hand-set with no sensitivity analysis; no code or data are provided; the Data section is literally marked “Section in Progress”; and some citations are missing. In its current form the central claim that these maps are meaningful conditional probabilities of origin is not supported.

Who is this for? A historian or digital-humanities researcher interested in the modeling template might get something from the setup. A statistician will want to see the proxy validated and parameters estimated before taking the maps seriously. I would not cite it yet, and I would not send this version to referees. The right move is to tell the authors to finish the data section, release code and data, add sensitivity analysis, and ideally validate against the linguistic name data they mention. If they do that, the pipeline deserves a serious look.

Referee Report

5 major / 6 minor

Summary. The paper proposes a two-stage statistical pipeline for mapping inland slave-capture origins in the Oyo region, ca. 1816-1836. In the first stage, the authors krige a conflict-intensity surface from recorded events such as battles and destroyed towns, normalize the surface to an annual density, and simulate slave capture locations from it by direct inversion. In the second stage, they feed these simulated capture locations into a Markov decision process over a manually coded trade network, with randomized point-of-sale rewards, to produce maps of the conditional probability of origin given a port of departure. The paper also describes an interactive Shiny application and frames the output as a data-driven answer to the historical question of where slaves sold at particular ports originated.

Significance. If the central claim held, the paper would offer a useful template for quantitative spatial inference in digital history, and the interactive visualization is a genuine public-facing contribution. The authors are transparent about several limitations, use standard tools (kriging, MDP, KDE), and clearly separate the simulation stage from the historical validation stage. However, the central claim of valid port-conditional origin maps is not supported: the capture-density proxy is unvalidated, key parameters are fixed heuristically, the reward distribution is unspecified, and the only empirical comparison targets port totals rather than spatial origins. The paper is therefore better read as a proof-of-concept than as an established answer to the research question it poses.

major comments (5)

[Section 2] Section 2 is explicitly incomplete: the text states 'Section in Progress pending collaboration: Describe the conflict data - what historical accounts were used?', 'The data were collected in ??', and the trade map relies on 'CITATION MISSING'. Because the entire pipeline depends on the provenance and coding of conflict events, city locations, and network edges, the missing data description prevents replication and evaluation of the central claim.
[Section 3.1.3] The kriged conflict surface is normalized into an 'implied probability density function' for slave capture and then used as the source distribution for all simulated slaves via direct inversion (Section 3.3.1). This is the load-bearing assumption of the paper, but it is asserted rather than validated: recorded battles and destroyed towns need not be an unbiased spatial sample of capture intensity, and captures during raids or marches could occur away from documented sites. The port-total data used for tuning (Section 2) constrain only aggregate volumes, not spatial origins, so they cannot validate this surface. The manuscript itself flags the lack of validation in Sections 3.3.3 and 4.
[Section 3.1.3] The Matern covariance parameters are fixed heuristically ('we found that a 10km range accomplished this'; smoothness fixed at '4.5 times differentiable'), and the sill and nugget are fit only to the 1828 data and reused for all years 1816-1836. No sensitivity analysis is provided, even though the normalized surface is directly proportional to the capture density and therefore to every conditional origin map. The authors should also state the smoothness parameter nu explicitly, since '4.5 times differentiable' is not a standard parameterization.
[Sections 3.3.1 and 3.3.3] The distribution of random reward vectors is never specified, and Section 3.3.3 admits 'our model includes a considerable amount of parameters with no mathematical optimization strategy.' Since port assignment is deterministic under equal rewards (Section 3.3.1), the stochastic port catchments shown in Figure 5 are entirely driven by the unspecified reward variance and the conflict cost C. Without specifying these distributions and performing optimization or systematic sensitivity analysis, the reported conditional probabilities are not reproducible and their uncertainty is not quantified. The proposed chi-square tuning relies on linguistic data that are not yet available, so it remains future work.
[Section 3.2.3] The conflict surface enters the model twice: as the capture density and as an additive edge cost, with C scaled to an annual maximum of 3. This is not circular by definition, but it means the same unvalidated proxy drives both the numerator and the routing denominator of the conditional maps, potentially amplifying artifacts. A concrete test would be to rerun the pipeline with C=0 or with C estimated from independent route-choice evidence and compare the port-conditional origin maps.

minor comments (6)

[Throughout] Placeholder text remains in the manuscript, including 'CITATION MISSING', 'website.com', 'maybe cite slavebiographies.org', and 'The data were collected in ??'; these must be completed before any resubmission.
[Figure 6] Figure 6 is referenced but no figure or quantitative summary is included in the text; the authors should include the figure with error bars, sample sizes, and a description of the fit.
[Section 3.1.1] The text refers to a '2-valued marker for intensity of battle' while Section 2 defines four intensity levels (0, 1, 5, 10); please clarify which variable is actually modeled.
[Section 3.2.1] The discount factor is set to gamma = 1 even though gamma in [0,1) was defined earlier; if the horizon is finite, state this explicitly.
[Figure 5] The caption says 'increasing variance in rewards' but no numerical variances are given; please report the actual reward distributions used.
[Throughout] There are several typographical and notation inconsistencies, including 'M´tern' for Matern and 'Translatlantic' for Transatlantic; a careful proofread is needed.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central model rests on domain assumptions about conflict-as-capture-proxy and the historical transport network, plus hand-set or fitted parameters. None of these are validated against independent data in the preprint. No new physical or conceptual entities are introduced; the MDP absorbing sale states and random reward vectors are methodological constructs, not new postulated objects.

free parameters (6)

Matern range a = 10 km (chosen by hand)
Section 3.1.3: 'we found that a 10km range accomplished this'; controls spatial extent of conflict smoothing.
Matern smoothness nu = 4.5 (chosen by hand)
Section 3.1.3: 'Smoothness was similarly fixed at a 4.5 times differentiable Matern'; affects ridge-like border shape.
Matern sill and nugget = Fitted via variogram to 1828 conflict data; numerical values not reported
Section 3.1.3: 'we fit them via variogram with Cressie weights to the 1828 data set, then used those parameters to fill in the remaining years'.
Conflict cost multiplier C = Scaled to annual maximum C = 3
Section 3.2.3: 'scaled to an annual maximum of C = 3' modifies edge costs in the MDP.
Point-of-sale reward variance = Not specified; randomized per slave
Section 3.3.1: 'generate a random reward vector from a distribution specifying the end reward'; the distribution and its variance are never given.
KDE bandwidth h = 0.5 to 2 km
Section 3.3.2: 'we allow h to vary from .5 - 2km for a sample of 10,000 simulated slaves'.

assumptions (4)

domain assumption Conflict sites and destroyed towns are the predominant sources of slave captures, and the kriged conflict surface can be treated as an implied probability density for capture locations.
Section 3.1.2: 'the conflicts and attacked towns themselves were the predominant sources of slaves at the time'; Section 3.1.3 calls the normalized surface an implied probability density function.
domain assumption Recorded conflict events are an unbiased spatial sample of slave capture intensity.
The kriging estimator uses only observed conflict event locations and intensities. If records are biased by region or event type, the normalized surface is not the capture distribution. Section 2 notes data collection is still being documented.
domain assumption The hand-built trade network adjacency matrix and city-to-city routes accurately reflect 19th century caravan movement.
Section 2: 'This map has been informed by both available historical records from the time (CITATION MISSING) and geographic ease of transit between cities'.
domain assumption Slaver behavior is well approximated by expected-reward maximization in an MDP with random reward vectors.
Section 3.3.1: random rewards are added to 'represent each slaver's knowledge of the conflicts and rewards present'; no empirical calibration is shown.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Mapping the uncertainty of 19th century West African slave origins using a Markov decision process model." pith.science (2026). https://pith.science/paper/WGWPX4FQ

@misc{pith2026190800431,
  author       = {Pith},
  title        = {Pith review of: Mapping the uncertainty of 19th century West African slave origins using a Markov decision process model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WGWPX4FQ}},
  note         = {Machine review of arXiv:1908.00431}
}

read the original abstract

The advent of modern computers has added an increased emphasis on channeling computational power and statistical methods into digital humanities. Including increased statistical rigor in history poses unique challenges due to the inherent uncertainties of word-of-mouth and poorly recorded data. African genealogies form an important such example, both in terms of individual ancestries and broader historical context in the absence of written records. Our project aims to bridge the lack of accurate maps of Africa during the trans-Atlantic slave trade with the personalized question of where within Africa an individual slave may have hailed. We approach this question with a two part mathematical model informed by two primary sets of data. We begin with a conflict intensity surface which can generate capture locations of theoretical slaves, and accompany this with a Markov decision process which models the transport of these slaves through existing cities to the coastal areas. Ultimately, we can use this two-step approach of providing capture locations to a historical trade network in a simulative fashion to generate and visualize the conditional probability of a slave coming from a certain spatial region given they were sold at a certain port. This is a data-driven visual answer to the research question of where the slaves departing these ports originated.

Figures

Figures reproduced from arXiv: 1908.00431 by the authors.

**Figure 2.** Left to Right: 1825 conflict map via a kernel density estimate with [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Example of MDP decision chain for a start in S3 with an absorbing state in S1 [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Example of MDP decision chains for 1825 (left) and 1826 (right) [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]

**Figure 5.** Figure 5: Simulated Slave Origins colored by their points-of-sale. Left to Right: increasing [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]

**Figure 6.** Figure 6: Estimated Versus Recorded Trans-Atlantic Slave Departures from the Bight of [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

**Figure 7.** Figure 7: Top: Model and Linguistic Data for a ship leaving Lagos, 1832; Bottom: for [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

[1]

Boucherie, R. J. and Van Dijk, N. M. (2017),Markov decision processes in practice, Springer

work page 2017
[2]

(2017), MDPtoolbox: Markov Decision Processes Toolbox, R package version 4.0.3

Chades, I., Chapron, G., Cros, M.-J., Garcia, F., and Sabbadin, R. (2017), MDPtoolbox: Markov Decision Processes Toolbox, R package version 4.0.3

work page 2017
[3]

The Transatlantic Slave Trade and Origins of the African Dias- pora in Texas,

Chambers, G. (2012), “The Transatlantic Slave Trade and Origins of the African Dias- pora in Texas,” http://www.pvamu.edu/tiphc/research-projects/the-diaspora-coming-to- texas/the-transatlantic-slave-trade-and-origins-of-the-african-diaspora-in-texas/. 20

work page 2012
[4]

Fitting variogram models by weighted least squares,

Cressie, N. (1985), “Fitting variogram models by weighted least squares,” Journal of the International Association for Mathematical Geology , 17, 563–586

work page 1985
[5]

Statistics for spatial data,

Cressie, N. (1992), “Statistics for spatial data,” Terra Nova, 4, 613–617

work page 1992
[6]

Kelley, S. M. (2016), The voyage of the slave ship hare: A journey into captivity from Sierra Leone to South Carolina , UNC Press Books

work page 2016
[7]

The origins of the African-born population of Antebellum Texas: A research note,

Kelley, S. M. and Lovejoy, H. B. (2016), “The origins of the African-born population of Antebellum Texas: A research note,” Southwestern Historical Quarterly , 120, 216–232

work page 2016
[8]

(2014), Geographies of the Holocaust, The Spatial

Knowles, A., Cole, T., and Giordano, A. (2014), Geographies of the Holocaust, The Spatial

work page 2014

Show all 13 references

[9]

Knowles, A. K. and Hillier, A. (2008), Placing history: how maps, spatial data, and GIS are changing historical scholarship , ESRI, Inc

2008
[10]

The Liberated Africans Project,

Lovejoy, H. (2016), “The Liberated Africans Project,” http://www.liberatedafricans.org

2016
[11]

Normalizing Metadata: Integrating Events, Places, Objects, and People into the Design of the Liberated Africans Project,

Lovejoy, H. (2017), “Normalizing Metadata: Integrating Events, Places, Objects, and People into the Design of the Liberated Africans Project,” Emerging Scholars and Scholarship in Digital History

2017
[12]

Redrawing historical maps of the Bight of Benin Hinterland, c. 1780,

Lovejoy, H. B. (2013), “Redrawing historical maps of the Bight of Benin Hinterland, c. 1780,” Canadian Journal of African Studies/La Revue canadienne des ´ etudes africaines , 47, 443–463

2013
[13]

Venables, W. N. and Ripley, B. D. (2002), Modern Applied Statistics with S , Springer, New York, fourth edn., ISBN 0-387-95457-0. 21

2002

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Boucherie, R. J. and Van Dijk, N. M. (2017),Markov decision processes in practice, Springer

work page 2017

[2] [2]

(2017), MDPtoolbox: Markov Decision Processes Toolbox, R package version 4.0.3

Chades, I., Chapron, G., Cros, M.-J., Garcia, F., and Sabbadin, R. (2017), MDPtoolbox: Markov Decision Processes Toolbox, R package version 4.0.3

work page 2017

[3] [3]

The Transatlantic Slave Trade and Origins of the African Dias- pora in Texas,

Chambers, G. (2012), “The Transatlantic Slave Trade and Origins of the African Dias- pora in Texas,” http://www.pvamu.edu/tiphc/research-projects/the-diaspora-coming-to- texas/the-transatlantic-slave-trade-and-origins-of-the-african-diaspora-in-texas/. 20

work page 2012

[4] [4]

Fitting variogram models by weighted least squares,

Cressie, N. (1985), “Fitting variogram models by weighted least squares,” Journal of the International Association for Mathematical Geology , 17, 563–586

work page 1985

[5] [5]

Statistics for spatial data,

Cressie, N. (1992), “Statistics for spatial data,” Terra Nova, 4, 613–617

work page 1992

[6] [6]

Kelley, S. M. (2016), The voyage of the slave ship hare: A journey into captivity from Sierra Leone to South Carolina , UNC Press Books

work page 2016

[7] [7]

The origins of the African-born population of Antebellum Texas: A research note,

Kelley, S. M. and Lovejoy, H. B. (2016), “The origins of the African-born population of Antebellum Texas: A research note,” Southwestern Historical Quarterly , 120, 216–232

work page 2016

[8] [8]

(2014), Geographies of the Holocaust, The Spatial

Knowles, A., Cole, T., and Giordano, A. (2014), Geographies of the Holocaust, The Spatial

work page 2014