PROJECT 1: Shell Midden Mortuary Inference based on the Globe-Tossing Model

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TL;DR: In this mini project, I adapt a Bayesian "globe-tossing" model to estimate how often Mesolithic shell middens were used for burials by country. This model uses archaeological theory (priors) to analyze small, messy excavation samples by moving beyond raw percentages.

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Project Overview

This project adapts the “globe-tossing model” from Statistical Rethinking Chapter 3 (McElreath, 2020) to an archaeological problem: estimating the prevalence of mortuary deposition within Mesolithic shell middens.

All shell midden data was aquired from the European Archaeological Project on Shell Middens (EAPSM) database (Dupont, n.d.). To ensure methodological clarity and manage uncertainty, Project 1 serves as a regional template by focusing on a single nation's dataset (e.g. France) before expanding to a pan-European analysis in Project 2 (tentative).

The goal is methodological rather than empirical in order to demonstrate how simple Bayesian models can formalize uncertainty, small sample sizes, and theoretical expectations within an archaeological context.

graph TD
    A[EAPSM Database] --> B{Project 1: Template}
    B --> C[Regional Subsets: France/Scotland]
    C --> D[Grid Approximation & Prior Comparison]
    D --> E{Project 2: Synthesis}
    E --> F[Full Dataset: N=339]
    F --> G[Hierarchical/Spatial Modeling]

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Archaeological Motivation

Historically, shell middens have been interpreted primarily as subsistence features, however many contain human burials (Astrup et al., 2021; Brinker et al., 2020; Pickard et al., 2025). Therefore, the archaeological question is not if a Mesolithic shell midden can contain burials, but how frequently Mesolithic people used shell middens for mortuary deposition relative to other depositional practices. Due to the uneven preservation and small excavation samples, raw proportions can be misleading. This mini project reframes this problem as a probabilistic inference. What can be reasonably inferred about the prevalence of mortuary deposition given incomplete observations?

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Conceptual Model

The model treats each midden layer as a binary observation:

1 = human remains present 0 = human remains absent

Each observation updates the belief about an unknown parameter: $p$ = the probability that a midden layer contains human remains

Globe Tossing	Shell Midden Model
Toss	Midden layer sampled
Water	Human remains present
Land	Human remains absent
$p$	Probability of mortuary deposition

Note: $p$ does not represent the frequency of deaths or individuals, but the probability that a midden layer preserves evidence of mortuary deposition given archaeological excavation or survey.

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Statistical Framing

Likelihood The number of layers containing human remains is modeled as a binomial process: $$W \sim \text{Binomial}(N, p)$$

Where: $N$ = number of midden layers examined $W$ = the number of layers with human remains

The goal is to calculate the posterior distribution, which is the probability of the parameter $p$ given our observed data $D$:

$$P(p|W,N) = \frac{\text{Binomial}(W|N,p) \times \text{Beta}(p|\alpha, \beta)}{P(W)}$$

This formulation assumes independence among shell midden layers and equal recovery probability, all of which are to be relaxed in later model extensions.

Priors Different priors reflect different archaeological expectations: Uniform Prior: no strong expectations about mortuary prevalence Skeptical Prior: mortuary use of middens is rare Theory-Informed Prior: mortuary deposition occurs but is not dominant

To make these priors reproducible, I define them using the Beta distribution, $p \sim \text{Beta}(\alpha, \beta)$, where $\alpha$ represents "virtual" successes (burials) and $\beta$ represents "virtual" failures (no burials):

Prior Type	Mathematical Form	Archaeological Justification
Uniform	$p$ ~ Beta(1,1)	Reference Model: used as a control to study the data's influence without theoretical weight
Skeptical	$p$ ~ Beta(1,10)	Conservative Model: assumes middens are primarily for refuse; requires heavy evidence to shift $p$ upward
Theory-Informed	$p$ ~ Beta(2,8)	Applied Model: Reflects the "burial within shell midden" tradition observed in the Atlantic Mesolithic but acknowledges it as a minority practice

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Data and Implementation

Below is the specific "test case" used for this project in R (as of 24 Jan 26)

#Example Implementation (R / rethinking)
#Data source: EAPSM Mesolithic 
observations <- c(1, 0, 1, 1, 0, 0, 0, 1) #1 = burial present, 0 = burial absent
N <- length(observations)
W <- sum(observations)

#Grid Approximation (McElreath, Ch. 3)
p_grid <- seq(from=0, to=1, length.out=1000)
prior  <- dbeta(p_grid, 2, 8) 
likelihood <- dbinom(W, size=N, prob=p_grid)
posterior  <- likelihood * prior
posterior  <- posterior / sum(posterior) #to standardize the distribution

#Extracting 89% HPDI (Highest Posterior Density Interval)
samples <- sample(p_grid, prob=posterior, size=1e4, replace=TRUE)

#Summary Output
#Mean: mean(samples)
#Uncertainty: HPDI(samples, prob=0.89)

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Scope, Limitations, and Future Applications

This project uses complete pooling at the country level. It intentionally ignores more regional spatial trends to focus on studying Bayesian mechanics.

Future Applications with Project 2 and Beyond:

1. utilize the full EAPSM dataset ($N$ = 339)
2. introduce hierarchial modeling (partial pooling) to analyze the spatiotemporal relationships between Mesolithic middens and Neolithic megaliths

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Why This Matters

This project demonstrates:

1. How Bayesian inference can formalize uncertainty in archaeological interpretation
2. Why raw proportions are insufficient for small-N data
3. How theory enters quantitative models through priors
4. Moves archaeology away from "black box" interpretations toward explicit, reproducible code

The model shows what can and cannot be inferred given limited evidence rather than providing a definitive claim about Mesolithic funerary behavior.

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References

Astrup, P. M., Benjamin, J., Stankiewicz, F., Woo, K., McCarthy, J., Wiseman, C., Baggaley, P., Jerbić, K., Fowler, M., Skriver, C., & Bailey, G. (2021). A drowned Mesolithic shell midden complex at Hjarnø Vesterhoved, Denmark and its wider significance. Quaternary Science Reviews, 258, 1–20. https://doi.org/10.1016/j.quascirev.2021.106854

Brinker, U., Bērziņš, V., Ceriņa, A., Gerhards, G., Kalniņš, M., Krause-Kyora, B., Lübke, H., Meadows, J., Meinel, D., Ritchie, K., Rudzīte, M., Tõrv, M., Zagorska, I., & Schmölcke, U. (2020). Two burials in a unique freshwater shell midden: Insights into transformations of Stone Age hunter-fisher daily life in Latvia. Archaeological and Anthropological Sciences, 12. https://doi.org/10.1007/s12520-020-01049-7

Dupont, C. (n.d.). EAPSM - DB [Dataset]. Retrieved December 10, 2025, from https://atlanticshellmiddens.cnrs.fr/index.php

McElreath, R. (2020). Statistical Rethinking: A Bayesian Course with Examples in R and STAN. Chapman and Hall/CRC. https://civil.colorado.edu/~balajir/CVEN6833/bayes- resources/RM-StatRethink-Bayes.pdf

Pickard, C., Greenberg, E., Smith, E., Barlow, A., & Bonsall, C. (2025). Diet, DNA, and the Mesolithic–Neolithic Transition in Western Scotland. Humans. https://doi.org/10.3390/humans5010008