[Paper Review] On building and fitting a spatio-temporal change-point model for settlement and growth at Bourewa, Fiji Islands

Geoff K. Nicholls, Patrick D. Nunn|arXiv (Cornell University)|Jun 29, 2010

Pacific and Southeast Asian Studies32 references3 citations

TL;DR

This paper develops a Bayesian spatio-temporal change-point model to infer the onset of human settlement at Bourewa, Fiji, using radiocarbon dates from 60 specimens across 100 pits. By modeling the spatial onset-field as a two-parameter contact process on a lattice, it estimates when deposition began at each location, revealing a central origin and gradual 40–50 meter spread along the beach over 150–200 years, with strong support for a single phase of deposition despite spatial heterogeneity.

ABSTRACT

The Bourewa beach site on the Rove Peninsula of Viti Levu is the earliest known human settlement in the Fiji Islands. How did the settlement at Bourewa develop in space and time? We have radiocarbon dates on sixty specimens, found in association with evidence for human presence, taken from pits across the site. Owing to the lack of diagnostic stratigraphy, there is no direct archaeological evidence for distinct phases of occupation through the period of interest. We give a spatio-temporal analysis of settlement at Bourewa in which the deposition rate for dated specimens plays an important role. Spatio-temporal mapping of radiocarbon date intensity is confounded by uneven post-depositional thinning. We assume that the confounding processes act in such a way that the absence of dates remains informative of zero rate for the original deposition process. We model and fit the onset-field, that is, we estimate for each location across the site the time at which deposition of datable specimens began. The temporal process generating our spatial onset-field is a model of the original settlement dynamics.

Motivation & Objective

• To model the spatio-temporal onset of human occupation at Bourewa, an early Lapita site in Fiji, where no clear stratigraphic phases exist.
• To address confounding from uneven post-depositional thinning of datable material by conditioning inference on the absence of dates being informative of zero deposition rate.
• To estimate the time and spatial pattern of initial human activity, accounting for variable sampling intensity and uncertain phase boundaries.
• To test whether a single-phase model or a multi-phase model better explains the data, using marginal likelihoods and Bayes factors.
• To visualize and quantify the expansion of settlement from a central core to the surrounding beach area using posterior onset-field maps.

Proposed method

• Models the deposition of datable specimens as a Cox process in time, with phase boundaries defined by a second Poisson process, allowing for variable rates across phases.
• Introduces an onset-field process on a 2D lattice, where each cell's onset time is governed by immigration from off-site and local spread from neighboring occupied cells.
• Uses a two-parameter contact process to define the onset-field prior, enabling wave-like expansion patterns resembling the non-linear Fisher equation.
• Applies Bayesian inference with MCMC sampling to estimate the joint posterior of onset times, phase counts, and model parameters, conditioning on the number of dates per pit and their ages.
• Employs marginal likelihood estimation and Bayes factors to compare models with one vs. multiple phases, adjusting for prior bias.
• Validates model robustness by comparing results across four models: single-phase without spatial structure, single-phase with onset-field, random-phase without spatial structure, and random-phase with onset-field.

Experimental results

Research questions

• RQ1 When and where did human occupation begin at the Bourewa site, given the absence of clear stratigraphic phases?
• RQ2 Does the spatial distribution of radiocarbon dates support a single-phase or multi-phase model of deposition?
• RQ3 How does the onset-field model improve upon standard phase models by incorporating spatial dynamics of settlement expansion?
• RQ4 To what extent do confounding processes like post-depositional thinning bias standard radiocarbon dating interpretations?
• RQ5 What is the posterior probability that the settlement began at a central location and spread gradually along the beach?

Key findings

• The posterior mean onset-field map shows that human occupation began in the central area between pits '1', '4', and 'X6', with a gradual spread along the beach over 150–200 years.
• The estimated onset time for the earliest deposition is 3000–3200 years before present, which is more reliable than the 200-year shift toward the present seen in models without an onset-field.
• The marginal likelihoods suggest that the single-phase model is most supported, with estimated Bayes factors of e₁ ≈ 0.8, e₂ ≈ 1, and e₃ ≈ 1.3, indicating no strong evidence for multiple phases.
• The random-phase model with onset-field supports the single-phase hypothesis, serving as a model-mis-specification check that confirms the robustness of the onset-field model.
• Phase assignment in the three-phase model shows a clear spatial trend: phase 3 (earliest) is centered in the middle, phase 2 spreads outward, and phase 1 (latest) is at the periphery, consistent with a wave-of-advance settlement pattern.
• The onset-field model effectively captures the spatial heterogeneity of deposition onset without over-shrinking early dates, unlike models that assume uniform phase boundaries across space.