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HiBASIL: Hierarchical Bayesian Source Inference and Localization for Spatial Epidemiology

HiBASIL is a novel hierarchical Bayesian framework that accurately infers the coordinates and dispersal mechanisms of multiple, overlapping biological sources from sparse, zero-inflated spatial data, demonstrating high precision and broad applicability across agricultural and human disease epidemiology through rigorous simulations and real-world case studies.

Original authors: Guo, F., Bhattacharyya, S., Chatterjee, S., Gent, D., Ojiambo, P.

Published 2026-07-30

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CC BY 4.0

Original authors: Guo, F., Bhattacharyya, S., Chatterjee, S., Gent, D., Ojiambo, P.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine you are a detective trying to solve a mystery, but instead of finding footprints or fingerprints, you are looking at a map covered in dots. Some dots are bright red (sick), some are pale yellow (a little sick), and most are blank white (healthy). Your job is to figure out where the trouble started. Did it start from one hidden factory spewing out trouble? Or maybe two factories working together? And how far did the trouble travel? This is the heart of spatial epidemiology, the science of tracking how diseases or invasions spread across a landscape. The tricky part is that the data is messy. Sometimes everything is perfectly healthy (zero), sometimes everything is completely destroyed (one), and in between, it's a blur. Traditional math tools often break when faced with these "all-or-nothing" extremes, leaving detectives guessing. But what if you had a super-smart, math-powered magnifying glass that could not only find the hidden starting points but also tell you exactly how the trouble traveled, even if the clues were sparse and confusing?

That is exactly what a team of researchers has built with a new tool called HiBASIL. Think of HiBASIL as a digital detective that uses a special kind of "math magic" called Bayesian inference. Instead of just guessing, it weighs every possible scenario—from one hidden source to two, from short-range spread to long-distance jumps—against the actual data it sees. The researchers tested this tool in two very different worlds: first, in a controlled garden where they deliberately infected plants with a fungus called cucurbit downy mildew, and second, by looking back at a famous historical mystery: the 1854 London cholera outbreak.

The results are impressive. In their computer simulations, HiBASIL was a perfect detective, correctly identifying the shape of the "spread trail" (called a dispersal kernel) 100% of the time, even when the data was tricky or the sources were very unbalanced (like one big source and one tiny one contributing only 5% of the trouble). When they applied it to the real-world garden experiments, the tool successfully pinpointed the exact location of the hidden infection sources, even when the researchers didn't tell the computer where to look. It found the sources with an average error of less than half a meter.

Perhaps the most thrilling test was the historical one. The researchers fed the tool the death records from the 1854 London cholera outbreak. Even though the disease actually spread through water pipes and city streets (a complex network), and the tool was designed to look for simple, circular spread, it still managed to zero in on the famous Broad Street pump. It located the source within about 33 meters of the true spot. The tool also proved it could tell the difference between a real mystery and a fake one; when there was no hidden source (like in the control groups of the garden), it correctly said, "There's nothing to see here," rather than inventing a fake culprit.

The paper shows that HiBASIL is a robust, open-source tool that can handle messy, real-world data where other methods struggle. It doesn't just find the "where"; it also figures out the "how" and the "how much," while being honest about its own uncertainty. Whether it's tracking a plant disease in a field or reconstructing a historical epidemic, HiBASIL offers a new way to turn a confusing map of dots into a clear story of where the trouble began.

Technical Summary: HiBASIL – Hierarchical Bayesian Source Inference and Localization

Problem Statement
Identifying the spatial origins of biological invasions, disease outbreaks, or environmental contaminants is critical for intervention, yet existing methods face significant limitations. Current approaches struggle to resolve overlapping signals from multiple sources (multi-focal superposition) and often fail to account for extreme zero/one inflation inherent in bounded spatial data (e.g., disease severity proportions ranging from 0 to 1). Standard statistical models, such as Gaussian processes, produce physically impossible predictions outside the [0, 1] interval, while transformations (e.g., logit) obscure biological interpretation. Furthermore, traditional hierarchical Bayesian frameworks typically require a priori knowledge of source locations, leaving a gap in general statistical methods capable of jointly inferring unknown source coordinates and mechanistic dispersal processes in continuous space.

Methodology
The authors developed HiBASIL (Hierarchical Bayesian Source Inference and Localization), a framework designed to jointly infer source coordinates and mechanistic dispersal kernels from zero-one-inflated spatial observations.

Statistical Core: HiBASIL utilizes a Zero-One-Inflated Beta (ZOIB) likelihood. This three-component mixture model explicitly decomposes structural zeros (healthy/uninfected), structural ones (complete infection/saturation), and continuous infection intensity ( $y \in (0, 1)$ ).
Mechanistic Integration: The framework integrates spatial dispersal kernels (Exponential, Gaussian, and Power Law) directly into the ZOIB parameters via identity link functions. This preserves parameter bounds without transformation. For multiple sources, the model treats the total intensity as a weighted sum of individual kernels, allowing for the deconvolution of overlapping dispersal gradients.
Hierarchical Structure: The model employs partial- or complete-pooling structures across experimental replicates. This allows for the stabilization of estimates in noisy or sparse datasets by borrowing information across replicates while accounting for block-to-block biological variation.
Inference Engine: Implemented in Python using PyMC, the framework employs the No-U-Turn Sampler (NUTS) for Markov Chain Monte Carlo (MCMC) sampling. It utilizes weakly informative priors to allow data dominance while constraining parameters to biologically plausible ranges.
Model Selection & Diagnostics: Model comparison is performed via Leave-One-Out Cross-Validation (LOO-CV) using the Expected Log Pointwise Predictive Density (ELPD). The framework includes intrinsic self-diagnostics: under-parameterization (missing sources) is signaled by posterior bimodality in source locations, while over-parameterization (redundant sources) is signaled by parameter collapse (negligible mixture weights).

Key Contributions

Joint Inference: HiBASIL is the first framework to simultaneously infer unknown source coordinates and mechanistic dispersal kernels in continuous space while handling bounded, zero-one-inflated data.
Multi-Focal Resolution: The method successfully resolves multiple overlapping sources, including minority sources contributing as little as 5% of the total observations, a task where standard clustering or kernel density estimation often fails.
Robustness to Data Sparsity: The framework demonstrates high performance even with sparse sampling (N = 50) and unbalanced foci mixtures.
Self-Diagnostic Capability: The model provides intrinsic signals for structural mismatch (e.g., bimodality indicating hidden sources), preventing the generation of misleading estimates when the model specification does not match the underlying reality.
Open-Source Implementation: The authors provide an open-source Python implementation, making the tool accessible for ecology, epidemiology, and environmental monitoring.

Results
The authors validated HiBASIL through 2,500 simulations and two empirical case studies:

Simulation Performance:
- Kernel Identification: Achieved 100% accuracy in identifying the correct dispersal kernel (Power Law, Exponential, or Gaussian) under correct model specification.
- Localization: Source localization was highly precise with a median bias of 0.11 m in simulations. The framework successfully resolved two-source scenarios even when one source contributed only 5% of the signal.
- Robustness: In under-parameterized scenarios (fitting a single-source model to two-source data), the framework detected the mismatch via posterior bimodality. In over-parameterized scenarios, it correctly collapsed redundant sources to negligible weights.
- Sample Size: Effective inference was maintained at sample sizes as low as N = 50, with parameter recovery improving as sample size increased to N = 500.
Empirical Validation 1: Cucurbit Downy Mildew:
- Applied to field experiments with single and two-foci treatments.
- The Power Law kernel was consistently selected as the best fit, aligning with previous literature on this pathogen.
- The model accurately localized unknown infection sources with sub-meter mean errors, effectively isolating transmission signals from landscape noise despite sparse sampling.
Empirical Validation 2: 1854 London Cholera:
- Applied to historical mortality data to test portability to human epidemiology.
- Despite the mechanistic mismatch (waterborne transmission via a street network vs. the model's assumption of isotropic radial dispersal), HiBASIL localized the Broad Street pump epicenter to within ~33 m.
- The framework correctly rejected a two-foci hypothesis (Broad Street + Little Marlborough Street) in favor of a parsimonious single-source model, even when the two-foci model was heavily favored by informative priors.

Significance
The paper posits that HiBASIL transforms how discrete transmission sources are identified in complex landscapes. By providing a rigorous inverse spatial inference tool that handles the specific statistical challenges of bounded, zero-inflated epidemiological data, it enables accurate source localization across diverse scenarios—from plant disease management to human outbreaks. The framework's ability to operate without a priori source lists and its capacity to signal model misspecification make it a valuable tool for biosecurity, invasion ecology, and environmental monitoring, particularly in situations where data is sparse or sources are unknown. The authors emphasize that while the model assumes isotropic spread, its successful application to the network-driven cholera outbreak demonstrates its utility as a robust signal isolation tool even when mechanistic assumptions are imperfect.

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