Joshua C. Macdonald

My work determines what actions to take, what experiments to run, and what measurements are worth collecting in systems where interventions are costly and uncertainty is unavoidable. I build the computational machinery — generative models, scientific machine learning methods, inference algorithms, forecasting pipelines, and design and evaluation tools — that makes this possible for partially observed systems across health, environmental, and earth sciences; concretely, the infectious disease tools are developed for CDC-funded scenario modeling that contributes to the process used to set influenza vaccination policy, while other tools support wildlife disease surveillance design in sub-Saharan Africa and public health resource allocation. Prediction alone is not enough; the structural assumptions buried in every model must be exposed, tested, and defended before anyone acts on the output.

Currently I am a postdoctoral scholar at the International Vaccine Access Center at Johns Hopkins, where I develop operational infectious disease forecasting and decision support systems for ACCIDDA, a CDC Center for Forecasting and Outbreak Analytics collaboration. This work contributes scenario projections to the CDC Flu Scenario Modeling Hub, which supports public health resource allocation and intervention timing. I also collaborate with the Jolles Lab at Oregon State University on cross-scale modeling of Crimean–Congo hemorrhagic fever (CCHF) in wildlife and livestock systems, designing surveillance strategies that balance information gain against field cost. Previously I was a Zuckerman STEM Leadership Fellow at Tel Aviv University, working with Yoav Ram on Bayesian dimensionality reduction for incomplete cultural and genetic datasets.

I hold a PhD in Mathematics from the University of Louisiana at Lafayette and a BA in Archaeology from UNC Greensboro — a combination that continues to shape how I think about inference from incomplete records.

---

The common structure

Every system I work on shares the same architecture: a latent process we care about, an observation process that distorts it, and the data we actually get. Whether the latent state is disease prevalence in a wildlife herd, nutrient cycling in a marine ecosystem, or cultural trait frequencies in a human population, the challenge is identical — the thing we need to make decisions about is never directly observed. The figure below maps this architecture across four domains.

This is not just a conceptual analogy. The mathematical structure is shared: each domain requires a generative model that encodes how hidden states produce observables, an inference engine that inverts the observation process under uncertainty, and a decision layer that translates posterior beliefs into actionable recommendations. Building this infrastructure so that it transfers across domains — rather than rebuilding it from scratch for each application — is the central goal of my research program.

The operational tools I build reflect this shared structure and compose into a stack — from model specification to numerical integration to orchestration to evaluation:

• Model specification. OP System provides a declarative language for specifying structured dynamical systems with multi-axis stratification; the compiler produces validated model objects consumed by downstream solvers.
• Numerical integration. OP Engine is an operator-partitioned ODE/PDE solver core with nine methods (explicit, IMEX, fully implicit), adaptive stepping, and zero per-step allocation.
• Orchestration. FlepiMoP2 drives configuration-driven batch campaigns over locations and scenarios, connecting the specification and solver stack to CDC scenario modeling hubs and contributing projections used in influenza vaccination policy.
• Design and evaluation. trade-study uses simulators with known ground truth to score competing configurations — model formulations, solver choices, measurement strategies, or any design decision — against ground truth using proper scoring rules and multi-objective Pareto optimization, so that decisions validated on benchmarks transfer to real data.
• Dimensionality reduction. vbpca-py and pp-eigentest recover latent population structure from incomplete datasets with full posterior uncertainty and principled rank determination.

Where this is going

The research program moves along three axes. First, enable decisions: determine what intervention to deploy, what experiment to run, and what to measure next — then package these recommendations into tested, documented, open-source software with CI pipelines so that collaborators and decision-makers can act on model output they have reason to trust. Second, harden the inference: build reusable tools for Bayesian rank selection (pp-eigentest), multi-objective design and evaluation (trade-study), and missing-data-native dimensionality reduction (vbpca-py) that work across application areas. Third, generalize: extend the partially observed decision framework to new domains and new classes of systems — multi-host zoonoses, marine ecosystems, cultural evolution, spatial processes.

The question that ties it all together: what should we do, given what we can’t observe?

---

Software

Tool	What it does	Status
op_system	Declarative language & compiler for structured dynamical systems	Active development · docs
op_engine	Operator-partitioned ODE/PDE solver (9 methods, adaptive, zero-alloc)	Developed for CDC-funded flu scenario modeling · docs
flepimop2	Configuration-driven orchestration for forecasting & scenario analysis	Active development · CDC scenario modeling
trade-study	Design & evaluation: score competing configurations against known ground truth via simulators, scoring rules, Pareto optimization, stacking	Released on PyPI (Python + Julia) · docs
vbpca-py	Variational Bayesian PCA for incomplete data with full posterior uncertainty	Released on PyPI · JOSS submission in preparation
pp-eigentest	Posterior predictive eigenvalue testing for signal rank determination	Pre-release · companion to arXiv:2409.12129

---

Methods & Expertise

These capabilities are deployed to design interventions, optimize surveillance strategies, and determine what experiments and measurements are worth their cost.

Modeling. Generative models (ODE/PDE/stochastic/hybrid); compartmental and agent-based models; scientific machine learning (physics-embedded surrogates, lawful learning); multivariate data analysis and dimensionality reduction; stability, bifurcation, and sensitivity analysis; parameter identifiability and inverse problems.

Inference. Bayesian hierarchical models; variational and simulation-based inference; data assimilation; uncertainty quantification; model calibration and validation; proper scoring rules and forecast evaluation.

Scientific computing. Python, Julia, C++, Stan, R, MATLAB. High-performance numerical solvers; operator splitting; reproducible workflows (Git, CI/CD, containerization); data pipelines and exploratory analysis.