Mechanistic and Scientific Models - Concept Notes
Routing Summary
Eight synthesis notes (“concept note, no raw source”) covering PyMC-example topics that no ingested paper covers directly: ODE likelihoods, universal differential equations, chaos and data assimilation, jump-diffusion SDEs, popPK dosing decisions, surplus-production fisheries models, Luria-Delbruck / telegraph count likelihoods, and weather-modified dose-response. Citations are from memory and flagged for verification.
- Need the general template for putting an ODE/PDE solver inside a likelihood (gradients, custom Ops, pitfalls)? → Likelihoods Built on Differential Equations (Concept Note)
- Need neural networks inside ODEs, Bayesian treatment? → Universal Differential Equations and Scientific ML (Concept Note)
- Need why chaotic likelihoods are rough and the remedies? → Chaos, Rough Likelihoods and Data Assimilation (Concept Note)
- Need jump-diffusion likelihoods? → Jump-Diffusion and Stochastic Differential Equation Models (Concept Note)
- Need dosing decisions from a popPK posterior? → Population PK Dosing Decisions from the Posterior (Concept Note)
- Need surplus-production state-space models? → Surplus-Production State-Space Models for Fisheries (Concept Note)
- Need Luria-Delbruck or bursting count likelihoods? → Luria-Delbruck and Telegraph Models as Compound Count Likelihoods (Concept Note)
- Need dose-response with weather covariates? → Dose-Response with Weather Covariates in Long-Term Field Trials (Concept Note)
Concept Map
| Concept | Note | Type | Depends On | Key Result |
|---|---|---|---|---|
| ODE-likelihood template | Likelihoods Built on Differential Equations (Concept Note) | definition | adjoint, sensitivities | solve, observe, add noise, differentiate |
| UDE | Universal Differential Equations and Scientific ML (Concept Note) | definition | neural ODE | NN replaces unknown terms |
| Ricker map benchmark | Chaos, Rough Likelihoods and Data Assimilation (Concept Note) | definition | Wood 2010 | rough trajectory-matching likelihood |
| Merton mixture density | Jump-Diffusion and Stochastic Differential Equation Models (Concept Note) | theorem | compound Poisson | Poisson-weighted normals |
| PTA and EU dosing | Population PK Dosing Decisions from the Posterior (Concept Note) | definition | popPK posterior | PTA peaks about 0.90 for 900-1200 mg q12h |
| Schaefer state-space model | Surplus-Production State-Space Models for Fisheries (Concept Note) | definition | logistic growth | MSY |
| LD recursion; Poisson-Beta | Luria-Delbruck and Telegraph Models as Compound Count Likelihoods (Concept Note) | theorem | compound Poisson | |
| Weather-modified Mitscherlich | Dose-Response with Weather Covariates in Long-Term Field Trials (Concept Note) | definition | Hierarchical Models |
Notes
- Likelihoods Built on Differential Equations (Concept Note) — CONTAINS: template, design-choice table, custom Op/VJP sketch, pitfalls, runnable fit.
- Universal Differential Equations and Scientific ML (Concept Note) — CONTAINS: UDE definition, Bayesian issue table, forward-model code.
- Chaos, Rough Likelihoods and Data Assimilation (Concept Note) — CONTAINS: Ricker benchmark, strategy table (synthetic likelihood, multiple shooting, data assimilation, particle MCMC), verified Lyapunov code.
- Jump-Diffusion and Stochastic Differential Equation Models (Concept Note) — CONTAINS: Merton model, mixture theorem, Euler vs exact, verified density check.
- Population PK Dosing Decisions from the Posterior (Concept Note) — CONTAINS: PTA, expected-utility dosing, verified PTA table.
- Surplus-Production State-Space Models for Fisheries (Concept Note) — CONTAINS: Schaefer SSM, identifiability table, verified collapse simulation.
- Luria-Delbruck and Telegraph Models as Compound Count Likelihoods (Concept Note) — CONTAINS: LD model and recursion (verified), telegraph Poisson-Beta (SSA-verified), identifiability.
- Dose-Response with Weather Covariates in Long-Term Field Trials (Concept Note) — CONTAINS: weather-modified curve, economic-optimum theorem, simulation.
Sources
No raw sources; see each note’s source field for literature to verify. Related ingested material: Synthetic Likelihood - Overview, Neural Simulation-Based Inference - Overview, ODE Filters and Smoothers.
See Also
Margossian 2022 - Bayesian Pharmacometrics - Overview, Chen 2018 - Neural ODEs - Overview.