A Bayesian model calibration framework for stochastic compartmental models with both time-varying and time-invariant parameters
Bibliographic record
Abstract
We consider state and parameter estimation for compartmental models having both time-varying and time-invariant parameters. In this manuscript, we first detail a general Bayesian computational framework as a continuation of our previous work. Subsequently, this framework is specifically tailored to the susceptible-infectious-removed (SIR) model which describes a basic mechanism for the spread of infectious diseases through a system of coupled nonlinear differential equations. The SIR model consists of three states, namely, the susceptible, infectious, and removed compartments. The coupling among these states is controlled by two parameters, the infection rate and the recovery rate. The simplicity of the SIR model and similar compartmental models make them applicable to many classes of infectious diseases. However, the combined assumption of a deterministic model and time-invariance among the model parameters are two significant impediments which critically limit their use for long-term predictions. The tendency of certain model parameters to vary in time due to seasonal trends, non-pharmaceutical interventions, and other random effects necessitates a model that structurally permits the incorporation of such time-varying effects. Complementary to this, is the need for a robust mechanism for the estimation of the parameters of the resulting model from data. To this end, we consider an augmented state vector, which appends the time-varying parameters to the original system states whereby the time evolution of the time-varying parameters are driven by an artificial noise process in a standard manner. Distinguishing between time-varying and time-invariant parameters in this fashion limits the introduction of artificial dynamics into the system, and provides a robust, fully Bayesian approach for estimating the time-invariant system parameters as well as the elements of the process noise covariance matrix. This computational framework is implemented by leveraging the robustness of the Markov chain Monte Carlo algorithm permits the estimation of time-invariant parameters while nested nonlinear filters concurrently perform the joint estimation of the system states and time-varying parameters. We demonstrate performance of the framework by first considering a series of examples using synthetic data, followed by an exposition on public health data collected in the province of Ontario.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.022 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".