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REVIEW 5 major objections 4 minor 98 references

Comparative study of Bayesian and Frequentist methods for epidemic forecasting: Insights from simulated and historical data

T0 review · 5 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Epidemic forecasting performance depends on outbreak phase and data quality, with Bayesian and frequentist methods each winning in different settings.

desk verdict A useful benchmark whose central phase-dependent claim is contradicted by its own tables, including Bayesian posterior estimates outside the stated prior range. read the letter →

arxiv 2509.05846 v1 pith:B7VB63Y5 submitted 2025-09-06 q-bio.QM

Hamed Karami , Ruiyan Luo , Pejman Sanaei , Gerardo Chowell This is my paper · ORCID
classification q-bio.QM
keywords epidemicforecastingBayesianinferencefrequentistmethodscompartmentalmodelspredictionintervalsweightedintervalscorenonlinearleastsquaresMCMC
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks how to estimate the parameters of a deterministic compartmental epidemic model when the goal is forecasting: should a forecaster use Bayesian estimation (which combines prior beliefs with the data) or frequentist estimation (which fits the curve by minimizing squared error)? The answer, drawn from simulated outbreaks and four historical epidemics, is that the better choice changes with the stage of the outbreak. Frequentist fitting tends to give more accurate single-number forecasts near and after the peak, while Bayesian fitting with uniform priors is more accurate before the peak and produces prediction intervals that more often contain what actually happened—an advantage when data are sparse or noisy. Since both approaches share the same model structure and error assumption, the paper attributes these differences to the estimation framework itself, and recommends selecting a method according to epidemic phase and data quality rather than by statistical allegiance.

What carries the argument

Three deterministic compartmental models (SEIR, SEIRD, SEIUR) with a reporting proportion are calibrated to incident case or death curves. The two estimation paradigms are forced to share the same normal observation-error structure: frequentist calibration is nonlinear least squares with parametric bootstrap for intervals, and Bayesian calibration is posterior sampling (MCMC) with specified priors. Forecasts are evaluated by calibration period (early, pre-peak, peak, post-peak) using MAE and RMSE for point accuracy and WIS plus 95% PI coverage for probabilistic accuracy, which together carry the phase-dependent comparison.

What would settle it

If a fresh set of simulated epidemics with known R0 and peak timing were run through the same calibration/forecast protocol, the claimed phase-dependent ranking should reproduce: Bayesian uniform-prior should win pre-peak and frequentist should win at/post-peak. A failure to reproduce, or a check showing that the reported Bayesian posterior draws for Simulated Data 2 lie outside the stated Uniform(0,1) prior support, would settle against the paper's central claim.

Watch

Extended reading notes

Core claim

The paper's central claim is that the relative merit of Bayesian versus frequentist estimation in epidemic forecasting is phase-dependent, not universal. The authors calibrate three compartmental models (SEIR, SEIRD, SEIUR) with a reporting proportion to case or death curves, using nonlinear least squares with parametric bootstrap for the frequentist side and Bayesian MCMC with a normal likelihood for the Bayesian side, and evaluate forecasts with MAE, RMSE, weighted interval score, and 95% prediction-interval coverage. Across simulated epidemics with R0 = 2 and 1.5 and the 1918 San Francisco flu, 1918 Cumberland flu, 1896–97 Bombay plague, and Switzerland COVID-19, the consistent pattern is

Load-bearing premise

The load-bearing assumption is that the Bayesian sampler enforces the stated priors and bounds; for one simulated dataset the reported posterior medians fall outside those bounds, undermining that dataset's Bayesian comparison.

Editorial extensions

If this is right

  • Selecting an estimation method by epidemic phase is warranted: Bayesian (uniform-prior) for early/pre-peak windows, frequentist for peak/post-peak windows.
  • Studies comparing forecast methods should classify calibration times relative to the epidemic peak, because that classification predicts which method wins.
  • Frequentist confidence intervals are less reliable when the forecast window contains the peak, so interval-based public health decisions should favor Bayesian outputs there.
  • Prior specification is consequential: different priors shift forecast rankings, so published forecasts should report priors.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An adaptive forecaster that begins with a uniform-prior Bayesian estimator and switches to frequentist nonlinear least squares after peak detection could exploit the phase-dependent strengths the paper identifies; the paper does not test such a switching rule.
  • For Simulated Data 2, the reported Bayesian prior-2 posterior medians for ρ at calibration periods 110, 120, and 130 (1.52, 1.34, 4.58) lie outside the stated Uniform(0,1) prior range; if these values are accurate, the Bayesian results for that dataset are not a clean test of the described method, and the low-R0 conclusions should be re-examined.
  • Because only a normal observation-error structure was tested, the phase-dependence may not hold under overdispersed count models such as negative binomial, which are common for real incidence data; repeating the comparison under that error structure is a natural test.
  • The four historical datasets are small and heterogeneous; testing the same protocol on a larger corpus of outbreaks would show whether the phase rule is a general property or an artifact of this particular selection.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 4 minor

Summary. This paper compares a Bayesian implementation (Stan MCMC with a normal likelihood) and a Frequentist implementation (nonlinear least squares with parametric bootstrap) for fitting deterministic compartmental epidemic models and generating forecasts. Performance is assessed with MAE, RMSE, WIS, and 95% PI coverage on two simulated SEIR datasets and four real outbreaks (1918 influenza in San Francisco and Cumberland, Bombay plague, COVID-19 in Switzerland). The paper claims that no estimation framework dominates; Bayesian methods are better pre-peak and provide stronger uncertainty quantification, while Frequentist methods often give better point forecasts and perform well at or after the peak in some real datasets.

Significance. The research question is practically relevant, and the design has genuine strengths: both arms share the same ODE structure and normal error assumption, the evaluation uses standard proper scoring rules, and the scope is explicitly limited to the tested implementations rather than the entire Bayesian/Frequentist paradigms. However, the empirical basis is currently undermined by several internal inconsistencies in the supplementary tables, including posterior estimates outside the stated prior support and duplicated tables for different forecast horizons. These issues directly affect the phase-dependent conclusions, so the findings cannot be accepted as they stand. If the analyses are corrected and the conclusions are recalibrated to the actual tables, the study could become a useful benchmark for selecting estimation methods in epidemic forecasting.

major comments (5)
  1. [Table S6, Tables 1–2] Table S6 reports Bayesian Prior 2 posterior medians for rho as 1.52 (CI 0.59–4.44), 1.34 (0.42–2.12), and 4.58 (4.05–5.19) at calibration periods 110, 120, and 130 for Simulated Data 2. Table 2 specifies rho ~ Uniform(0,1) for both Bayesian priors, so the posterior support is necessarily contained in [0,1]. These values cannot be produced by the stated model. This means the Stan model likely used a different parameterization, the columns were mislabeled, or the MCMC/posterior summary was corrupted. Because the Bayesian performance metrics in Tables S4–S5 at these calibrations support the claimed post-peak Bayesian advantage in Simulated Data 2, the phase-dependent comparison is unsupported until this discrepancy is resolved.
  2. [Abstract; Results, Simulated Data 1, Table S1] The abstract and the results text state that Frequentist methods perform well at peak and post-peak phases. Table S1 (10-day horizon, Simulated Data 1) contradicts this: at calibration 70, which Table S21 labels post-peak, the Frequentist MAE is 196.71 versus Bayesian Prior1 7.45 and Prior2 6.34; at calibration 90, the Frequentist MAE is 34.50 versus 4.85 and 6.87. WIS shows the same pattern. Table S22 also lists Bayesian methods as the best post-peak performers for this dataset. The headline claim is therefore contradicted by the paper's own summary tables.
  3. [Tables S10–S11 and S14–S15] Table S11, labeled as the 30-day forecasting horizon for Cumberland, is identical to Table S10, labeled as the 10-day horizon. Similarly, Table S15, labeled as the 6-biweek horizon for Bombay, is identical to Table S14, labeled as the 4-biweek horizon. Either the tables were copied without updating, or the forecast horizons genuinely produce identical metrics, which is implausible. The discussions in Sections 'Cumberland 1918 Flu' and 'Bombay Plague 1896-97' rely on these tables, so the forecast-horizon results for those datasets are not currently reported in a trustworthy form.
  4. [Simulated Data 1 and 2; Tables 1–2] In both simulated studies, Bayesian Prior 2 is centered at the true parameter values: beta ~ N(0.5,100), gamma ~ N(0.25,100), kappa ~ N(1,100) for Data 1, and the analogous known-true prior for Data 2. Although the variances are large, these priors are oracle-informed and misspecification-free by construction. The simulated-data comparison therefore conflates the Bayesian estimation framework with favorable prior information that would not be available in practice. The authors should either justify this design or include a sensitivity analysis with priors not centered on the generative values; otherwise the strength of the Bayesian early-phase advantage is overstated.
  5. [Results, Simulated Data 1 and 2; Tables S4–S5] The simulated experiments use a single generated trajectory per R0 scenario, with no replication or standard errors for the performance metrics. Statements such as 'Bayesian methods consistently outperform Frequentist approaches across all metrics and calibration periods' (Simulated Data 2) are not supported by the tables; for example, at calibration 100 with a 10-day horizon the Frequentist MAE is 7.95 versus Bayesian values of 14.08 and 14.68, and at calibration 120 with a 30-day horizon the Frequentist MAE is 4.73 versus 5.42 and 5.27. Multiple simulation seeds with interval estimates for MAE/WIS/coverage, or substantially weakened claims, are needed.
minor comments (4)
  1. [Simulated Data 1, Results] There is a placeholder in the text: 'In Section , we discuss parameter identifiability...' The section number is missing.
  2. [Figure S6 caption] The caption says 'the first simulated data' but the figure displays parameter estimates for Simulated Data 2 (R0=1.5).
  3. [Table S20] The iteration-count table uses the labels 'normal' and 'uniform' for Prior 1 and Prior 2, which may confuse readers since both priors include a normal component and a uniform component. Consistent naming would help.
  4. [General] The paper does not include a data/code availability statement. Since both the Bayesian and Frequentist arms use the authors' own toolboxes, providing the exact scripts, Stan models, and data files would be essential for reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation; the comparison is empirical. The strongest non-circular concern is internal (Table S6 rho > 1 under a Uniform(0,1) prior), which is a correctness issue, not a circularity.

full rationale

The paper's central claim is an empirical ranking of Bayesian versus Frequentist forecast performance across simulated and historical epidemics, obtained by running two estimation implementations and tabulating MAE/RMSE/WIS/coverage. There is no derivation chain in which an output equation is identical to an input equation. The Bayesian arm uses priors, and for simulated data Prior 2 is deliberately centered on the true parameter values ('For simulated data, we utilize prior distributions centered around the true parameter values with varying degrees of variance'), but this is an experimental design choice that favors the Bayesian arm rather than a definitional reduction: the forecasts are still generated by solving the ODE and evaluating future trajectories, and the qualitative conclusion ('particularly with uniform priors') is not forced by the prior means. The self-citations to the authors' BayesianFitForecast and QuantDiffForecast toolboxes and to the identifiability tutorial (Chowell et al. 2023) are implementation or background references; they do not supply the phase-dependent performance ranking. The reported posterior medians for rho in Table S6 (1.52, 1.34, 4.58) exceeding the Uniform(0,1) prior support are an internal inconsistency that undermines the stated Bayesian model for Simulated Data 2, but this is a correctness/reproducibility defect, not circular reasoning. Overall the paper is self-contained against external benchmarks and its conclusions are not equivalent to its inputs by construction.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The comparison rests on a chain of design choices: prior hyperparameters, parameter bounds, simulation noise, initial conditions, and a post-hoc phase taxonomy. None of these choices are derived from data; they are inputs that shape the tabulated results.

free parameters (5)
  • Bayesian Prior 2 hyperparameters for simulated data (means set to true parameter values) = e.g., Normal(0.5, 100) for beta in SimData1; Normal(0.375, 100) in SimData2
    Gives the Bayesian method an advantage in simulations because the prior mean equals the true value; results depend on this choice.
  • Frequentist parameter bound ranges = e.g., [0,25] for beta, gamma, kappa in simulated data; [0,2] for SF flu; [0,10] for Bombay
    Author-chosen optimization bounds affect whether the algorithm finds global minima or gets stuck.
  • Simulation noise standard deviation = sigma = 5
    Added to simulated case curves; chosen ad hoc and affects both methods' relative performance.
  • MCMC iteration counts = 20,000 to 400,000 depending on case (Table S20)
    Iteration counts vary by case and were adjusted for convergence, influencing reported posterior precision.
  • Phase mapping for calibration periods = Labels in Table S21 (early, pre-peak, peak, post-peak)
    Assigned post hoc after seeing the results; drives the phase-dependent conclusion.
assumptions (5)
  • domain assumption Structural identifiability of (beta, kappa, gamma, rho) from the observation operators
    Invoked in Models section citing Chowell et al. 2023; necessary for both estimation approaches to recover parameters from data.
  • domain assumption Normal error structure with constant variance and independent observations
    Used in Equations (5)-(7) for both Bayesian and frequentist arms; no autocorrelation or heteroscedasticity is modeled.
  • domain assumption Initial conditions and population sizes known exactly
    Every case study fixes S0, I0, E0, and N; misspecification would bias parameter estimates.
  • standard math ODE solvers produce accurate enough solutions
    Frequentist uses MATLAB ode45; Stan uses its own ODE solver; the comparison assumes both are accurate.
  • domain assumption All Markov chains converged (Rhat below 1.1)
    The text states convergence was ensured but does not report Rhat values for every result; the rho estimates in Table S6 cast doubt on this for SimData2.

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Cite this review

Pith. "Pith review of Comparative study of Bayesian and Frequentist methods for epidemic forecasting: Insights from simulated and historical data." pith.science (2026). https://pith.science/paper/B7VB63Y5

@misc{pith2026250905846,
  author       = {Pith},
  title        = {Pith review of: Comparative study of Bayesian and Frequentist methods for epidemic forecasting: Insights from simulated and historical data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B7VB63Y5}},
  note         = {Machine review of arXiv:2509.05846}
}
read the original abstract

Accurate epidemic forecasting is critical for effective public health interventions. This study compares Bayesian and Frequentist estimation frameworks within deterministic compartmental epidemic models, focusing on nonlinear least squares optimization versus Bayesian inference using MCMC sampling via Stan. We compare forecasting performance under shared modeling structure and error assumptions for specific implementations of both approaches. We assess performance on simulated datasets (with R0 values of 2 and 1.5) and historical datasets including the 1918 influenza pandemic, 1896-97 Bombay plague, and COVID-19 pandemic. Evaluation metrics include Mean Absolute Error, Root Mean Squared Error, Weighted Interval Score, and 95% prediction interval coverage. Forecasting performance depends on epidemic phase and dataset characteristics, with no method consistently outperforming across all contexts. Frequentist methods perform well at peak and post-peak phases but are less accurate pre-peak. Bayesian methods, particularly with uniform priors, offer better early-epidemic accuracy and stronger uncertainty quantification, especially valuable when data are sparse or noisy. Frequentist methods often yield more accurate point forecasts with lower error metrics, though their interval estimates may be less robust. We examine how prior choice influences Bayesian forecasts and how extending forecasting horizons affects convergence. These findings offer practical guidance for choosing estimation strategies tailored to epidemic phase and data quality, supporting more effective public health interventions.

Figures

Figures reproduced from arXiv: 2509.05846 by the authors.

Figure 1
Figure 1. Compartmental diagram of the SEIR model with underreporting. Circles show the epidemiological compartments for the different states of the system. Solid arrows indicate the transitions between compartments. The dashed arrow indicate the source of the observations, which are the newly reported infected individuals. S E I R D Observations are new deaths; y(t) = γρI(t) βSI N κE γ(1 − ρ)I γρI [PITH_FULL_IMAGE:figures/f… view at source ↗
Figure 2
Figure 2. Compartmental diagram of the SEIRD model with underreporting. Circles show the epidemiological compartments for the different states of the system. Solid arrows indicate the transitions between compartments. The dashed arrow indicate the source of the observations, which are the daily deaths. the reporting proportion, and N the total popula￾tion size, which is assumed to be known. The ini￾tial conditions are defined… view at source ↗
Figure 3
Figure 3. Compartmental diagram of the SEIUR model with underreporting. Circles show the epidemiological compartments for the different states of the system. Solid arrows indicate the transitions between compartments. The dashed arrow indicate the source of the observations, which are the newly reported infected individuals. number of reported and unreported infected cases as dS dt = −β (I + U)S N , dE dt = β (I + U)S N − κE,… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: (F). The outbreak peaked on day 54 with 1468 new cases. The first 22 data points are zero, indicating no reported cases initially, likely before widespread virus detection. We fit the number of new reported cases, dC dt , in the SEIUR model to the epidemic curve. Calib…

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Works this paper leans on

98 extracted references · 74 canonical work pages

  1. [1]

    BMC Public Health 23(1), 1500

    Cheng, Chieh and Jiang, Wei-Ming and Fan, Byron and Cheng, Yu-Chieh and Hsu, Ya-Ting and Wu, Hsiao-Yu and Chang, Hsiao-Han and Tsou, Hsiao-Hui (2023) Real-time forecasting of COVID-19 spread according to protective behavior and vaccination: autoregressive integrated moving average models. BMC Public Health 23(1), 1500

    2023

  2. [2]

    BMC Public Health 19, 1--12

    Lutz, Chelsea S and Huynh, Mimi P and Schroeder, Monica and Anyatonwu, Sophia and Dahlgren, F Scott and Danyluk, Gregory and Fernandez, Danielle and Greene, Sharon K and Kipshidze, Nodar and Liu, Leann and others (2019) Applying infectious disease forecasting to public health: a path forward using influenza forecasting examples. BMC Public Health 19, 1--12

    2019

  3. [3]

    PLoS Medicine 17(1), e1003018

    Shearer, Freya M and Moss, Robert and McVernon, Jodie and Ross, Joshua V and McCaw, James M (2020) Infectious disease pandemic planning and response: Incorporating decision analysis. PLoS Medicine 17(1), e1003018

    2020

  4. [4]

    Neural Computing and Applications 35(33), 23671--23681

    Rahimi, Iman and Chen, Fang and Gandomi, Amir H (2023) A review on COVID-19 forecasting models. Neural Computing and Applications 35(33), 23671--23681

    2023

  5. [5]

    SN Computer Science 1(4), 197

    Shinde, Gitanjali R and Kalamkar, Asmita B and Mahalle, Parikshit N and Dey, Nilanjan and Chaki, Jyotismita and Hassanien, Aboul Ella (2020) Forecasting models for coronavirus disease (COVID-19): a survey of the state-of-the-art. SN Computer Science 1(4), 197

    2020

  6. [6]

    Proceedings of the National Academy of Sciences 117(29), 16732--16738

    Bertozzi, Andrea L and Franco, Elisa and Mohler, George and Short, Martin B and Sledge, Daniel (2020) The challenges of modeling and forecasting the spread of COVID-19. Proceedings of the National Academy of Sciences 117(29), 16732--16738

    2020

  7. [7]

    International Journal of Forecasting 38(2), 423--438

    Ioannidis, John PA and Cripps, Sally and Tanner, Martin A (2022) Forecasting for COVID-19 has failed. International Journal of Forecasting 38(2), 423--438

    2022

  8. [8]

    PLoS Computational Biology 18(10), e1010602

    Chowell, Gerardo and Dahal, Sushma and Tariq, Amna and Roosa, Kimberlyn and Hyman, James M and Luo, Ruiyan (2022) An ensemble n-sub-epidemic modeling framework for short-term forecasting epidemic trajectories: Application to the COVID-19 pandemic in the USA. PLoS Computational Biology 18(10), e1010602

    2022

Show all 98 references
  1. [9]

    In: Mathematics of Public Health: Proceedings of the Seminar on the Mathematical Modelling of COVID-19

    Chowell, Gerardo and Rothenberg, Richard and Roosa, Kimberlyn and Tariq, Amna and Hyman, James M and Luo, Ruiyan (2022) Sub-epidemic model forecasts during the first wave of the COVID-19 pandemic in the USA and European hotspots. In: Mathematics of Public Health: Proceedings o...

    2022

  2. [10]

    Scientific Reports 9(1), 683

    McGowan, Craig J and Biggerstaff, Matthew and Johansson, Michael and Apfeldorf, Karyn M and Ben-Nun, Michal and Brooks, Logan and Convertino, Matteo and Erraguntla, Madhav and Farrow, David C and Freeze, John and others (2019) Collaborative efforts to forecast seasonal influen...

    2019

  3. [11]

    BMC Infectious Diseases 14(1), 1--20

    Biggerstaff, Matthew and Cauchemez, Simon and Reed, Carrie and Gambhir, Manoj and Finelli, Lyn (2014) Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: a systematic review of the literature. BMC Infectious Diseases 14(1), 1--20

    2014

  4. [12]

    eLife 4, e09186

    Chretien, Jean-Paul and Riley, Steven and George, Dylan B (2015) Mathematical modeling of the West Africa Ebola epidemic. eLife 4, e09186

    2015

  5. [13]

    PLoS Currents 6

    Chowell, Gerardo and Simonsen, Lone and Viboud, Céline and Kuang, Yang (2014) Is West Africa approaching a catastrophic phase or is the 2014 Ebola epidemic slowing down? Different models yield different answers for Liberia. PLoS Currents 6

    2014

  6. [14]

    Journal of The Royal Society Interface 17(169), 20200447

    Roosa, Kimberlyn and Tariq, Amna and Yan, Ping and Hyman, James M and Chowell, Gerardo (2020) Multi-model forecasts of the ongoing Ebola epidemic in the Democratic Republic of Congo, March--October 2019. Journal of The Royal Society Interface 17(169), 20200447

    2020

  7. [15]

    Bleichrodt, Amanda and Luo, Ruiyan and Kirpich, Alexander and Chowell, Gerardo (2023) Retrospective evaluation of short-term forecast performance of ensemble sub-epidemic frameworks and other time-series models: The 2022-2023 mpox outbreak across multiple geographical scales, ...

    2023

  8. [16]

    Scientific Reports 14(1), 1630

    Chowell, Gerardo and Bleichrodt, Amanda and Dahal, Sushma and Tariq, Amna and Roosa, Kimberlyn and Hyman, James M and Luo, Ruiyan (2024) GrowthPredict: A toolbox and tutorial-based primer for fitting and forecasting growth trajectories using phenomenological growth models. Sci...

    2024

  9. [17]

    Epidemics, 100755

    Charniga, Kelly and Madewell, Zachary J and Masters, Nina B and Asher, Jason and Nakazawa, Yoshinori and Spicknall, Ian H (2024) Nowcasting and forecasting the 2022 US Mpox outbreak: Support for public health decision making and lessons learned. Epidemics, 100755

    2024

  10. [18]

    Journal of the Royal Statistical Society Series A: Statistics in Society 171(2), 319--321

    Gneiting, Tilmann (2008) Probabilistic forecasting. Journal of the Royal Statistical Society Series A: Statistics in Society 171(2), 319--321

    2008

  11. [19]

    Statistical Methods in Medical Research 20(5), 551--570

    Mwambi, H and Ramroop, S and White, LJ and Okiro, EA and Nokes, D James and Shkedy, Z and Molenberghs, Geert (2011) A frequentist approach to estimating the force of infection for a respiratory disease using repeated measurement data from a birth cohort. Statistical Methods in...

    2011

  12. [20]

    Infectious Disease Modelling 2(3), 379--398

    Chowell, Gerardo (2017) Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts. Infectious Disease Modelling 2(3), 379--398

    2017

  13. [21]

    Epidemics 30, 100379

    Chowell, Gerardo and Luo, Ruiyan and Sun, K and Roosa, Kimberlyn and Tariq, Amna and Viboud, C (2020) Real-time forecasting of epidemic trajectories using computational dynamic ensembles. Epidemics 30, 100379

    2020

  14. [22]

    arXiv preprint arXiv:2403.00753

    Pruitt, CD and Lovell, AE and Hebborn, C and Nunes, FM (2024) The role of the likelihood for elastic scattering uncertainty quantification. arXiv preprint arXiv:2403.00753

    2024 arXiv

  15. [23]

    BMC Bioinformatics 13, 1--12

    Transtrum, Mark K and Qiu, Peng (2012) Optimal experiment selection for parameter estimation in biological differential equation models. BMC Bioinformatics 13, 1--12

    2012

  16. [24]

    arXiv preprint arXiv:2402.05342

    Huang, Hsin-Hsiung and He, Qing (2024) Nonlinear regression analysis. arXiv preprint arXiv:2402.05342

    2024 arXiv

  17. [25]

    Statistics in Medicine, Wiley Online Library

    Chowell, Gerardo and Bleichrodt, Amanda and Luo, Ruiyan (2024) Parameter estimation and forecasting with quantified uncertainty for ordinary differential equation models using QuantDiffForecast: A MATLAB toolbox and tutorial. Statistics in Medicine, Wiley Online Library

    2024

  18. [26]

    Statistics in Medicine 40(27), 6209--6234

    Grinsztajn, Léo and Semenova, Elizaveta and Margossian, Charles C and Riou, Julien (2021) Bayesian workflow for disease transmission modeling in Stan. Statistics in Medicine 40(27), 6209--6234

    2021

  19. [27]

    PLoS Computational Biology 20(4), e1011575

    Bouman, Judith A and Hauser, Anthony and Grimm, Simon L and Wohlfender, Martin and Bhatt, Samir and Semenova, Elizaveta and Gelman, Andrew and Althaus, Christian L and Riou, Julien (2024) Bayesian workflow for time-varying transmission in stratified compartmental infectious di...

    2024

  20. [28]

    arXiv preprint arXiv:2011.01808

    Gelman, Andrew and Vehtari, Aki and Simpson, Daniel and Margossian, Charles C and Carpenter, Bob and Yao, Yuling and Kennedy, Lauren and Gabry, Jonah and Bürkner, Paul-Christian and Modrák, Martin (2020) Bayesian workflow. arXiv preprint arXiv:2011.01808

    2020 arXiv

  21. [29]

    Frontiers in Aging Neuroscience 15, 1225816

    Belasso, Clyde J and Cai, Zhengchen and Bezgin, Gleb and Pascoal, Tharick and Stevenson, Jenna and Rahmouni, Nesrine and Tissot, Cécile and Lussier, Firoza and Rosa-Neto, Pedro and Soucy, Jean-Paul and others (2023) Bayesian workflow for the investigation of hierarchical class...

    2023

  22. [30]

    Behavior Research Methods 49, 863--886

    Annis, Jeffrey and Miller, Brent J and Palmeri, Thomas J (2017) Bayesian inference with Stan: A tutorial on adding custom distributions. Behavior Research Methods 49, 863--886

    2017

  23. [31]

    Measurement: Interdisciplinary Research and Perspectives 18(2), 101--109

    Kelter, Riko (2020) Bayesian survival analysis in STAN for improved measuring of uncertainty in parameter estimates. Measurement: Interdisciplinary Research and Perspectives 18(2), 101--109

    2020

  24. [32]

    arXiv preprint arXiv:1808.06399

    Sennhenn-Reulen, Holger (2018) Bayesian regression for a Dirichlet distributed response using Stan. arXiv preprint arXiv:1808.06399

    2018 arXiv

  25. [33]

    arXiv preprint arXiv:1506.06201

    Sorensen, Tanner and Vasishth, Shravan (2015) Bayesian linear mixed models using Stan: A tutorial for psychologists, linguists, and cognitive scientists. arXiv preprint arXiv:1506.06201

    2015 arXiv

  26. [34]

    Methods in Ecology and Evolution 8(3), 339--348

    Monnahan, Cole C and Thorson, James T and Branch, Trevor A (2017) Faster estimation of Bayesian models in ecology using Hamiltonian Monte Carlo. Methods in Ecology and Evolution 8(3), 339--348

    2017

  27. [35]

    Journal of Statistical Software 80, 1--28

    Bürkner, Paul-Christian (2017) brms: An R package for Bayesian multilevel models using Stan. Journal of Statistical Software 80, 1--28

    2017

  28. [36]

    (2020) Outbreak datasets

    Chowell, G. (2020) Outbreak datasets. GitHub Repository. Accessed: 5 Aug 2020. Available at: https://github.com/gchowell/outbreak_datasets

    2020

  29. [37]

    System Dynamics Review 37(4), 283--309

    Andrade, Jair and Duggan, Jim (2021) A Bayesian approach to calibrate system dynamics models using Hamiltonian Monte Carlo. System Dynamics Review 37(4), 283--309

    2021

  30. [38]

    BMC Infectious Diseases 18, 1--15

    Czumbel, Ida and Quinten, Chantal and Lopalco, Pierluigi and Semenza, Jan C and ECDC expert panel working group (2018) Management and control of communicable diseases in schools and other child care settings: systematic review on the incubation period and period of infectiousn...

    2018

  31. [39]

    PloS One 15(4), e0231256

    White, Lauren A and Mordechai, Lee (2020) Modeling the Justinianic Plague: Comparing hypothesized transmission routes. PloS One 15(4), e0231256

    2020

  32. [40]

    arXiv preprint arXiv:2006.02985

    Grinsztajn, L and Semenova, E and Margossian, C.C and Riou, J (2006) Bayesian workflow for disease transmission modeling in Stan. arXiv preprint arXiv:2006.02985

    2006 arXiv

  33. [41]

    Math Biosci Eng 16(5), 4299--313

    Roosa, Kimberlyn and Luo, Ruiyan and Chowell, Gerardo (2019) Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study. Math Biosci Eng 16(5), 4299--313

    2019

  34. [42]

    Journal of the American Statistical Association 102(477), 359--378

    Gneiting, Tilmann and Raftery, Adrian E (2007) Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association 102(477), 359--378

    2007

  35. [43]

    Springer, volume 26

    Kuhn, Max and Johnson, Kjell (2013) Applied Predictive Modeling. Springer, volume 26

    2013

  36. [44]

    University of Nicosia

    University of Nicosia (2018) M4 Competition Competitor’s Guide: Prizes and Rules. University of Nicosia. Accessed: 2023-10-04. Available at: http://www.unic.ac.cy/test/wp-content/uploads/sites/2/2018/09/M4-Competitors-Guide.pdf

    2018

  37. [45]

    PLoS Computational Biology 17(2), e1008618

    Bracher, Johannes and Ray, Evan L and Gneiting, Tilmann and Reich, Nicholas G (2021) Evaluating epidemic forecasts in an interval format. PLoS Computational Biology 17(2), e1008618

    2021

  38. [46]

    Proceedings of the National Academy of Sciences 119(15), e2113561119

    Cramer, Estee Y and Ray, Evan L and Lopez, Velma K and Bracher, Johannes and Brennen, Andrea and Castro Rivadeneira, Alvaro J and Gerding, Aaron and Gneiting, Tilmann and House, Katie H and Huang, Yuxin and others (2022) Evaluation of individual and ensemble probabilistic fore...

    2022

  39. [47]

    arXiv preprint arXiv:2110.13017

    Margossian, Charles C and Hoffman, Matthew D and Sountsov, Pavel and Riou-Durand, Lionel and Vehtari, Aki and Gelman, Andrew (2021) Nested \( R \): Assessing the convergence of Markov chain Monte Carlo when running many short chains . arXiv preprint arXiv:2110.13017

    2021 arXiv

  40. [48]

    PLoS Computational Biology 20(5), e1011200

    Lopez, Velma K and Cramer, Estee Y and Pagano, Robert and Drake, John M and O’Dea, Eamon B and Adee, Madeline and Ayer, Turgay and Chhatwal, Jagpreet and Dalgic, Ozden O and Ladd, Mary A and others (2024) Challenges of COVID-19 Case Forecasting in the US, 2020--2021. PLoS Comp...

    2024

  41. [49]

    Proceedings of the National Academy of Sciences 116(8), 3146--3154

    Reich, Nicholas G and Brooks, Logan C and Fox, Spencer J and Kandula, Sasikiran and McGowan, Craig J and Moore, Evan and Osthus, Dave and Ray, Evan L and Tushar, Abhinav and Yamana, Teresa K and others (2019) A collaborative multiyear, multimodel assessment of seasonal influen...

    2019

  42. [50]

    MMWR Surveillance Summaries 63(Suppl 3), 1--14

    Meltzer, Martin I and Atkins, Charisma Y and Santibanez, Scott and Knust, Barbara and Petersen, Brett W and Ervin, Elizabeth D and Nichol, Stuart T and Damon, Inger K and Washington, Michael L and others (2014) Estimating the future number of cases in the Ebola epidemic—Liberi...

    2014

  43. [51]

    PLoS Computational Biology 15(2), e1006785

    Funk, Sebastian and Camacho, Anton and Kucharski, Adam J and Lowe, Rachel and Eggo, Rosalind M and Edmunds, W John (2019) Assessing the performance of real-time epidemic forecasts: A case study of Ebola in the Western Area region of Sierra Leone, 2014-15. PLoS Computational Bi...

    2019

  44. [52]

    BMC Medicine 15, 1--8

    Chowell, Gerardo and Viboud, Cécile and Simonsen, Lone and Merler, Stefano and Vespignani, Alessandro (2017) Perspectives on model forecasts of the 2014--2015 Ebola epidemic in West Africa: lessons and the way forward. BMC Medicine 15, 1--8

    2017

  45. [53]

    BMC Medicine 21(1), 19

    Bleichrodt, Amanda and Dahal, Sushma and Maloney, Kevin and Casanova, Lisa and Luo, Ruiyan and Chowell, Gerardo (2023) Real-time forecasting the trajectory of monkeypox outbreaks at the national and global levels, July--October 2022. BMC Medicine 21(1), 19

    2023

  46. [54]

    CRC Press

    Banks, Harvey Thomas and Hu, Shuhua and Thompson, W Clayton (2014) Modeling and inverse problems in the presence of uncertainty. CRC Press

    2014

  47. [55]

    Statistics in Medicine 37(29), 4490--4506

    Ganyani, Tapiwa and Faes, Christel and Chowell, Gerardo and Hens, Niel (2018) Assessing inference of the basic reproduction number in an SIR model incorporating a growth-scaling parameter. Statistics in Medicine 37(29), 4490--4506

    2018

  48. [56]

    Theoretical Computer Science 408(1), 4--16

    Girolami, Mark (2008) Bayesian inference for differential equations. Theoretical Computer Science 408(1), 4--16

    2008

  49. [57]

    Mathematical Biosciences 287, 42--53

    Kypraios, Theodore and Neal, Peter and Prangle, Dennis (2017) A tutorial introduction to Bayesian inference for stochastic epidemic models using Approximate Bayesian Computation. Mathematical Biosciences 287, 42--53

    2017

  50. [58]

    Computational Statistics & Data Analysis 71, 434--447

    McKinley, Trevelyan J and Ross, Joshua V and Deardon, Rob and Cook, Alex R (2014) Simulation-based Bayesian inference for epidemic models. Computational Statistics & Data Analysis 71, 434--447

    2014

  51. [59]

    The Pediatric Infectious Disease Journal 20(4), 380--391

    Richardson, Martin and Elliman, David and Maguire, Helen and Simpson, John and Nicoll, Angus (2001) Evidence base of incubation periods, periods of infectiousness and exclusion policies for the control of communicable diseases in schools and preschools. The Pediatric Infectiou...

    2001

  52. [60]

    American Academy of Pediatrics

    Book, Red (2003) Report of the Committee on Infectious Diseases. American Academy of Pediatrics

    2003

  53. [61]

    Bureau of Epidemiology and Center for Disease Control

    Center for Disease Control. Bureau of Epidemiology and Center for Disease Control. Quarantine Division and Center for Prevention Services (US). Quarantine Division and National Center for Prevention Services (US). Division of Quarantine and National Center for Infectious Disea...

    1987

  54. [62]

    Annual Review of Medicine 51(1), 407--421

    Cox, Nancy J and Subbarao, K (2000) Global epidemiology of influenza: past and present. Annual Review of Medicine 51(1), 407--421. Annual Reviews 4139 El Camino Way, PO Box 10139, Palo Alto, CA 94303-0139, USA

    2000

  55. [63]

    Epidemiologic Reviews 18(1), 64--76

    Glezen, W Paul (1996) Emerging infections: pandemic influenza. Epidemiologic Reviews 18(1), 64--76. Citeseer

    1996

  56. [64]

    Journal of the American Medical Association 73(5), 313--318

    Frost, Wade H (1919) The epidemiology of influenza. Journal of the American Medical Association 73(5), 313--318. American Medical Association

    1919

  57. [65]

    Journal of the Royal Society Interface 4(12), 155--166

    Chowell, Gerardo and Nishiura, Hiroshi and Bettencourt, Luis MA (2007) Comparative estimation of the reproduction number for pandemic influenza from daily case notification data. Journal of the Royal Society Interface 4(12), 155--166. The Royal Society London

    2007

  58. [66]

    International Journal of Epidemiology 36(4), 881--889

    Vynnycky, Emilia and Trindall, Amy and Mangtani, Punam (2007) Estimates of the reproduction numbers of Spanish influenza using morbidity data. International Journal of Epidemiology 36(4), 881--889. Oxford University Press

    2007

  59. [67]

    International Journal of Environmental Research and Public Health 16(14), 2487

    kland, Helene and Mamelund, Svenn-Erik (2019) Race and 1918 influenza pandemic in the United States: A review of the literature. International Journal of Environmental Research and Public Health 16(14), 2487. MDPI

    2019

  60. [68]

    Annals of Internal Medicine 172(9), 577--582

    Lauer, Stephen A and Grantz, Kyra H and Bi, Qifang and Jones, Forrest K and Zheng, Qulu and Meredith, Hannah R and Azman, Andrew S and Reich, Nicholas G and Lessler, Justin (2020) The incubation period of coronavirus disease 2019 (COVID-19) from publicly reported confirmed cas...

    2020

  61. [69]

    (2020) Seroprevalence of anti-SARS-CoV-2 IgG antibodies in Geneva, Switzerland (SEROCoV-POP): a population-based study

    Stringhini, Silvia and Wisniak, Ania and Piumatti, Giovanni and Azman, Andrew S and Lauer, Stephen A and Baysson, Hélène and De Ridder, David and Petrovic, Dusan and Schrempft, Stephanie and Marcus, Kailing et al. (2020) Seroprevalence of anti-SARS-CoV-2 IgG antibodies in Gene...

    2020

  62. [70]

    Proceedings of the Royal Society of London

    Kermack, William Ogilvy and McKendrick, Anderson G (1927) A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 115(772), 700--721. The Royal Society London

    1927

  63. [71]

    Journal of Mathematical Biology 64(3), 403--422

    Bacaër, Nicolas (2012) The model of Kermack and McKendrick for the plague epidemic in Bombay and the type reproduction number with seasonality. Journal of Mathematical Biology 64(3), 403--422. Springer

    2012

  64. [72]

    A historical case study and implications for the epidemiology of bubonic plague

    Monecke, Stefan and Monecke, Hannelore and Monecke, Jochen (2009) Modelling the black death. A historical case study and implications for the epidemiology of bubonic plague. International Journal of Medical Microbiology 299(8), 582--593. Elsevier

    2009

  65. [73]

    Mathematical Biosciences 301, 83--92

    Pell, Bruce and Phan, Tin and Rutter, Erica M and Chowell, Gerardo and Kuang, Yang (2018) Simple multi-scale modeling of the transmission dynamics of the 1905 plague epidemic in Bombay. Mathematical Biosciences 301, 83--92. Elsevier

    2018

  66. [74]

    Chaos, Solitons & Fractals 81, 184--196

    Mangiarotti, Sylvain (2015) Low dimensional chaotic models for the plague epidemic in Bombay (1896--1911). Chaos, Solitons & Fractals 81, 184--196. Elsevier

    2015

  67. [75]

    (2024) BayesianFitForecast: An R toolbox for parameter estimation and forecasting with quantified uncertainty in ordinary differential equation models

    Karami, H., Bleichrodt, A., Luo, R., Chowell, G. (2024) BayesianFitForecast: An R toolbox for parameter estimation and forecasting with quantified uncertainty in ordinary differential equation models. Under review

    2024

  68. [76]

    Bias analysis via missing-data methods

    Greenland, Sander (2009) Bayesian perspectives for epidemiologic research: III. Bias analysis via missing-data methods. International Journal of Epidemiology 38(6), 1662--1673. Oxford University Press

    2009

  69. [77]

    American Journal of Epidemiology 187(3), 576--584

    Harel, Ofer and Mitchell, Emily M and Perkins, Neil J and Cole, Stephen R and Tchetgen Tchetgen, Eric J and Sun, BaoLuo and Schisterman, Enrique F (2018) Multiple imputation for incomplete data in epidemiologic studies. American Journal of Epidemiology 187(3), 576--584. Oxford...

    2018

  70. [78]

    American Journal of Epidemiology 153(12), 1222--1226

    Dunson, David B (2001) Commentary: practical advantages of Bayesian analysis of epidemiologic data. American Journal of Epidemiology 153(12), 1222--1226. Oxford University Press

    2001

  71. [79]

    arXiv preprint arXiv:2004.06425

    Martin, Gael M and Frazier, David T and Robert, Christian P (2020) Computing Bayes: Bayesian computation from 1763 to the 21st century. arXiv preprint arXiv:2004.06425

    2020 arXiv

  72. [80]

    (2021) Bayesian statistics and modelling

    van de Schoot, Rens and Depaoli, Sarah and King, Ruth and Kramer, Bianca and M \"a rtens, Kaspar and Tadesse, Mahlet G and Vannucci, Marina and Gelman, Andrew and Veen, Duco and Willemsen, Joukje et al. (2021) Bayesian statistics and modelling. Nature Reviews Methods Primers 1...

    2021

  73. [81]

    Pathogens 11(2), 185

    Dixon, Samuel and Keshavamurthy, Ravikiran and Farber, Daniel H and Stevens, Andrew and Pazdernik, Karl T and Charles, Lauren E (2022) A comparison of infectious disease forecasting methods across locations, diseases, and time. Pathogens 11(2), 185. MDPI

    2022

  74. [82]

    Journal of Mathematical Biology 87(6), 79

    Chowell, Gerardo and Dahal, Sushma and Liyanage, Yuganthi R and Tariq, Amna and Tuncer, Necibe (2023) Structural identifiability analysis of epidemic models based on differential equations: a tutorial-based primer. Journal of Mathematical Biology 87(6), 79. Springer

    2023

  75. [83]

    Bates, Douglas M and Watts, Donald G (1988) Nonlinear regression analysis and its applications. Vol. 2. Wiley, New York

    1988

  76. [84]

    Journal of Computational and Graphical Statistics 21(1), 42--56

    Cao, Jiguo and Huang, Jianhua Z and Wu, Hulin (2012) Penalized nonlinear least squares estimation of time-varying parameters in ordinary differential equations. Journal of Computational and Graphical Statistics 21(1), 42--56. Taylor & Francis

    2012

  77. [85]

    Springer, New York, NY

    Ramsay, James and Hooker, Giles (2017) Dynamic data analysis. Springer, New York, NY

    2017

  78. [86]

    John Wiley & Sons, Hoboken, New Jersey

    Seber, George AF and Wild, Christopher John (2003) Nonlinear regression. John Wiley & Sons, Hoboken, New Jersey

    2003

  79. [87]

    In: Mathematical Modeling for Women’s Health: Collaborative Workshop for Women in Mathematical Biology, 213--237

    Luo, Ruiyan and Herrera-Reyes, Alejandra D and Kim, Yena and Rogowski, Susan and White, Diana and Smirnova, Alexandra (2024) Estimation of time-dependent transmission rate for COVID-19 SVIRD model using predictor--corrector algorithm. In: Mathematical Modeling for Women’s Heal...

    2024

  80. [88]

    SIAM Journal on Scientific and Statistical Computing 3(1), 28--46

    Varah, James M (1982) A spline least squares method for numerical parameter estimation in differential equations. SIAM Journal on Scientific and Statistical Computing 3(1), 28--46. SIAM

    1982

  81. [89]

    Journal of the American Statistical Association 103(484), 1570--1583

    Liang, Hua and Wu, Hulin (2008) Parameter estimation for differential equation models using a framework of measurement error in regression models. Journal of the American Statistical Association 103(484), 1570--1583. Taylor & Francis

    2008

  82. [90]

    Journal of the Royal Statistical Society Series B: Statistical Methodology 69(5), 741--796

    Ramsay, Jim O and Hooker, Giles and Campbell, David and Cao, Jiguo (2007) Parameter estimation for differential equations: a generalized smoothing approach. Journal of the Royal Statistical Society Series B: Statistical Methodology 69(5), 741--796. Oxford University Press

    2007

  83. [91]

    In: Mathematical and Scientific Machine Learning, 781--808

    Rudi, Johann and Bessac, Julie and Lenzi, Amanda (2022) Parameter estimation with dense and convolutional neural networks applied to the FitzHugh--Nagumo ODE. In: Mathematical and Scientific Machine Learning, 781--808. PMLR

    2022

  84. [92]

    Journal of the American Statistical Association 91(436), 1400--1412

    Gelman, Andrew and Bois, Frederic and Jiang, Jiming (1996) Physiological pharmacokinetic analysis using population modeling and informative prior distributions. Journal of the American Statistical Association 91(436), 1400--1412. Taylor & Francis

    1996

  85. [93]

    Biometrics 62(2), 413--423

    Huang, Yangxin and Liu, Dacheng and Wu, Hulin (2006) Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system. Biometrics 62(2), 413--423. Oxford University Press

    2006

  86. [94]

    Computational Statistics 35, 1481--1499

    Huang, Hanwen and Handel, Andreas and Song, Xiao (2020) A Bayesian approach to estimate parameters of ordinary differential equation. Computational Statistics 35, 1481--1499. Springer

    2020

  87. [95]

    , " * write output.state after.block = add.period write newline

    ENTRY address author booktitle chapter doi edition editor eid howpublished institution isbn journal key month note number organization pages publisher school series title type url volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence...

  88. [96]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

  89. [97]

    , " * write output.state after.block = add.period write newline

    ENTRY address archive author booktitle chapter doi edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type url volume year label INTEGERS output.state before.all mid.sentence after.sentence aft...

  90. [98]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.