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A comparative study of simulation-based inference methods for epidemic models with identifiability considerations.

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7 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

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  1. [1] § 4. Methods › 4.5. Experiments › 4.5.1. Methodological configurations. ↔ temp_backup/src/inference.py, lines 40–87 · score 0.72 · Euclidean distance, quantile epsilon, simulation budgets, configuration, population, ABC
  2. [2] § 4. Methods › 4.5. Experiments › 4.5.1. Methodological configurations. ↔ temp_backup/src/distance.py, lines 4–17 · score 0.64 · L2 norm, Euclidean distance, trajectories, epidemic, simulation
  3. [3] § 4. Methods › 4.5. Experiments › 4.5.1. Methodological configurations. ↔ temp_backup/src/embedding.py, the whole file · a weak match · score 0.61 · embedding network, NPE LSTM, bidirectional, dropout, hidden, layer
  4. [4] § 4. Methods › 4.2. Simulation-based inference › 4.2.3. Neural Posterior Estimation with temporal embedding (NPE-LSTM). ↔ temp_backup/src/embedding.py, the whole file · a weak match · score 0.60 · fully connected, embedding network, NPE, LSTM
  5. [5] § 4. Methods › 4.5. Experiments › 4.5.2. Computational environment. ↔ temp_backup/src/utils.py, lines 8–27 · score 0.53 · PyTorch, Python, reproducibility, NumPy
  6. [6] § 4. Methods › 4.4. Performance metrics › 4.4.5. Computational runtime. ↔ temp_backup/src/inference.py, lines 139–174 · score 0.52 · generating simulated, refines, NPE LSTM, SMC, preconditioning, populations
  7. [7] § 4. Methods › 4.4. Performance metrics › 4.4.2. Quantitative metrics. ↔ episbi/metric.py, lines 139–175 · score 0.51 · weighted interval score, MAE, coverage, metrics, error

Paper

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The authors' code

Python · 174 lines · 6.8 KB · no license · 2 matches

  1. import torch
  2. import torch.nn as nn
  3. import pyabc
  4. import tempfile
  5. from sbi.inference import NPE
  6. from sbi.neural_nets import posterior_nn
  7. from .embedding import LSTMembedding
  8. from .distance import euclidean_distance
  11. class SBIEngine:
  12. """
  13. Unified Inference Engine for Epidemic Models.
  14. Provides three main methods: run_abc, run_npe, and run_pnpe.
  15. """
  16. def __init__(self, density_estimator='maf', device='cpu', batch_size=256):
  17. """
  18. Initialize the inference engine.
  19. Args:
  20. density_estimator (str): Type of flow-based model ('maf' or 'nsf').
  21. device (str): Device for neural network training ('cpu' or 'cuda').
  22. batch_size (int): Batch size for NPE training.
  23. low (list): Lower bounds for uniform prior.
  24. high (list): Upper bounds for uniform prior.
  25. """
  26. self.de_type = density_estimator
  27. self.device = device
  28. self.batch_size = batch_size
  30. def _get_neural_net(self, use_embedding=False, input_dim=1):
  31. """Builds the neural posterior architecture (MAF/NSF) with optional
  32. LSTM embedding."""
  33. embedding_net = (LSTMembedding(input_dim=input_dim).to(self.device)
  34. if use_embedding else nn.Identity())
  35. return posterior_nn(
  36. model=self.de_type,
  37. embedding_net=embedding_net
  38. )
  40. def run_abc(self, obs_data, prior, simulator_func, distance=None,
  41. num_simulations=10000, population_size=1000,
  42. num_samples=10000):
  43. """
  44. Runs Approximate Bayesian Computation (ABC) with SMC.
  45. Args:
  46. obs_data (dict): Observed data in dictionary format
  47. (e.g.,{"data":array}).
  48. prior: pyabc.Distribution object.
  49. simulator_func: Simulator function returning a dictionary.
  50. num_simulations (int): Total simulation budget.
  51. population_size (int): Size of the ABC population.
  52. num_samples (int): Number of samples to draw from the posterior.
  53. """
  54. print("[*] Running SMC-ABC...")
  55. if distance is None:
  56. distance = euclidean_distance
  58. if not isinstance(obs_data, dict):
  59. obs_data = {"data": obs_data}
  61. def simulator_pyabc(x):
  62. return {"data": simulator_func(x)}
  64. # Configure Epsilon and Transition as requested
  65. eps = pyabc.QuantileEpsilon(initial_epsilon='from_sample', alpha=0.2)
  66. transition = pyabc.MultivariateNormalTransition(scaling=0.5)
  68. abc = pyabc.ABCSMC(
  69. simulator_pyabc,
  70. prior,
  71. distance,
  72. eps=eps,
  73. transitions=transition,
  74. population_size=population_size
  75. )
  77. db_path = "sqlite:///" + tempfile.mkstemp(suffix=".db")[1]
  78. abc.new(db_path, obs_data)
  80. history = abc.run(max_total_nr_simulations=num_simulations)
  82. # Draw samples from the posterior distribution
  83. df, weights = history.get_distribution()
  84. kde = pyabc.transition.MultivariateNormalTransition()
  85. kde.fit(df, weights)
  87. return kde.rvs(num_samples)
  89. def run_npe(self, obs_data, prior=None, thetas=None, xs=None,
  90. use_lstm=False, input_dim=1,
  91. learning_rate=0.001, num_samples=10000, batch_size=256):
  92. """
  93. Runs Neural Posterior Estimation (NPE).
  94. Args:
  95. prior: sbi prior object.
  96. thetas (Tensor): Simulated parameters.
  97. xs (Tensor): Simulated trajectories.
  98. use_lstm (bool): Whether to use LSTM embedding (NPE-LSTM).
  99. learning_rate (float): Optimizer learning rate.
  100. num_samples (int): Number of samples to draw from the posterior.
  101. batch_size (int or None): Training batch size.
  102. """
  103. batch_size = batch_size if batch_size is not None else self.batch_size
  105. print(f"[*] Running NPE (use_lstm={use_lstm}) with batch size "
  106. f"{batch_size}...")
  108. # 1. Handle Observation Data (Convert to Tensor)
  109. if isinstance(obs_data, dict):
  110. x_obs = torch.tensor(obs_data["data"], dtype=torch.float32).to(self.device)
  111. else:
  112. x_obs = torch.tensor(obs_data, dtype=torch.float32).to(self.device)
  114. # 2. Normalization Logic (Z-score)
  115. if xs.dim() >= 2:
  116. # Calculate stats along the batch and sequence dimensions
  117. mean_xs = xs.mean(dim=0, keepdim=True)
  118. std_xs = xs.std(dim=0, keepdim=True) + 1e-6
  119. xs = (xs - mean_xs) / std_xs
  120. x_obs = (x_obs - mean_xs.squeeze(0)) / std_xs.squeeze(0)
  122. # 3. Setup and Train
  123. neural_net = self._get_neural_net(use_embedding=use_lstm,
  124. input_dim=input_dim)
  125. inference = NPE(prior=prior, density_estimator=neural_net,
  126. device=self.device)
  128. density_estimator = inference.append_simulations(thetas, xs).train(
  129. training_batch_size=batch_size,
  130. learning_rate=learning_rate,
  131. show_train_summary=True
  132. )
  134. posterior = inference.build_posterior(density_estimator)
  135. samples = posterior.sample((num_samples,), x=x_obs)
  137. return posterior, samples
  139. def run_pnpe(self, obs_data, pyabc_prior, sbi_prior, simulator_func,
  140. num_simulations=10000, num_samples=10000, batch_size=256):
  141. """
  142. Runs Preconditioned Neural Posterior Estimation (PNPE).
  143. Stage 1: ABC-SMC preconditioning to narrow parameter space.
  144. Stage 2: Training NPE on the refined region.
  145. """
  146. print("[*] PNPE Stage 1: ABC Preconditioning...")
  148. # Step 1: Rapid ABC-SMC to find the high-probability region
  149. refined_thetas = self.run_abc(
  150. obs_data,
  151. pyabc_prior,
  152. simulator_func,
  153. num_simulations=num_simulations//2,
  154. population_size=100,
  155. num_samples=num_simulations//2
  156. )
  158. print("[*] PNPE Stage 2: Training NPE with preconditioned samples...")
  160. thetas_t = torch.tensor(refined_thetas.values, dtype=torch.float32)
  162. # Generate simulations for the refined parameters
  163. xs_list = []
  164. for i, p in refined_thetas.iterrows():
  165. sim_res = simulator_func(p)
  166. xs_list.append(torch.tensor(sim_res, dtype=torch.float32))
  167. xs_t = torch.stack(xs_list)
  169. # Step 2: Train NPE (NPE-LSTM is standard for PNPE)
  170. _, samples = self.run_npe(obs_data, sbi_prior, thetas_t, xs_t,
  171. use_lstm=True, num_samples=num_samples,
  172. batch_size=batch_size)
  174. return samples

inference.py at commit 4b03ef1, no license · at the source

Overview

Authors: Geunsoo Jang1, K Selçuk Candan1, Gerardo Chowell2,3
ORCID iDs: Geunsoo Jang
  1. School of Computing and Augmented Intelligence, Arizona State University, Tempe, Arizona, United States of America
  2. Department of Population Health Sciences, School of Public Health, Georgia State University, Atlanta, Georgia, United States of America
  3. Department of Applied Mathematics, Kyung Hee University, Yongin, Korea
Institutions: Arizona State University (United States); Georgia State University (United States); Kyung Hee University (South Korea)
Journal: PLoS computational biology, volume 22, issue 6, article e1014364
Dates: received 16 October 2025; accepted 26 May 2026; published online 2 June 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1371/journal.pcbi.1014364 · PMID 42228739 · PMCID PMC13252848 · OpenAlex W7163199700
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: computational modeling (no new data) (modality), human (organism), computational (subfield)
Methods: Graphs, Machine learning
MeSH: Computer Simulation*, Epidemics*, Epidemiological Models*, Models, Biological*, Algorithms, Bayes Theorem, Computational Biology, Humans, Likelihood Functions (* major topic)
Topic: COVID-19 epidemiological studies (Modeling and Simulation, Mathematics), according to OpenAlex
Funding: National Science Foundation (2412115, 2435886)
Citations: not cited yet (Europe PMC); 60 references in the paper

Abstract

Epidemic models play a critical role in understanding transmission dynamics, generating forecasts, and informing public health interventions when they are properly calibrated to epidemiological data. Traditional Bayesian inference methods rely on the likelihood function to update prior knowledge using observed data. However, for realistic epidemic models, likelihood functions are often analytically intractable or computationally prohibitive, which can limit the applicability of these methods. Simulation-based inference provides a promising alternative by approximating posterior distributions through forward simulations rather than an explicit likelihood evaluation. In this study, we present a systematic comparison of four approaches: Approximate Bayesian Computation (ABC), Neural Posterior Estimation (NPE), a neural method with temporal embedding, and Preconditioned Neural Posterior Estimation (PNPE), which integrates elements of both classical and neural techniques. These methods are evaluated across epidemic models of increasing complexity under fixed simulation budgets and varying levels of observational noise, with explicit attention to both structural and practical identifiability. Our results show that neural methods generally improve posterior fidelity and predictive accuracy compared with ABC under constrained simulation budgets. PNPE achieved strong performance in several simulation settings, whereas temporal embeddings improved inference in models with complex epidemic dynamics by capturing sequential dependencies. These gains come with important trade-offs: PNPE required substantially greater computational resources and, unlike fully amortized NPE-based methods, may require reconditioning for each new observation. In contrast, ABC remained computationally efficient and provided reasonable, though often more conservative, posterior estimates. Overall, our findings highlight trade-offs among computational efficiency, posterior accuracy, uncertainty calibration, and inference reusability, suggesting that method selection should depend on model complexity, data quality, identifiability, and available computational resources.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above, with 7 matches between paragraphs and lines of code.

geunsoojang/EpiSBI

License: none: the authors keep all their rights
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: 4b03ef1342fb10f2e3f47f275a3d05f16750682d, 5 August 2026
Languages: Jupyter (37), Python (25)
Size: 81 files, 62 scripts
Software Heritage: not archived
Found in: “Data Availability”
Holds: README, environment (pyproject.toml, requirements.txt), 37 notebooks
Not found: license file, CITATION.cff, tests, continuous integration, documentation
Tools: NumPy (54 files), pandas (36 files), Matplotlib (31 files), PyTorch (26 files), SciPy (22 files), SymPy (4 files), h5py (1 file), Numba (1 file), scikit-learn (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
63 files
At the source: github.com/geunsoojang/EpiSBI

The paper's code and data availability statement is in the Data section.

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Data

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Data Availability

All data and code used in this study are publicly available in an online repository. The code and processed datasets can be accessed at: https://github.com/geunsoojang/EpiSBI.

Reproduced under the paper's license (CC BY), from the paper cited above.

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Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 9 MeSH terms, 1 funder, 37 references.

Cite

This paper

Jang, G., Candan, K. S., & Chowell, G. (2026). A comparative study of simulation-based inference methods for epidemic models with identifiability considerations. PLoS computational biology, 22(6), e1014364. https://doi.org/10.1371/journal.pcbi.1014364

BibTeX

@article{jang2026comparative,
author = {Jang, Geunsoo and Candan, K Selçuk and Chowell, Gerardo},
title = {{A comparative study of simulation-based inference methods for epidemic models with identifiability considerations}},
journal = {PLoS computational biology},
year = {2026},
month = jun,
volume = {22},
number = {6},
pages = {e1014364},
publisher = {PLOS},
issn = {1553-734X},
doi = {10.1371/journal.pcbi.1014364},
url = {https://doi.org/10.1371/journal.pcbi.1014364},
pmid = {42228739},
pmcid = {PMC13252848}
}

RIS

TY - JOUR
AU - Jang, Geunsoo
AU - Candan, K Selçuk
AU - Chowell, Gerardo
TI - A comparative study of simulation-based inference methods for epidemic models with identifiability considerations
T2 - PLoS computational biology
J2 - PLoS Comput Biol
PY - 2026
DA - 2026/06/02
VL - 22
IS - 6
SP - e1014364
SN - 1553-734X
PB - PLOS
DO - 10.1371/journal.pcbi.1014364
UR - https://doi.org/10.1371/journal.pcbi.1014364
LA - en
ER -

CSL-JSON

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