Comparing Data Assimilation and Likelihood-Based Inference on Latent State Estimation in Agent-Based Models

Blas Kolic; Corrado Monti; Gianmarco De Francisci Morales; Marco Pangallo

arxiv: 2509.17625 · v3 · submitted 2025-09-22 · 💻 cs.LG · cs.CY· physics.soc-ph· stat.ME

Comparing Data Assimilation and Likelihood-Based Inference on Latent State Estimation in Agent-Based Models

Blas Kolic , Corrado Monti , Gianmarco De Francisci Morales , Marco Pangallo This is my paper

Pith reviewed 2026-05-18 15:08 UTC · model grok-4.3

classification 💻 cs.LG cs.CYphysics.soc-phstat.ME

keywords agent-based modelsdata assimilationlikelihood-based inferencelatent state estimationopinion dynamicsbounded confidence model

0 comments

The pith

Likelihood-based inference recovers latent agent opinions more accurately than data assimilation in bounded-confidence models.

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

The paper systematically compares data assimilation and likelihood-based inference for recovering hidden agent states that drive observable time series in agent-based models. Data assimilation approximates the likelihood in a model-agnostic manner and is therefore broadly applicable, while likelihood-based inference uses a hand-crafted model-specific likelihood for greater precision at the cost of requiring that function to be derived. On the bounded-confidence opinion dynamics model, likelihood-based inference recovers individual agent opinions more accurately and improves individual-level forecasts, even when the model is misspecified. At aggregate levels the two approaches perform comparably, with data assimilation remaining competitive under some parameter choices. The work therefore indicates that the preferred method depends on whether the target is agent-level or group-level accuracy.

Core claim

When applied to the Bounded-Confidence Model, likelihood-based inference recovers the latent opinions of individual agents more accurately than data assimilation, leading to better individual-level forecasts. This advantage holds even under model misspecification. At the aggregate level, both methods deliver comparable performance, with data assimilation remaining competitive depending on parameter settings.

What carries the argument

The Bounded-Confidence Model, in which agents interact only with others holding sufficiently similar opinions, serves as the testbed for comparing how data assimilation and likelihood-based inference estimate evolving latent microstates from observable time series.

If this is right

Likelihood-based inference is preferable when the goal is accurate recovery of individual agent states.
Data assimilation remains suitable for aggregate-level predictions across varying degrees of aggregation.
The performance advantage of likelihood-based inference at the agent level persists even when the model used for inference does not perfectly match the data-generating process.
Method choice can be guided by the required level of resolution rather than a blanket preference for one approach.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

For agent-based models whose interaction rules make an exact likelihood intractable, data assimilation may still be the only practical route to any level of forecast.
The pattern of results could be tested in other domains such as epidemiological or financial agent-based models that also track latent individual behaviors.
Extending the comparison to models with qualitatively different interaction rules would show whether the agent-level advantage of likelihood-based inference is general.

Load-bearing premise

A tractable, hand-crafted likelihood function can be derived for the agent-based model under study.

What would settle it

Observing that data assimilation recovers individual agent opinions more accurately than likelihood-based inference on the bounded-confidence model under misspecification would falsify the central performance claim.

Figures

Figures reproduced from arXiv: 2509.17625 by Blas Kolic, Corrado Monti, Gianmarco De Francisci Morales, Marco Pangallo.

**Figure 1.** Figure 1: Estimation results for LBI and DA for two levels of ϵ. The box plots in the center represent the reconstruction error on the y-axis at the end of training (T = 250) for DA and LBI (x-axis). Beside each box, we depict one of the corresponding traces, with the true (in black) and estimated (blue for DA, red for LBI) positions in one single estimation experiment (whose error is represented with a star in the … view at source ↗

**Figure 2.** Figure 2: Estimation results for LBI and DA under noisy and mis-specified scenarios. Each row corresponds to a different setting: weak noise (σ = 0.0004, top), strong noise (σ = 0.0016, middle), and mis-specified confidence bound ϵ (bottom, polarization and consensus regimes swapped). Otherwise, settings are identical to those of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Forecasting accuracy of DA and LBI in the observation space. Boxplots show normalized mean absolute error (MAE) at three levels of granularity: edge (interaction-level), node (number of interactions per agent), and global (total number of interactions over time). Results are reported for polarization (ϵ = 0.2, left) and consensus (ϵ = 0.3, right). In polarization, LBI achieves substantially lower forecas… view at source ↗

read the original abstract

In this paper, we present the first systematic comparison of Data Assimilation (DA) and Likelihood-Based Inference (LBI) in the context of an Agent-Based Model (ABM). These models generate observable time series driven by evolving, partially-latent microstates. Latent states must be estimated to align simulations with real-world data, a task traditionally addressed by DA, particularly in continuous and equation-based models used in weather forecasting. However, the nature of ABMs poses challenges for standard DA methods. Solving such issues requires adapting previous DA techniques or using ad hoc alternatives such as LBI. DA approximates the likelihood in a model-agnostic way, making it broadly applicable but potentially less precise. In contrast, LBI provides more accurate state estimation by directly leveraging the model's likelihood, but at the cost of requiring a hand-crafted, model-specific likelihood function, which may be complex or infeasible to derive. We compare the two methods on the Bounded-Confidence Model, a well-known opinion dynamics ABM, where agents are affected only by others holding sufficiently similar opinions. We find that LBI better recovers latent agent-level opinions, even under model mis-specification, leading to improved individual-level forecasts. At the aggregate level, however, both methods perform comparably, and DA remains competitive across levels of aggregation under certain parameter settings. Our findings suggest that DA is well-suited for aggregate predictions, while LBI is preferable for agent-level inference.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

LBI recovers individual opinions better than DA in the bounded confidence model while both match at aggregate level, but the single-model scope limits how far the advice travels.

read the letter

The main thing to know is that this paper runs a direct comparison of data assimilation and likelihood-based inference for estimating hidden agent states in an agent-based model, and finds LBI does better at recovering individual opinions even when the model is misspecified, while the two methods perform similarly once you aggregate up to population trends. They test this on the bounded confidence model and break results out by level of aggregation and by parameter settings where DA stays competitive. That distinction is the useful part. The work is new because it is the first head-to-head on this task for ABMs rather than continuous equation-based systems. The experiments are internally consistent, they include misspecification checks, and they give clear patterns on when each method is preferable for forecasting. That supplies practical guidance for people who actually run these simulations against data. The soft spot is the narrow scope. Everything rests on one model with a simple pairwise similarity rule. For ABMs that use networks, group updates, or different thresholds the hand-crafted likelihood may become harder to derive or less accurate, and the paper does not test whether the micro-level advantage reverses. The stress-test note correctly flags that the method-selection claim is extrapolated from a single case. This paper is for computational social scientists and opinion dynamics researchers who need to choose an inference tool when aligning ABMs to real time series. Readers who care about agent-level forecasts will find the level-specific results directly applicable. It deserves a serious referee because the comparison is clean, the results are reproducible from the described setup, and the question it answers is one that modelers face in practice. I would send it out for review.

Referee Report

1 major / 1 minor

Summary. The paper presents the first systematic comparison of Data Assimilation (DA) and Likelihood-Based Inference (LBI) for latent state estimation in Agent-Based Models (ABMs). Focusing on the Bounded-Confidence Model, the authors show that LBI better recovers latent agent-level opinions even under model mis-specification, leading to improved individual-level forecasts. At the aggregate level, both methods perform comparably, and DA remains competitive under certain parameter settings. The findings lead to suggestions that DA is suitable for aggregate predictions while LBI is preferable for agent-level inference.

Significance. This work is significant in providing empirical guidance on choosing between model-agnostic DA and precise but model-specific LBI for ABMs. The distinction between agent-level and aggregate performance is a key insight for practitioners in opinion dynamics and complex systems. The results on the Bounded-Confidence Model are internally consistent, but the single-model scope limits the broader impact.

major comments (1)

[Abstract] The recommendation that LBI is preferable for agent-level inference (Abstract) is based exclusively on experiments with the Bounded-Confidence Model. The manuscript provides no tests on ABMs with qualitatively different interaction rules (e.g., network topology effects or multi-agent group updates), where the tractability of the hand-crafted likelihood could degrade differently than DA's approximation and potentially reverse the observed micro-level performance gap.

minor comments (1)

[Abstract] The abstract does not detail error bars or full controls for the reported patterns, although the internal consistency of the agent-level versus aggregate distinctions is noted.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The major comment correctly identifies a scope limitation in our study. We address this point directly below and propose targeted revisions to qualify our claims without overstating generalizability.

read point-by-point responses

Referee: [Abstract] The recommendation that LBI is preferable for agent-level inference (Abstract) is based exclusively on experiments with the Bounded-Confidence Model. The manuscript provides no tests on ABMs with qualitatively different interaction rules (e.g., network topology effects or multi-agent group updates), where the tractability of the hand-crafted likelihood could degrade differently than DA's approximation and potentially reverse the observed micro-level performance gap.

Authors: We agree that the empirical results and the resulting recommendation in the abstract are derived from the Bounded-Confidence Model (BCM). This model was deliberately chosen because it is a standard, well-studied ABM for which an exact likelihood can be derived, enabling a direct and controlled comparison between LBI and DA. Our central contribution is to demonstrate that, in settings where both approaches are applicable, LBI recovers latent agent states more accurately than DA at the individual level. We do not assert that this micro-level advantage necessarily extends to every ABM; as the referee notes, in models with more complex interaction structures the computational cost or feasibility of constructing the likelihood could shift the relative performance. To address the concern, we will revise the abstract to state that the preference for LBI applies to the BCM and similar models where the likelihood remains tractable. We will also add a dedicated paragraph in the discussion section that explicitly acknowledges the single-model scope, discusses how likelihood tractability may vary across ABM families, and outlines this as an important direction for future comparative work. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical comparison of established methods on fixed ABM

full rationale

The paper performs a direct empirical comparison of Data Assimilation versus Likelihood-Based Inference on the Bounded-Confidence Model, reporting performance differences from simulation experiments at agent, aggregate, and forecast levels. No derivation chain, first-principles result, or prediction is claimed that reduces by construction to fitted inputs, self-definitions, or self-citations. The central findings rest on observable experimental outcomes rather than any mathematical equivalence or load-bearing prior result from the same authors. This is the standard case of a self-contained empirical study whose claims can be checked against the reported runs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work applies standard DA and LBI techniques to one established ABM without introducing new free parameters, axioms beyond domain assumptions, or invented entities.

axioms (1)

domain assumption The Bounded-Confidence Model is a representative test case for challenges in latent state estimation within opinion dynamics ABMs.
Used as the sole experimental platform for the comparison.

pith-pipeline@v0.9.0 · 5813 in / 1207 out tokens · 20060 ms · 2026-05-18T15:08:50.644155+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages · 1 internal anchor

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S. Wiese, J. Kaszowska-Mojsa, J. Dyer, J. Moran, M. Pangallo, F. Lafond, J. Muellbauer, A. Ca- linescu, and J. D. Farmer. Forecasting macroe- conomic dynamics using a calibrated data- driven agent-based model.arXiv preprint arXiv:2409.18760, 2024. 7

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P. Windrum, G. Fagiolo, and A. Moneta. Empir- ical validation of agent-based models: Alterna- tivesandprospects.Journal of Artificial Societies and Social Simulation, 10(2):8, 2007. 2 13 A Appendix In this appendix, we present additional figures that complement the results discussed in the main text. A.1 Latent State Reconstruction Aggregate reconstructio...

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[1] [1]

Benedetti, G

M. Benedetti, G. Catapano, F. De Sclavis, M. Fa- vorito, A. Glielmo, D. Magnanimi, and A. Muci. Black-it: A ready-to-use and easy-to-extend cali- bration kit for agent-based models.Journal of Open Source Software, 7(79):4622, 2022. 2

work page 2022

[2] [2]

Brenner and C

T. Brenner and C. Werker. A taxonomy of in- ference in simulation models.Computational Economics, 30:227–244, 2007. 2

work page 2007

[3] [3]

Cranmer, J

K. Cranmer, J. Brehmer, and G. Louppe. The frontier of simulation-based inference.Proceed- ings of the National Academy of Sciences, 117 (48):30055–30062, 2020. 2

work page 2020

[4] [4]

Deffuant, D

G. Deffuant, D. Neau, F. Amblard, and G. Weis- buch. Mixing Beliefs among Interacting Agents. Advances in Complex Systems, 03(01n04):87–98,

work page

[5] [5]

1, 2, 6, 7

doi: 10.1142/S0219525900000078. 1, 2, 6, 7

work page doi:10.1142/s0219525900000078

[6] [6]

Fagiolo, M

G. Fagiolo, M. Guerini, F. Lamperti, A. Mon- eta, and A. Roventini. Validation of agent-based modelsineconomicsandfinance.Computer simu- lation validation: fundamental concepts, method- ological frameworks, and philosophical perspec- tives, pages 763–787, 2019. 2

work page 2019

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Grazzini and M

J. Grazzini and M. Richiardi. Estimation of er- godic agent-based models by simulated minimum distance.Journal of Economic Dynamics and Control, 51:148–165, 2015. 2

work page 2015

[8] [8]

P. L. Houtekamer and F. Zhang. Review of the ensemble kalman filter for atmospheric data as- similation.Monthly Weather Review, 144(12): 4489–4532, 2016. 8

work page 2016

[9] [9]

Kim, T.-S

D. Kim, T.-S. Yun, I.-C. Moon, and J. W. Bae. Automatic calibration of dynamic and heteroge- neous parameters in agent-based models.Au- tonomous Agents and Multi-Agent Systems, 35 (2):46, 2021. 2

work page 2021

[10] [10]

Kolic, J

B. Kolic, J. Sabuco, and J. D. Farmer. Estimat- ing initial conditions for dynamical systems with incomplete information.Nonlinear Dynamics, 108(4):3783–3805, 2022. 2, 8

work page 2022

[11] [11]

Lanchier

N. Lanchier. The critical value of the deffuant model equals one half.ALEA, 9(2):383–402, 2012. 7

work page 2012

[12] [12]

Lenti, C

J. Lenti, C. Monti, and G. De Francisci Morales. Likelihood-Based Methods Improve Parameter Estimation in Opinion Dynamics Models. InIn- ternational Conference on Web Search and Data Mining, WSDM, pages 350–359. ACM, Mar. 2024. doi: 10.1145/3616855.3635785. 2, 8

work page doi:10.1145/3616855.3635785 2024

[13] [13]

Lenti, F

J. Lenti, F. Silvestri, and G. De Francisci Morales. Variational Inference of Parameters in Opinion Dynamics Models, Mar. 2024. 2, 8

work page 2024

[14] [14]

H.-L. Li. A straightforward proof of the critical value in the Hegselmann-Krause model: up to one-half, Aug. 2024. URL http://arxiv.org/ abs/2408.03718. arXiv:2408.03718 [math]. 7

work page arXiv 2024

[15] [15]

J. Lorenz. Continuous opinion dynamics under bounded confidence: A survey.International Journal of Modern Physics C, 18(12):1819–1838,

work page

[16] [16]

Lux and R

T. Lux and R. C. Zwinkels. Empirical validation of agent-based models. InHandbook of com- putational economics, volume 4, pages 437–488. Elsevier, 2018. 2

work page 2018

[17] [17]

Monti, G

C. Monti, G. De Francisci Morales, and F. Bonchi. Learning opinion dynamics from social traces. In Proceedings of the 26th ACM SIGKDD Inter- national Conference on Knowledge Discovery & Data Mining, pages 764–773, 2020. 2, 7, 8

work page 2020

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Pangallo and R

M. Pangallo and R. M. del Rio-Chanona. Data- driven economic agent-based models.arXiv preprint arXiv:2412.16591, 2024. 2 12

work page arXiv 2024

[19] [19]

Pangallo, A

M. Pangallo, A. Aleta, R. M. del Rio-Chanona, A. Pichler, D. Martín-Corral, M. Chinazzi, F. La- fond, M. Ajelli, E. Moro, Y. Moreno, A. Vespig- nani, and J. D. Farmer. The unequal effects of the health–economy trade-off during the covid-19 pandemic.Nature Human Behaviour, pages 1–12,

work page

[20] [20]

D. Platt. A comparison of economic agent-based model calibration methods.Journal of Economic Dynamics and Control, 113:103859, 2020. 2

work page 2020

[21] [21]

S. F. Railsback and V. Grimm.Agent-based and individual-based modeling: a practical introduc- tion. Princeton University Press, 2019. 1

work page 2019

[22] [22]

Sebastiani

F. Sebastiani. Evaluation measures for quantification: an axiomatic approach.In- formation Retrieval Journal, 23(3):255–288, June 2020. ISSN 1386-4564, 1573-7659. doi: 10.1007/s10791-019-09363-y. URL https://link.springer.com/10.1007/ s10791-019-09363-y. 11

work page doi:10.1007/s10791-019-09363-y 2020

[23] [23]

Opinion dynamics: Statistical physics and beyond

M. Starnini, F. Baumann, T. Galla, D. Garcia, G. Iñiguez, M. Karsai, J. Lorenz, and K. Sznajd- Weron. Opinion dynamics: Statistical physics and beyond.arXiv preprint arXiv:2507.11521,

work page internal anchor Pith review arXiv

[24] [24]

Stephens

M. Stephens. Dealing with label switching in mixture models.Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62 (4):795–809, 2000. 11

work page 2000

[25] [25]

Tang and N

D. Tang and N. Malleson. Data assimilation with agent-based models using markov chain sampling. arXiv preprint arXiv:2205.01616, 2022. 2

work page arXiv 2022

[26] [26]

Wiese, J

S. Wiese, J. Kaszowska-Mojsa, J. Dyer, J. Moran, M. Pangallo, F. Lafond, J. Muellbauer, A. Ca- linescu, and J. D. Farmer. Forecasting macroe- conomic dynamics using a calibrated data- driven agent-based model.arXiv preprint arXiv:2409.18760, 2024. 7

work page arXiv 2024

[27] [27]

Wilensky and W

U. Wilensky and W. Rand.An introduction to agent-based modeling: modeling natural, social, and engineered complex systems with NetLogo. Mit Press, 2015. 1

work page 2015

[28] [28]

Windrum, G

P. Windrum, G. Fagiolo, and A. Moneta. Empir- ical validation of agent-based models: Alterna- tivesandprospects.Journal of Artificial Societies and Social Simulation, 10(2):8, 2007. 2 13 A Appendix In this appendix, we present additional figures that complement the results discussed in the main text. A.1 Latent State Reconstruction Aggregate reconstructio...

work page 2007