Paper List
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Exactly Solvable Population Model with Square-Root Growth Noise and Cell-Size Regulation
This paper addresses the fundamental gap in understanding how microscopic growth fluctuations, specifically those with size-dependent (square-root) no...
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Assessment of Simulation-based Inference Methods for Stochastic Compartmental Models
This paper addresses the core challenge of performing accurate Bayesian parameter inference for stochastic epidemic models when the likelihood functio...
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Realistic Transition Paths for Large Biomolecular Systems: A Langevin Bridge Approach
This paper addresses the core challenge of generating physically realistic and computationally efficient transition paths between distinct protein con...
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MoRSAIK: Sequence Motif Reactor Simulation, Analysis and Inference Kit in Python
This work addresses the computational bottleneck in simulating prebiotic RNA reactor dynamics by developing a Python package that tracks sequence moti...
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The BEAT-CF Causal Model: A model for guiding the design of trials and observational analyses of cystic fibrosis exacerbations
This paper addresses the critical gap in cystic fibrosis exacerbation management by providing a formal causal framework that integrates expert knowled...
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A Theoretical Framework for the Formation of Large Animal Groups: Topological Coordination, Subgroup Merging, and Velocity Inheritance
This paper addresses the core problem of how large, coordinated animal groups form in nature, challenging the classical view of gradual aggregation by...
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ANNE Apnea Paper
This paper addresses the core challenge of achieving accurate, event-level sleep apnea detection and characterization using a non-intrusive, multimoda...
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DeeDeeExperiment: Building an infrastructure for integrating and managing omics data analysis results in R/Bioconductor
This paper addresses the critical bottleneck of managing and organizing the growing volume of differential expression and functional enrichment analys...
Beyond Bayesian Inference: The Correlation Integral Likelihood Framework and Gradient Flow Methods for Deterministic Sampling
Institute of Mathematics, Polish Academy of Sciences | Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw | Institute for Mathematics, Heidelberg University
The 30-Second View
IN SHORT: This paper addresses the core challenge of calibrating complex biological models (e.g., PDEs, agent-based models) with incomplete, noisy, or heterogeneous data, where traditional pointwise comparison methods fail due to system sensitivity and intrinsic variability.
Innovation (TL;DR)
- Methodology Introduces the Correlation Integral Likelihood (CIL) framework, a unified approach for parameter estimation in systems with heterogeneous or chaotic dynamics (e.g., pattern formation, individual-based models), moving beyond classical Bayesian methods.
- Methodology Proposes integration of deterministic gradient flow methods within the CIL framework to enhance inference efficiency and accuracy, compared to traditional stochastic sampling (e.g., MCMC).
- Theory Generalizes the concept of correlation dimension from chaos theory to construct a robust metric for comparing the global geometric structure of model outputs (e.g., attractors, spatial patterns) rather than relying on unstable pointwise comparisons.
Key conclusions
- The CIL method provides a theoretically grounded framework for parameter estimation in systems where solution heterogeneity (e.g., in Turing patterns or chaotic attractors) makes conventional likelihoods ineffective.
- Integrating deterministic gradient flow sampling with the CIL framework can potentially enhance computational efficiency and inference accuracy compared to purely stochastic methods like MCMC, especially for high-dimensional parameter spaces.
- The approach enables reliable model calibration and validation even with incomplete, noisy, or single-snapshot data, advancing the predictive capability and mechanistic understanding of complex biological systems.
Abstract: Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due to limited and noisy data, significant biological variability, and the computational complexity of the models themselves. In this method's article, we explore a range of approaches for parameter inference in partial differential equation (PDE) models of biological systems. We introduce a unified mathematical framework, the Correlation Integral Likelihood (CIL) method, for parameter estimation in systems exhibiting heterogeneous or chaotic dynamics, encompassing both pattern formation models and individual-based models. Departing from classical Bayesian inverse problem methodologies, we motivate the development of the CIL method, demonstrate its versatility, and highlight illustrative applications within mathematical biology. Furthermore, we compare stochastic sampling strategies, such as Markov Chain Monte Carlo (MCMC), with deterministic gradient flow approaches, highlighting how these methods can be integrated within the proposed framework to enhance inference performance. Our work provides a practical and theoretically grounded toolbox for researchers seeking to calibrate complex biological models using incomplete, noisy, or heterogeneous data, thereby advancing both the predictive capability and mechanistic understanding of such systems.