An inverse transformation algorithm to infer parameter distributions from population snapshot data

Wagner, Vincent; Höpfl, Sebastian; Klingel, Viviane; Pop, Maria C.; Radde, Nicole

doi:10.1016/j.ifacol.2023.01.020

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…Empirically, we assume that the temperature y is proportional to the location's cosine of the latitude q. Together with the estimated temperatures of 30 • C at the equator and −30 • C close to the poles, the model reads 30,30], q → y = s(q) := 60 cos (q) − 30.…”

Section: Demonstrating Epi Using An Arithmetic Climate Model To Descr...mentioning

confidence: 99%

“…While they conclude that, in some scenarios, cheap approximation techniques can be used, the same methods fail in other examples. In a review about change of variables formulas, Köthe [29] hints at the use of AD to evaluate the Jacobian and cites our proof of concept work [30] as a first promising try in this direction. Indeed, we strongly encourage employing AD to evaluate the Jacobian in Eq.…”

Section: Generalising Epi Towards the Challenge Of Inferring Variable...mentioning

confidence: 99%

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Eulerian Parameter Inference: A Probabilistic Change of Variables for Model-Based Inference with High-Variability Data Sets

Wagner,

Castellaz,

Kaiser

et al. 2024

Preprint

Self Cite

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Advances in measurement technology have led to the generation of increasingly large data sets across various scientific fields. Data that capture the variability of the underlying system or process, such as single-cell or imaging data, are particularly interesting. However, calibrating computational models to explain this type of data remains challenging. We interpret the model calibration as a Stochastic Inverse Problem (SIP), where the measurements are interpreted as probabilistic samples. Our new SIP solution approach, Eulerian Parameter Inference (EPI), only requires data with high variability and a deterministic simulation model that maps model parameters to simulation results. EPI solves the SIP through a change of variables. This computationally efficient approach allows for direct and point-wise evaluation of parameter densities without ever inverting the simulation model. The resulting parameter distribution captures data variability completely, enabling full data reconstruction. Further, estimating multivariate model parameters can bereduced to a series of one-dimensional problems under the assumption of stochasticallyindependent parameters. Particularly for complex simulation models andinvolved problems, this property is vital. With EPI, we explain 1) annual average temperature data of 3,168 weather stations around the world with an arithmetic model, 2) German district-specific COVID-19 infection data through a differential equation model, and 3) artificial data generated via a partial differential equation model with independent parameters. With a robust mathematical foundation and an easily accessible Python package, we provide a versatile solution framework for integrating data with high variability into simulation models that promotes application to various research questions.

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Section: Demonstrating Epi Using An Arithmetic Climate Model To Descr...mentioning

confidence: 99%

Section: Generalising Epi Towards the Challenge Of Inferring Variable...mentioning

confidence: 99%

Eulerian Parameter Inference: A Probabilistic Change of Variables for Model-Based Inference with High-Variability Data Sets

Wagner,

Castellaz,

Kaiser

et al. 2024

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Eulerian Parameter Inference: a probabilistic change of variables for model-based inference with high-variability data sets

Wagner,

Castellaz,

Kaiser

et al. 2024

Comput. Sci. Eng.

View full text Add to dashboard Cite

Advances in measurement technology have led to the generation of increasingly large data sets across various scientific fields. Data that capture the variability of the underlying system or process, such as single-cell or imaging data, are particularly interesting. However, calibrating computational models to explain this type of data remains challenging.We interpret the model calibration as a Stochastic Inverse Problem (SIP), where the measurements are interpreted as probabilistic samples. Our new SIP solution approach, Eulerian Parameter Inference (EPI), only requires data with large empirical variance and a deterministic simulation model that maps model parameters to simulation results. EPI solves the SIP through a change of variables. This computationally efficient approach allows for direct and point-wise evaluation of parameter densities without ever inverting the simulation model. The resulting parameter distribution captures data variability completely, enabling full data reconstruction. Further, estimating multivariate model parameters can be reduced to a series of one-dimensional problems under the assumption of stochastically independent parameters. This property is vital for complex simulation models and involved problems.With EPI, we explain 1) annual average temperature data of 3168 weather stations around the world with an arithmetic model, 2) German district-specific COVID-19 infection data through a differential equation model, and 3) artificial data generated via a partial differential equation model with independent parameters. With a robust mathematical foundation and an easily accessible package, we provide a versatile solution framework for integrating data with a high variance into simulation models that promotes application to various research questions.

show abstract

An inverse transformation algorithm to infer parameter distributions from population snapshot data

Cited by 2 publications

References 15 publications

Eulerian Parameter Inference: A Probabilistic Change of Variables for Model-Based Inference with High-Variability Data Sets

Eulerian Parameter Inference: A Probabilistic Change of Variables for Model-Based Inference with High-Variability Data Sets

Eulerian Parameter Inference: a probabilistic change of variables for model-based inference with high-variability data sets

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