Parameter estimation and uncertainty quantification using information geometry

Sharp, John; Browning, Alexander P; Burrage, Kevin; Simpson, Matthew J.

doi:10.1098/rsif.2021.0940

Cited by 9 publications

(2 citation statements)

References 113 publications

(244 reference statements)

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“…Since shrinkage in the posterior distribution is facilitated through the global behaviour of the model likelihood, (1.1) is able to capture uncertainty arising from complex model fits, such as bimodality in the likelihood surface. As with traditional approaches to PI, δ u is a local measure of information gain, in the sense that changing the true dynamics θ∗ will, in general, give different answers [15]. This allows the effect of particular values of θ∗ to be studied.…”

Section: Introductionmentioning

confidence: 99%

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Accurately summarizing an outbreak using epidemiological models takes time

Case,

Young,

Hébert-Dufresne

2023

R. Soc. open sci.

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Recent outbreaks of Mpox and Ebola, and worrying waves of COVID-19, influenza and respiratory syncytial virus, have all led to a sharp increase in the use of epidemiological models to estimate key epidemiological parameters. The feasibility of this estimation task is known as the practical identifiability (PI) problem. Here, we investigate the PI of eight commonly reported statistics of the classic susceptible–infectious–recovered model using a new measure that shows how much a researcher can expect to learn in a model-based Bayesian analysis of prevalence data. Our findings show that the basic reproductive number and final outbreak size are often poorly identified, with learning exceeding that of individual model parameters only in the early stages of an outbreak. The peak intensity, peak timing and initial growth rate are better identified, being in expectation over 20 times more probable having seen the data by the time the underlying outbreak peaks. We then test PI for a variety of true parameter combinations and find that PI is especially problematic in slow-growing or less-severe outbreaks. These results add to the growing body of literature questioning the reliability of inferences from epidemiological models when limited data are available.

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Section: Introductionmentioning

confidence: 99%

“…Open Sci. 10: 230634 true dynamics u Ã will, in general, give different answers [15]. This allows the effect of particular values of u Ã to be studied.…”

Section: Introductionmentioning

confidence: 99%

Accurately summarizing an outbreak using epidemiological models takes time

Case,

Young,

Hébert-Dufresne

2023

R. Soc. open sci.

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Uncertainty quantification in real-time parameter updating for digital twins using Bayesian inverse mapping models

Kessels,

Fey,

van de Wouw

2024

Nonlinear Dyn

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To achieve its full predictive potential, a digital twin must consistently and accurately reflect its physical counterpart throughout its operational lifetime.To this end, the inverse mapping parameter updating method enables physically interpretable parameter values to be updated, in real-time, for a wide range of (nonlinear) dynamical models using features extracted from measured response data. This paper proposes to extend this method by employing a probabilistic Bayesian neural network, which is trained offline using simulated data, to infer, again in real-time, probability distributions for the updating parameter values instead of (traditionally obtained) point estimates. As a result, the user obtains a quantification of the (un)certainty, providing insight into the degree of trust to be placed in the updated parameter values, which supports the decision-making process for which the digital twin is used. Additionally, it is proposed to include so-called ‘input parameters’ (that characterize the specific settings on the physical setup) as inputs to the neural network to allow for a broader applicability of the updating method. To validate the proposed methodology, it is applied, using both simulated and real-world measurements, to a medical mechanical ventilation system, in which information about uncertainty in the inferred parameter values is important. Parameter values of this system and their uncertainties are shown to be inferred with sufficient accuracy.

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A Continuation Technique for Maximum Likelihood Estimators in Biological Models

Cassidy

2023

Bull Math Biol

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Estimating model parameters is a crucial step in mathematical modelling and typically involves minimizing the disagreement between model predictions and experimental data. This calibration data can change throughout a study, particularly if modelling is performed simultaneously with the calibration experiments, or during an on-going public health crisis as in the case of the COVID-19 pandemic. Consequently, the optimal parameter set, or maximal likelihood estimator (MLE), is a function of the experimental data set. Here, we develop a numerical technique to predict the evolution of the MLE as a function of the experimental data. We show that, when considering perturbations from an initial data set, our approach is significantly more computationally efficient that re-fitting model parameters while producing acceptable model fits to the updated data. We use the continuation technique to develop an explicit functional relationship between fit model parameters and experimental data that can be used to measure the sensitivity of the MLE to experimental data. We then leverage this technique to select between model fits with similar information criteria, a priori determine the experimental measurements to which the MLE is most sensitive, and suggest additional experiment measurements that can resolve parameter uncertainty.

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Parameter estimation and uncertainty quantification using information geometry

Cited by 9 publications

References 113 publications

Accurately summarizing an outbreak using epidemiological models takes time

Accurately summarizing an outbreak using epidemiological models takes time

Uncertainty quantification in real-time parameter updating for digital twins using Bayesian inverse mapping models

A Continuation Technique for Maximum Likelihood Estimators in Biological Models

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