Estimating Parameters in Physical Models through Bayesian Inversion: A Complete Example

Allmaras, Moritz; Bangerth, Wolfgang; Linhart, Jean Marie; Polanco, Javier; Wang, Fang; Wang, Kainan; Webster, Jennifer; Zedler, Sarah E.

doi:10.1137/100788604

Cited by 43 publications

(43 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Bayesian inference and ensemble model techniques [38–43], are used to compute a sample of the posterior distribution of parameter sets as a way of quantifying the uncertainty in the estimation of parameters. Each parameter set in the sample provides a parametrization of the system of differential equations that yields a potential predicted trajectory of analytes that is sufficiently close to experimental data and obeys the heuristics described above.…”

Section: Methodsmentioning

confidence: 99%

The inflammatory response to influenza A virus (H1N1): An experimental and mathematical study

Price

Mochan

Swigon

et al. 2015

Journal of Theoretical Biology

View full text Add to dashboard Cite

Mortality from influenza infections continues as a global public health issue, with the host inflammatory response contributing to fatalities related to the primary infection. Based on Ordinary Differential Equation (ODE) formalism, a computational model was developed for the in-host response to influenza A virus, merging inflammatory, innate, adaptive and humoral responses to virus and linking severity of infection, the inflammatory response, and mortality. The model was calibrated using dense cytokine and cell data from adult BALB/c mice infected with the H1N1 influenza strain A/PR/8/34 in sublethal and lethal doses. Uncertainty in model parameters and disease mechanisms was quantified using Bayesian inference and ensemble model methodology that generates probabilistic predictions of survival, defined as viral clearance and recovery of the respiratory epithelium. The ensemble recovers the expected relationship between magnitude of viral exposure and the duration of survival, and suggests mechanisms primarily responsible for survival, which could guide the development of immunomodulatory interventions as adjuncts to current anti-viral treatments. The model is employed to extrapolate from available data survival curves for the population and their dependence on initial viral aliquot. In addition, the model allows us to illustrate the positive effect of controlled inflammation on influenza survival.

show abstract

Section: Methodsmentioning

confidence: 99%

The inflammatory response to influenza A virus (H1N1): An experimental and mathematical study

Price

Mochan

Swigon

et al. 2015

Journal of Theoretical Biology

View full text Add to dashboard Cite

show abstract

“…with a normalization constant κ (Allmaras et al, 2013). The likelihood ρ D (d|m), for measurements d given a set of parameters m, is computed by comparing d sim to d obs (assuming a noise-free d obs for the synthetic data).…”

Section: Inversion Methodsmentioning

confidence: 99%

Offset errors in probabilistic inversion of small-loop frequency-domain electromagnetic data: A synthetic study on their influence on magnetic susceptibility estimation

Bobe

Vijver

2019

International Workshop on Gravity, Electrical &Amp; Magnetic Methods and Their Applications, Xi'an, China, 19–22 May 2019

View full text Add to dashboard Cite

Small-loop frequency-domain electromagnetic (FDEM) devices measure a secondary magnetic field caused by the application of a stronger primary magnetic field. Both the in-phase and quadrature component of the secondary field commonly suffer from systematic measurement errors, which would result in a non-zero response in free space. The inphase response is typically strongly correlated to subsurface magnetic susceptibility. Considering common applications on weakly to moderately susceptible grounds, the in-phase component of the secondary field is usually weaker than the quadrature component, making it relatively more prone to systematic errors. Incorporating coil-specific offset parameters in a probabilistic inversion framework, we show how systematic errors in FDEM measurements can be estimated jointly with electrical conductivity and magnetic susceptibility. Including FDEM measurements from more than one height, the offset estimate becomes closer to the true offset, allowing an improved inversion result for the subsurface magnetic susceptibility.

show abstract

“…(8) is to find a solution by calculating the relative entropy projection from the overall prior distribution p 0 (w, γ, y) to the admissible set of distributions p that are consistent with the constraints. In what follows, we develop the computational algorithm to solve this formulation Eq.…”

mentioning

confidence: 99%

DL-CHI: a dictionary learning-based contemporaneous health index for degenerative disease monitoring

Samareh

Huang

2018

EURASIP J. Adv. Signal Process.

View full text Add to dashboard Cite

Developing a knowledge-driven contemporaneous health index (CHI) that can precisely reflect the underlying patient condition across the course of the condition's progression holds a unique value, like facilitating a range of clinical decision-making opportunities. This is particularly important for monitoring degenerative conditions such as Alzheimer's disease (AD), where the condition of the patient will decay over time. Detecting early symptoms and progression signs, and continuous severity evaluation, are all essential for disease management. While a few methods have been developed in the literature, uncertainty quantification of those health index models has been largely neglected. To ensure the continuity of the care, we should be more explicit about the level of confidence in model outputs. Ideally, decision-makers should be provided with recommendations that are robust in the face of substantial uncertainty about future outcomes. In this paper, we aim at filling this gap by developing an uncertainty quantification based contemporaneous longitudinal index, named UQ-CHI, with a particular focus on continuous patient monitoring of degenerative conditions. Our method is to combine convex optimization and Bayesian learning using the maximum entropy learning (MEL) framework, integrating uncertainty on labels as well. Our methodology also provides closed-form solutions in some important decision making tasks, e.g., such as predicting the label of a new sample. Numerical studies demonstrate the effectiveness of the proposed UQ-CHI method in prediction accuracy, monitoring efficacy, and unique advantages if uncertainty quantification is enabled in practice. (Shuai Huang) communications between clinicians, healthcare providers, and patients. It will also be a crucial enabling factor for the development of many envisioned AI systems to implement adaptive interventions for better healthcare management, given a representation of the dynamic evolution of the patient's condition.Thus, to ensure continuity of care, we should be more explicit about our level of confidence in model outputs. Ideally, decision-makers should be provided with recommendations that are robust in the face of substantial uncertainty about future outcomes. However, computational models are an abstraction of clinical observations, as such, they are usually built on analytically tractable assumptions that may simplify the realworld problem. Also, most of these models are estimated from

show abstract

Estimating Parameters in Physical Models through Bayesian Inversion: A Complete Example

Cited by 43 publications

References 18 publications

The inflammatory response to influenza A virus (H1N1): An experimental and mathematical study

The inflammatory response to influenza A virus (H1N1): An experimental and mathematical study

Offset errors in probabilistic inversion of small-loop frequency-domain electromagnetic data: A synthetic study on their influence on magnetic susceptibility estimation

DL-CHI: a dictionary learning-based contemporaneous health index for degenerative disease monitoring

Contact Info

Product

Resources

About