Related papers: Bayesian parameter estimation of miss-specified mo…

Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…

Bayesian inference is a powerful tool for combining information in complex settings, a task of increasing importance in modern applications. However, Bayesian inference with a flawed model can produce unreliable conclusions. This review…

Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…

We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale…

There are many issues that can cause problems when attempting to infer model parameters from data. Data and models are both imperfect, and as such there are multiple scenarios in which standard methods of inference will lead to misleading…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…

Suppose data are fitted to some parametric model but that the true model happens to be one with an additional parameter. When a parameter is to be estimated one can use likelihood estimation in the wider model or in the narrow model.…

Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…

Model selection methods are used in different scientific contexts to represent a characteristic data set in terms of a reduced number of parameters. Apparently, these methods have not found their way into the literature on multibody systems…

Mathematical models are invaluable for understanding and predicting how biological systems behave, although their construction requires specifying mechanisms and relationships that are often not perfectly known. In the presence of multiple…

Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…

Statistical estimation of the prediction uncertainty of physical models is typically hindered by the inadequacy of these models due to various approximations they are built upon. The prediction errors due to model inadequacy can be handled…

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…

Ordinary differential equation (ODE) models are widely used to describe systems in many areas of science. To ensure these models provide accurate and interpretable representations of real-world dynamics, it is often necessary to infer…

The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…

In the context of computer models, calibration is the process of estimating unknown simulator parameters from observational data. Calibration is variously referred to as model fitting, parameter estimation/inference, an inverse problem, and…

Bayesian inference is a powerful tool in gravitational-wave astronomy. It enables us to deduce the properties of merging compact-object binaries and to determine how these mergers are distributed as a population according to mass, spin, and…

Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…

In particle physics, as in many areas of science, parameter inference relies on simulations to bridge the gap between theory and experiment. Recent developments in simulation-based inference have boosted the sensitivity of analyses;…

The application of machine learning to physics problems is widely found in the scientific literature. Both regression and classification problems are addressed by a large array of techniques that involve learning algorithms. Unfortunately,…