Related papers: The parameters uncertainty inflation fallacy
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 uncertainty is a crucial issue in statistics, econometrics and machine learning, yet its definition remains ambiguous and is subject to various interpretations in the literature. So far, there has not been a universally accepted…
Models necessarily capture only parts of a reality. Prediction models aim at capturing a future reality. In this paper we address the question of how the future is constructed (or: imagined) in an investment context where market…
In a data-scarce field such as healthcare, where models often deliver predictions on patients with rare conditions, the ability to measure the uncertainty of a model's prediction could potentially lead to improved effectiveness of decision…
Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…
Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…
Dynamical systems are frequently used to model biological systems. When these models are fit to data it is necessary to ascertain the uncertainty in the model fit. Here we present prediction deviation, a new metric of uncertainty that…
With present and future observations becoming of higher and higher quality, it is timely and necessary to investigate the most significant theoretical uncertainties in the predictions of inflation. We show that our ignorance of the entire…
We discuss several aspects of creation of adequate mathematical models in other sciences. In particular, many difficulties stem from great complexity of the source systems and the presence of a variety of uncertain factors. We illustrate…
The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…
Quantum multiparameter estimation focuses on the simultaneous inference of multiple parameters in quantum systems through measurement and data processing. Its complexity stems from two key factors: measurement incompatibility and parameter…
Thermal history models, that have been used to understand the geological history of Earth, are now being coupled to climate models to map conditions that allow planets to maintain surface water over geologic time - a criteria considered…
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…
Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions. However, methods for doing this can be…
Our understanding of physical systems generally depends on our ability to match complex computational modelling with measured experimental outcomes. However, simulations with large parameter spaces suffer from inverse problem instabilities,…
In a real expert system, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. It is important for decision making that the information present in this aggregate somehow find its way into use.…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…
Ensemble forecasts of weather and climate are subject to systematic biases in the ensemble mean and variance, leading to inaccurate estimates of the forecast mean and variance. To address these biases, ensemble forecasts are post-processed…
Deterministic mathematical models, such as those specified via differential equations, are a powerful tool to communicate scientific insight. However, such models are necessarily simplified descriptions of the real world. Generalised…