Related papers: Connecting the forward problem to the inverse prob…
Increasingly high-stakes decisions are made using neural networks in order to make predictions. Specifically, meteorologists and hedge funds apply these techniques to time series data. When it comes to prediction, there are certain…
Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…
In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a…
Mathematical models can provide quantitative insight into immunoreceptor signaling, but require parameterization and uncertainty quantification before making reliable predictions. We review currently available methods and software tools to…
We explore the application of uncertainty quantification methods to agent-based models (ABMs) using a simple sheep and wolf predator-prey model. This work serves as a tutorial on how techniques like emulation can be powerful tools in this…
The uncertainty quantification of prediction models (e.g., neural networks) is crucial for their adoption in many robotics applications. This is arguably as important as making accurate predictions, especially for safety-critical…
We propose a novel inverse-modelling approach which estimates the parameters of a simple land-surface model (LSM) by assimilating data into a differentiable physics-based forward model. The governing equations are expressed within a…
Explainability and uncertainty quantification are key to trustable artificial intelligence. However, the reasoning behind uncertainty estimates is generally left unexplained. Identifying the drivers of uncertainty complements explanations…
Accurately characterizing migration velocity models is crucial for a wide range of geophysical applications, from hydrocarbon exploration to monitoring of CO2 sequestration projects. Traditional velocity model building methods such as…
This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a…
Dynamic factor models are often estimated by point-estimation methods, disregarding parameter uncertainty. We propose a method accounting for parameter uncertainty by means of posterior approximation, using variational inference. Our…
Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governing the discretization as part of the unknown to be estimated…
A covariant energy density functional is calibrated using a principled Bayesian statistical framework informed by experimental binding energies and charge radii of several magic and semi-magic nuclei. The Bayesian sampling required for the…
Deep neural network controllers for autonomous driving have recently benefited from significant performance improvements, and have begun deployment in the real world. Prior to their widespread adoption, safety guarantees are needed on the…
Bayesian approaches are one of the primary methodologies to tackle an inverse problem in high dimensions. Such an inverse problem arises in hydrology to infer the permeability field given flow data in a porous media. It is common practice…
This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…
We propose a statistical emulator for a climate-economy deterministic integrated assessment model ensemble, based on a functional regression framework. Inference on the unknown parameters is carried out through a mixed effects hierarchical…