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Found 10 papers, 3 papers with code
Bayesian Numerical Methods for Nonlinear Partial Differential Equations
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied.
A probabilistic Taylor expansion with Gaussian processes
We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order.
Probabilistic Iterative Methods for Linear Systems
This paper presents a probabilistic perspective on iterative methods for approximating the solution $\mathbf{x}_* \in \mathbb{R}^d$ of a nonsingular linear system $\mathbf{A} \mathbf{x}_* = \mathbf{b}$.
Testing whether a Learning Procedure is Calibrated
A learning procedure takes as input a dataset and performs inference for the parameters $\theta$ of a model that is assumed to have given rise to the dataset.
Bayesian Inference
Statistics Theory
Statistics Theory
Probabilistic Gradients for Fast Calibration of Differential Equation Models
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering.
Optimal Thinning of MCMC Output
The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced.
A Bayesian Conjugate Gradient Method
The estimates obtained in this case are of little value unless further information can be provided about the numerical error.
Methodology Numerical Analysis Numerical Analysis Statistics Theory Statistics Theory
Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment
The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation.
Applications
On the Sampling Problem for Kernel Quadrature
The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the smoothness and dimension of the integrand.
Probabilistic Numerical Methods for PDE-constrained Bayesian Inverse Problems
This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations.
Methodology Numerical Analysis Numerical Analysis Statistics Theory Statistics Theory
