Bayes–Hermite quadrature

By Anthony OʼHagan. 1991

Subfields: Numerical Methods & Scientific Computing

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In Numerical Methods & Scientific Computing

Citations in the corpus

On the Equivalence between Herding and Conditional Gradient Algorithms (2012, methodology): “from a given distribution), the Bayes-Hermite quadrature of O’Hagan (1991) essentially computes an orthogonal projection of μ onto the affine hull of this set of points.”
Convergence guarantees for kernel-based quadrature rules in misspecified settings (2016, methodology): “Reproducing kernel Hilbert spaces (RKHS) have been successfully used for this purpose, with examples being Quasi Monte Carlo (QMC) methods based on RKHSs [13] and Bayesian quadratures [19]; see e.”
Control functionals for Monte Carlo integration (2014, methodology): “These include (a) importance sampling and its extensions (Cornuet et al., 2012; Li et al., 2013), (b) stratified sampling and related techniques (Rubinstein and Kroese, 2011), (c) antithetic variables (Green and Han, 1992) and more generally (randomized) quasi- Monte-Carlo (RQMC) sampling (Dick and ”
Optimally-Weighted Herding is Bayesian Quadrature (2012, methodology): “These methods operate by directly minimising some sort of discrepancy between the empirical distribution of pseudo-samples and the target distribution.”
Probabilistic machine learning and artificial intelligence (2015, background): “More generally, Bayesian optimization is a special case of Bayesian numerical computation 75,76 , which is re-emerging as a very active area of research (http://www.probabilistic-numerics.org), and includes topics such as solving ordinary differential equations and numerical integration.”
Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees (2015, methodology): “For the task of computing integrals, Bayesian Quadrature (BQ) [22] and more recent work by [20] provide probabilistic numerics methods that produce a full posterior distribution on the output of numerical schemes.”
Convex Optimization: Algorithms and Complexity (2015, unknown): “21 is also Gaussian, and the posterior moments are given by O’Hagan [1991]”
Bayesian Monte Carlo (2002, methodology): “a result which has previously been derived under the name of Bayes-Hermite Quadrature [O’Hagan, 1991].”
Probabilistic ODE Solvers with Runge-Kutta Means (2014, background): “An ODE Initial Value Problem (IVP) is to find a function x(t) ∶ R → RN such that the ordinary differential equation ẋ = f(x, t) (where ẋ = ∂x/∂t) holds for all t ∈ T = [t0, tH], and x(t0) = x0.”
Bayesian Filtering and Smoothing (2013, methodology): “It is also possible to use other methods such as the Bayes–Hermite quadrature (O’Hagan, 1991) or Monte Carlo integration for approximating the integrals.”
Probabilistic Meshless Methods for Partial Differential Equations and Bayesian Inverse Problems (2016, background): “This permits the residual error of the meshless solution to be quantified by a distribution over an appropriate function space.”