11 citations · 40 across the 18 of their papers we have counts for
6 papers · 1 filter
On the positivity and magnitudes of Bayesian quadrature weights
Toni Karvonen, Motonobu Kanagawa, Simo Särkkä
This article reviews and studies the properties of Bayesian quadrature weights, which strongly affect stability and robustness of the quadrature rule. Specifically, we investigate…
Improved Calibration of Numerical Integration Error in Sigma-Point Filters
Jakub Prüher, Toni Karvonen, Chris J. Oates +2
The sigma-point filters, such as the UKF, which exploit numerical quadrature to obtain an additional order of accuracy in the moment transformation step, are popular alternatives t…
Symmetry Exploits for Bayesian Cubature Methods
Toni Karvonen, Simo Särkkä, Chris. J. Oates
Bayesian cubature provides a flexible framework for numerical integration, in which a priori knowledge on the integrand can be encoded and exploited. This additional flexibility, c…
On stability of a class of filters for non-linear stochastic systems
Toni Karvonen, Silvère Bonnabel, Eric Moulines +1
This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with no…
A Bayes-Sard Cubature Method
Toni Karvonen, Chris J. Oates, Simo Särkkä
This paper focusses on the formulation of numerical integration as an inferential task. To date, research effort has largely focussed on the development of Bayesian cubature, whose…
Gaussian kernel quadrature at scaled Gauss-Hermite nodes
Toni Karvonen, Simo Särkkä
This article derives an accurate, explicit, and numerically stable approximation to the kernel quadrature weights in one dimension and on tensor product grids when the kernel and i…