-
A Fourier State Space Model for Bayesian ODE Filters
Gaussian ODE filtering is a probabilistic numerical method to solve ordi...
read it
-
Probabilistic Linear Multistep Methods
We present a derivation and theoretical investigation of the Adams-Bashf...
read it
-
Bayesian Filtering for ODEs with Bounded Derivatives
Recently there has been increasing interest in probabilistic solvers for...
read it
-
A Probabilistic Taylor Expansion with Applications in Filtering and Differential Equations
We study a class of Gaussian processes for which the posterior mean, for...
read it
-
Active Uncertainty Calibration in Bayesian ODE Solvers
There is resurging interest, in statistics and machine learning, in solv...
read it
-
Uniform Rates of Convergence of Some Representations of Extremes : a first approach
Uniform convergence rates are provided for asymptotic representations of...
read it
-
Mix and Match: Markov Chains Mixing Times for Matching in Rideshare
Rideshare platforms such as Uber and Lyft dynamically dispatch drivers t...
read it
Convergence Rates of Gaussian ODE Filters
A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution x and its first q derivatives a priori as a Gauss--Markov process X, which is then iteratively conditioned on information about ẋ. We prove worst-case local convergence rates of order h^q+1 for a wide range of versions of this Gaussian ODE filter, as well as global convergence rates of order h^q in the case of q=1 and an integrated Brownian motion prior, and analyze how inaccurate information on ẋ coming from approximate evaluations of f affects these rates. Moreover, we present explicit formulas for the steady states and show that the posterior confidence intervals are well calibrated in all considered cases that exhibit global convergence---in the sense that they globally contract at the same rate as the truncation error.
READ FULL TEXT
Comments
There are no comments yet.