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Treatment effects of stochastic policy shifts quantify differences in outcomes across counterfactual scenarios with varying treatment distributions. Stochastic policy shifts may be of interest in settings where it is unrealistic or…
Quantum phase estimation requires simulating the evolution of the Hamiltonian, for which product formulas are attractive due to their smaller qubit cost and ease of implementation. However, the estimation of the error incurred by product…
In cluster-randomized trials (CRTs), there is emerging interest in exploring the causal mechanism in which a cluster-level treatment affects the outcome through an intermediate outcome. The majority of existing causal mediation methods are…
Many algorithms for finding reaction pathways require an initial estimate of the minimum energy path (MEP). Most estimation methods use a variational approach and thus must be seeded from an even simpler path, such as one generated by…
Fixed effect estimators of nonlinear panel data models suffer from the incidental parameter problem. This leads to two undesirable consequences in applied research: (1) point estimates are subject to large biases, and (2) confidence…
In this paper, we consider a class of continuous-time, continuous-space stochastic optimal control problems. Building upon recent advances in Markov chain approximation methods and sampling-based algorithms for deterministic path planning,…
A heuristic formula for 5-point approximation of the first derivative of an unknown function whose values are measured with an error at unequally spaced points is proposed. The derivative at a given point is calculated using the effective…
Numerical analysis for the stochastic Stokes equations is still challenging even though it has been well done for the corresponding deterministic equations. In particular, the pre-existing error estimates of finite element methods for the…
This paper presents a practical computational approach to quantify the effect of individual observations in estimating the state of a system. Such an analysis can be used for pruning redundant measurements, and for designing future sensor…
Information estimates such as the ``direct method'' of Strong et al. (1998) sidestep the difficult problem of estimating the joint distribution of response and stimulus by instead estimating the difference between the marginal and…
The goal of this paper is to define stochastic integrals and to solve stochastic differential equations for typical paths taking values in a possibly infinite dimensional separable Hilbert space without imposing any probabilistic structure.…
This article studies the effect of discretisation error on the stationary distribution of stochastic partial differential equations (SPDEs). We restrict the analysis to the effect of space discretisation, performed by finite element…
Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman equations in the context of stochastic optimal control, or…
In this study, we consider a numerical implementation of the nonlinear Rosenbluth-Trubnikov collision operator for particle simulations in plasma physics in the framework of the finite element method (FEM). The relevant particle evolution…
We present Path Integral Sampler~(PIS), a novel algorithm to draw samples from unnormalized probability density functions. The PIS is built on the Schr\"odinger bridge problem which aims to recover the most likely evolution of a diffusion…
In this paper, we investigate diagonal estimation for large or implicit matrices, aiming to develop a novel and efficient stochastic algorithm that incorporates adaptive parameter selection. We explore the influence of different eigenvalue…
Timesteppers constitute a powerful tool in modern computational science and engineering. Although they are typically used to advance the system forward in time, they can also be viewed as nonlinear mappings that implicitly encode steady…
For problems of time-harmonic scattering by rational polygonal obstacles, embedding formulae express the far-field pattern induced by any incident plane wave in terms of the far-field patterns for a relatively small (frequency-independent)…
We study a chaotic ratchet system under the influence of a thermal environment. By direct integration of the Lindblad equation we are able to analyze its behavior for a wide range of couplings with the environment, and for different finite…
Real-time time-dependent density functional theory (TDDFT) is presently the most accurate available method for computing electronic stopping powers from first principles. However, obtaining application-relevant results often involves either…