Related papers: A new approach to unbiased estimation for SDE's
Small area estimators that ignore the sampling design lack design consistency when the sampling mechanism is complex and may be severely biased under informative designs. Existing procedures that account for the survey weights under…
Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…
The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…
In this article we design a novel quasi-regression Monte Carlo algorithm in order to approximate the solution of discrete time backward stochastic differential equations (BSDEs), and we analyze the convergence of the proposed method. The…
In this paper we introduce a new multilevel Monte Carlo (MLMC) estimator for multi-dimensional SDEs driven by Brownian motions. Giles has previously shown that if we combine a numerical approximation with strong order of convergence…
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…
We introduce a new class of Monte Carlo based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically…
The randomized unbiased estimators of Rhee and Glynn (Operations Research:63(5), 1026-1043, 2015) can be highly efficient at approximating expectations of path functionals associated with stochastic differential equations (SDEs). However,…
The expected value of partial perfect information (EVPPI) denotes the value of eliminating uncertainty on a subset of unknown parameters involved in a decision model. The EVPPI can be regarded as a decision-theoretic sensitivity index, and…
This paper introduces a new approach to generating sample paths of unknown Markovian stochastic differential equations (SDEs) using diffusion models, a class of generative AI methods commonly employed in image and video applications. Unlike…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
Eliciting relevance judgments for ranking evaluation is labor-intensive and costly, motivating careful selection of which documents to judge. Unlike traditional approaches that make this selection deterministically, probabilistic sampling…
Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…
Three classes of stochastic networks and their performance measures are considered. These performance measures are defined as the expected value of some random variables and cannot normally be obtained analytically as functions of network…
In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…
Posterior distributions often feature intractable normalizing constants, called marginal likelihoods or evidence, that are useful for model comparison via Bayes factors. This has motivated a number of methods for estimating ratios of…
In state space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has…
In this paper, we introduce an unbiased gradient simulation algorithms for solving convex optimization problem with stochastic function compositions. We show that the unbiased gradient generated from the algorithm has finite variance and…
In an increasing number of applications, it is of interest to recover an approximately low-rank data matrix from noisy observations. This paper develops an unbiased risk estimate---holding in a Gaussian model---for any spectral estimator…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…