Related papers: A general method for debiasing a Monte Carlo estim…
Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…
Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes…
We describe Monte Carlo methods for estimating lower envelopes of expectations of real random variables. We prove that the estimation bias is negative and that its absolute value shrinks with increasing sample size. We discuss fairly…
A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active…
We provide a detailed importance sampling analysis for variance reduction in stochastic volatility models. The optimal change of measure is obtained using a variety of results from large and moderate deviations: small-time, large-time,…
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the…
Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…
We consider two recent suggestions for how to perform an empirically motivated Monte Carlo study to help select a treatment effect estimator under unconfoundedness. We show theoretically that neither is likely to be informative except under…
We introduce a class of Monte Carlo estimators that aim to overcome the rapid growth of variance with dimension often observed for standard estimators by exploiting the target's independence structure. We identify the most basic…
This paper presents a study using the Bayesian approach in stochastic volatility models for modeling financial time series, using Hamiltonian Monte Carlo methods (HMC). We propose the use of other distributions for the errors in the…
We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
In this paper, we present extensions of the exact simulation algorithm introduced by Beskos et al. (2006). First, a modification in the order in which the simulation is done accelerates the algorithm. In addition, we propose a truncated…
For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and…
This paper examines estimation of skill formation models, a critical component in understanding human capital development and its effects on individual outcomes. Existing estimators are either based on moment conditions and only applicable…
We consider distributed optimization problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We develop unbiased parameter averaging methods for randomized second order optimization…
We develop a new primitive for stochastic optimization: a low-bias, low-cost estimator of the minimizer $x_\star$ of any Lipschitz strongly-convex function. In particular, we use a multilevel Monte-Carlo approach due to Blanchet and Glynn…