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Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…
Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…
Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sam- pling in the framework of diffusion process and consider the change…
Distortion risk measures play a critical role in quantifying risks associated with uncertain outcomes. Accurately estimating these risk measures in the context of computationally expensive simulation models that lack analytical tractability…
Hypothesis tests calibrated by (re)sampling methods (such as permutation, rank and bootstrap tests) are useful tools for statistical analysis, at the computational cost of requiring Monte-Carlo sampling for calibration. It is common and…
This paper presents a tool for addressing a key component in many algorithms for planning robot trajectories under uncertainty: evaluation of the safety of a robot whose actions are governed by a closed-loop feedback policy near a nominal…
Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parameterized many-body wave functions, especially with modern neural-network quantum states. In practice, however, the stochastic estimators…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…
Importance sampling Monte-Carlo methods are widely used for the approximation of expectations with respect to partially known probability measures. In this paper we study a deterministic version of such an estimator based on quasi-Monte…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…
Sequential analysis encompasses simulation theories and methods where the sample size is determined dynamically based on accumulating data. Since the conceptual inception, numerous sequential stopping rules have been introduced, and many…
Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…
For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…