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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…
We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…
Extreme mesoscale weather, including tropical cyclones, squall lines, and floods, can be enormously damaging and yet challenging to simulate; hence, there is a pressing need for more efficient simulation strategies. Here we present a new…
The deployment of deep neural networks in safety-critical systems necessitates reliable and efficient uncertainty quantification (UQ). A practical and widespread strategy for UQ is repurposing stochastic regularizers as scalable approximate…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
This paper proposes a new Sequential Monte Carlo algorithm to perform online estimation in the context of state space models when either the transition density of the latent state or the conditional likelihood of an observation given a…
We propose to compute physical properties by Monte Carlo calculations using conditional expectation values. The latter are obtained on top of the usual Monte Carlo sampling by partitioning the physical space in several subspaces or…
This manuscript outlines a software package that facilitates working with probability distributions by means of Monte-Carlo methods, in a way that allows for propagation of multivariate probability distributions through arbitrary functions.…
Simulation-based inference methods that feature correct conditional coverage of confidence sets based on observations that have been compressed to a scalar test statistic require accurate modeling of either the p-value function or the…
The number of resident space objects is rising at an alarming rate. Mega-constellations and breakup events are proliferating in most orbital regimes, and safe navigation is becoming increasingly problematic. It is important to be able to…
We develop and analyze a class of unbiased Monte Carlo estimators for multivariate jump-diffusion processes with state-dependent drift, volatility, jump intensity and jump size. A change of measure argument is used to extend existing…
In recent years dynamical systems (of deterministic and stochastic nature), describing many models in mathematics, physics, engineering and finances, become more and more complex. Numerical analysis narrowed only to deterministic algorithms…
Multimodal distributions of some physics based model parameters are often encountered in engineering due to different situations such as a change in some environmental conditions, and the presence of some types of damage and nonlinearity.…
We consider the numerical approximation of $\mathbb{P}[G\in \Omega]$ where the $d$-dimensional random variable $G$ cannot be sampled directly, but there is a hierarchy of increasingly accurate approximations $\{G_\ell\}_{\ell\in\mathbb{N}}$…
The efficient simulation of the mean value of a non-linear functional of the solution to a linear stochastic partial differential equation (SPDE) with additive Gaussian noise is considered. A Galerkin finite element method is employed along…
We compare estimators of the (essential) supremum and the integral of a function $f$ defined on a measurable space when $f$ may be observed at a sample of points in its domain, possibly with error. The estimators compared vary in their…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
An efficient Path Integral Monte Carlo procedure is proposed to simulate the behavior of quantum many-body dissipative systems described within the framework of the influence functional. Thermodynamic observables are obtained by Monte Carlo…
This paper studies multi-level stochastic approximation algorithms. Our aim is to extend the scope of the multilevel Monte Carlo method recently introduced by Giles (Giles 2008) to the framework of stochastic optimization by means of…
In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…