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This is an introductory article about Markov Chain Monte Carlo (MCMC) simulation for pedestrians. Actual simulation codes are provided, and necessary practical details, which are skipped in most textbooks, are shown. The second half is…
Motivated by the construction of the It\^o stochastic integral, we consider a step function method to discretize and simulate volatility modulated L\'evy semistationary processes. Moreover, we assess the accuracy of the method with a…
In this paper the computational aspects of probability calculations for dynamical partial sum expressions are discussed. Such dynamical partial sum expressions have many important applications, and examples are provided in the fields of…
Computational atomic-scale methods continue to provide new information about geometry, energetics, and transition states for interstitial elements in crystalline lattices. This data can be used to determine the diffusivity of interstitials…
Dynamic discrete choice models often discretize the state vector and restrict its dimension in order to achieve valid inference. I propose a novel two-stage estimator for the set-identified structural parameter that incorporates a…
Sensitivity analysis (SA) is a procedure for studying how sensitive are the output results of large-scale mathematical models to some uncertainties of the input data. The models are described as a system of partial differential equations.…
A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using…
Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around $\mathbb{R}\subset \mathbb{C}$. The Fourier transform techniques reduces calculation…
Molecular motors and other complex nonequilibrium systems are controlled by large sets of design parameters, and optimizing those parameters requires computing sensitivities -- derivatives of dynamical observables with respect to the…
We apply the Direct Simulation Monte Carlo (DSMC) method, developed originally to calculate rarefied gas dynamical problems, to study the gas flow in an accretion disc in a close binary system. The method involves viscosity and thermal…
We consider the problem of active learning for global sensitivity analysis of expensive black-box functions. Our aim is to efficiently learn the importance of different input variables, e.g., in vehicle safety experimentation, we study the…
Constrained Markov Decision Processes (CMDPs) are notably more complex to solve than standard MDPs due to the absence of universally optimal policies across all initial state distributions. This necessitates re-solving the CMDP whenever the…
Many chemical reactions and molecular processes occur on timescales that are significantly longer than those accessible by direct simulation. One successful approach to estimating dynamical statistics for such processes is to use many short…
Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact…
The ability to construct a realistic simulator of financial exchanges, including reproducing the dynamics of the limit order book, can give insight into many counterfactual scenarios, such as a flash crash, a margin call, or changes in…
We study an algorithm which has been proposed by Chinesta et al. to solve high-dimensional partial differential equations. The idea is to represent the solution as a sum of tensor products and to compute iteratively the terms of this sum.…
This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated systems experiencing multiple excitations. The aim of such an approach is to focus on the evolution of a signal (e.g., heart…
Exponential divided differences arise in numerical linear algebra, matrix-function evaluation, and quantum Monte Carlo simulations, where they serve as kernel weights for time evolution and observable estimation. Efficient and numerically…
A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…
We propose a new class of mappings, called Dynamic Limit Growth Indices, that are designed to measure the long-run performance of a financial portfolio in discrete time setup. We study various important properties for this new class of…