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Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in…
We study and develop the stochastic Markov reward model (sMRM), which extends the Markov chain where transition time/reward as modelled as random variables. Techniques are presented to enable computing first-passage time distributions (or…
Continuous-time quantum Monte Carlo refers to a class of algorithms designed to sample the thermal distribution of a quantum Hamiltonian through exact expansions of the Boltzmann exponential in terms of stochastic trajectories which are…
We present the first treatment of the arc length of the Gaussian Process (GP) with more than a single output dimension. GPs are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest.…
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…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we…
This article analyzes the stochastic runtime of a Cross-Entropy Algorithm on two classes of traveling salesman problems. The algorithm shares main features of the famous Max-Min Ant System with iteration-best reinforcement. For simple…
We present an approach to interface branching random walks with Markov chain Monte Carlo sampling, and to switch seamlessly between the two. The approach is discussed in the context of auxiliary-field quantum Monte Carlo (AFQMC) but is…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain…
Statistical inference for discretely observed jump-diffusion processes is a complex problem which motivates new methodological challenges. Thus existing approaches invariably resort to time-discretisations which inevitably lead to…
We investigate the large deviation probabilities of first passage times (FPT) of discrete-time supercritical non-lattice branching random walks (BRWs) in $\mathbb{R}^d$ where $d\geq 1$. The FPT refers to the first time the BRW enters a ball…
Solving optimization problems leads to elegant and practical solutions in a wide variety of real-world applications. In many of those real-world applications, some of the information required to specify the relevant optimization problem is…
The preferential sampling of locations chosen to observe a spatio-temporal process has been identified as a major problem across multiple fields. Predictions of the process can be severely biased when standard statistical methodologies are…
The behaviour of the one--dimensional random--forced Burgers equation is investigated in the path integral formalism, using a discrete space--time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as…
A novel method for extracting physical parameters from experimental and simulation data is presented. The method is based on statistical concepts and it relies on Monte Carlo simulation techniques. It identifies and determines with maximal…
We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…
This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the…
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…