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Monte Carlo (MC) methods for numerical integration seem to be embarassingly parallel on first sight. When adaptive schemes are applied in order to enhance convergence however, the seemingly most natural way of replicating the whole job on…
While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
Markov Chain Monte Carlo (MCMC) methods such as Gibbs sampling are finding widespread use in applied statistics and machine learning. These often lead to difficult computational problems, which are increasingly being solved on parallel and…
What is called "numerical reproducibility" is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing…
It is shown that superefficient Monte Carlo computations can be carried out by using chaotic dynamical systems as non-uniform random-number generators. Here superefficiency means that the expectation value of the square of the error…
Soft error of exascale application is a challenge problem in modern HPC. In order to quantify an application's resilience and vulnerability, the application-level fault injection method is widely adopted by HPC users. However, it is not…
The parallel computational complexity of the quadratic map is studied. A parallel algorithm is described that generates typical pseudotrajectories of length t in a time that scales as log t and increases slowly in the accuracy demanded of…
A Quantum Computer is a new type of computer which can efficiently solve complex problems such as prime factorization. A quantum computer threatens the security of public key encryption systems because these systems rely on the fact that…
The simulation of the expectation of a stochastic quantity E[Y] by Monte Carlo methods is known to be computationally expensive especially if the stochastic quantity or its approximation Y_n is expensive to simulate, e.g., the solution of a…
We show that linear congruential pseudo-random-number generators can cause systematic errors in Monte Carlo simulations using the Swendsen-Wang algorithm, if the lattice size is a multiple of a very large power of 2 and one random number is…
We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or…
The aim of this Thesis is to present five new tests for random numbers, which are widely used {\em e.g.} in computer simulations in physics applications. The first two tests, the cluster test and the autocorrelation test, are based on…
Parallel supercomputer-based Monte Carlo and stochastic simulations require pseudorandom number generators that can produce distinct pseudorandom streams across many independent processes. We propose a scalable class of parallel and…
This paper examines the use of Monte Carlo simulations to understand statistical concepts in A/B testing and Randomized Controlled Trials (RCTs). We discuss the applicability of simulations in understanding false positive rates and estimate…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
High-performance streams of (pseudo) random numbers are crucial for the efficient implementation for countless stochastic algorithms, most importantly, Monte Carlo simulations and molecular dynamics simulations with stochastic thermostats.…
We report large systematic errors in Monte Carlo simulations of the tricritical Blume-Capel model using single spin Metropolis updating. The error, manifest as a $20\%$ asymmetry in the magnetisation distribution, is traced to the interplay…
The heart of every Monte Carlo simulation is a source of high quality random numbers and the generator has to be picked carefully. Since the ``Ferrenberg affair'' it is known to a broad community that statistical tests alone do not suffice…