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The main focus of this article is to provide a mathematical study of the algorithm proposed in \cite{boyaval2010variance} where the authors proposed a variance reduction technique for the computation of parameter-dependent expectations…
We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random…
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…
For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte…
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…
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…
A simple Monte Carlo (MC) algorithm for the simulation of the passage of low-energy gamma rays and electrons through any material medium is presented. The algorithm includes several approximations that accelerate the simulation while…
Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…
The efficiency of a Markov chain Monte Carlo algorithm might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated…
Metrics of model goodness-of-fit, model comparison, and model parameter estimation are the main categories of statistical problems in science. Bayesian and frequentist methods that address these questions often rely on a likelihood…
The pseudo-marginal algorithm is a popular variant of the Metropolis--Hastings scheme which allows us to sample asymptotically from a target probability density $\pi$, when we are only able to estimate an unnormalized version of $\pi$…
Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…
Permutation tests are amongst the most commonly used statistical tools in modern genomic research, a process by which p-values are attached to a test statistic by randomly permuting the sample or gene labels. Yet permutation p-values…
Expectation values of physical quantities may accurately be obtained by the evaluation of integrals within Many-Body Quantum mechanics, and these multi-dimensional integrals may be estimated using Monte Carlo methods. In a previous…
Say $X_1,X_2,\ldots$ are independent identically distributed Bernoulli random variables with mean $p$. This paper builds a new estimate $\hat p$ of $p$ that has the property that the relative error, $\hat p /p - 1$, of the estimate does not…
We compute a Monte Carlo approximation of {\pi} using importance sampling with shots coming out of a Mossberg 500 pump-action shotgun as the proposal distribution. An approximated value of 3.131 is obtained, corresponding to a 0.33% error…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
We consider a multi-step algorithm for the computation of the historical expected shortfall such as defined by the Basel Minimum Capital Requirements for Market Risk. At each step of the algorithm, we use Monte Carlo simulations to reduce…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…
We present an implementation of a Monte Carlo algorithm that generates points randomly and uniformly on a set of arbitrary surfaces. The algorithm is completely general and only requires the geometry modeling software to provide the…