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This paper contributes to the study of optimal experimental design for Bayesian inverse problems governed by partial differential equations (PDEs). We derive estimates for the parametric regularity of multivariate double integration…
Monte Carlo integration using quantum computers has been widely investigated, including applications to concrete problems. It is known that quantum algorithms based on quantum amplitude estimation (QAE) can compute an integral with a…
The fast computation of large kernel sums is a challenging task, which arises as a subproblem in any kernel method. We approach the problem by slicing, which relies on random projections to one-dimensional subspaces and fast Fourier…
Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the…
We investigate quasi-Monte Carlo integration using higher order digital nets in weighted Sobolev spaces of arbitrary fixed smoothness $\alpha \in \mathbb{N}$, $\alpha \ge 2$, defined over the $s$-dimensional unit cube. We prove that…
For a long time, people have been focusing on how to extract more information, such as off-diagonal observables, from the quantum Monte Carlo (QMC) simulation of the partition function, but there have been numerous difficulties, and many of…
Sequential Monte Carlo algorithms (also known as particle filters) are popular methods to approximate filtering (and related) distributions of state-space models. However, they converge at the slow $1/\sqrt{N}$ rate, which may be an issue…
Quasi-Monte Carlo (QMC) rules $1/N \sum_{n=0}^{N-1} f(\boldsymbol{y}_n A)$ can be used to approximate integrals of the form $\int_{[0,1]^s} f(\boldsymbol{y} A) \,\mathrm{d} \boldsymbol{y}$, where $A$ is a matrix and $\boldsymbol{y}$ is row…
Symmetric polynomial quadrature rules for triangles are commonly used to efficiently integrate two-dimensional domains in finite-element-type problems. While the development of such rules focuses on the maximum degree a given number of…
In Quasi-Monte Carlo integration, the integration error is believed to be generally smaller than in classical Monte Carlo with the same number of integration points. Using an appropriate definition of an ensemble of quasi-randompoint sets,…
In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain classes of elliptic partial differential equations with random…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
Maximum simulated likelihood estimation of mixed multinomial logit (MMNL) or probit models requires evaluation of a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as shuffled and scrambled Halton sequences and modified…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e., samples) of the function (integrand). For $N$ queries of the integrand, Monte Carlo integration achieves the…
Digital nets provide an efficient way to generate integration nodes of quasi-Monte Carlo (QMC) rules. For certain applications, as e.g. in Uncertainty Quantification, we are interested in obtaining a speed-up in computing products of a…
In the present paper we study quasi-Monte Carlo rules for approximating integrals over the $d$-dimensional unit cube for functions from weighted Sobolev spaces of regularity one. While the properties of these rules are well understood for…
Most scientific domains elicit the development of efficient algorithms and accessible scientific software. This thesis unifies our developments in three broad domains: Quasi-Monte Carlo (QMC) methods for efficient high-dimensional…
This paper investigates the construction of space-filling designs for computer experiments. The space-filling property is characterized by the covering and separation radii of a design, which are integrated through the unified criterion of…
Sequential Monte Carlo (SMC) methods offer a principled approach to Bayesian uncertainty quantification but are traditionally limited by the need for full-batch gradient evaluations. We introduce a scalable variant by incorporating…