Related papers: Conditional Quasi-Monte Carlo with Constrained Act…
We propose the variable selection procedure incorporating prior constraint information into lasso. The proposed procedure combines the sample and prior information, and selects significant variables for responses in a narrower region where…
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…
This paper proposes a new importance sampling (IS) that is tailored to quasi-Monte Carlo (QMC) integration over $\mathbb{R}^s$. IS introduces a multiplicative adjustment to the integrand by compensating the sampling from the proposal…
Simulation studies are used to evaluate and compare the properties of statistical methods in controlled experimental settings. In most cases, performing a simulation study requires knowledge of the true value of the parameter, or estimand,…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
We present a preconditioned Monte Carlo method for computing high-dimensional multivariate normal and Student-$t$ probabilities arising in spatial statistics. The approach combines a tile-low-rank representation of covariance matrices with…
The theme of the present paper is numerical integration of $C^r$ functions using randomized methods. We consider variance reduction methods that consist in two steps. First the initial interval is partitioned into subintervals and the…
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…
Preconditioning is at the core of modern many-fermion Monte Carlo algorithms, such as Hybrid Monte Carlo, where the repeated solution of a linear problem involving an ill-conditioned matrix is needed. We report on a performance comparison…
This paper develops a comprehensive probabilistic setup to compute approximating functions in active subspaces. Constantine et al. proposed the active subspace method in (Constantine et al., 2014) to reduce the dimension of computational…
Classical Monte Carlo algorithms can theoretically be sped up on a quantum computer by employing amplitude estimation (AE). To realize this, an efficient implementation of state-dependent functions is crucial. We develop a straightforward…
We present a formalism that allows for the direct manipulation and optimization of subspaces, circumventing the need to optimize individual states when using subspace methods. Using the determinant state mapping, we can naturally extend…
Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more…
In this paper, we study the approximation of $d$-dimensional $\rho$-weighted integrals over unbounded domains $\mathbb{R}_+^d$ or $\mathbb{R}^d$ using a special change of variables, so that quasi-Monte Carlo (QMC) or sparse grid rules can…
Quasi-Monte Carlo (QMC) is a powerful method for evaluating high-dimensional integrals. However, its use is typically limited to distributions where direct sampling is straightforward, such as the uniform distribution on the unit hypercube…
Monte Carlo integration with variance reduction by means of control variates can be implemented by the ordinary least squares estimator for the intercept in a multiple linear regression model with the integrand as response and the control…
Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively.…
Monte Carlo methods are widely used for approximating complicated, multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC) is an important class of Monte Carlo methods, which utilizes a population of proposals to…
We study randomized quasi-Monte Carlo (RQMC) estimation of a multivariate integral where one of the variables takes only a finite number of values. This problem arises when the variable of integration is drawn from a mixture distribution as…
Active subspaces can effectively reduce the dimension of high-dimensional parameter studies enabling otherwise infeasible experiments with expensive simulations. The key components of active subspace methods are the eigenvectors of a…