Related papers: A Discrepancy Bound for a Deterministic Acceptance…
A number of distributions that arise in statistical applications can be expressed in the form of a weighted density: the product of a base density and a nonnegative weight function. Generating variates from such a distribution may be…
Approximate Bayesian Computation (ABC) methods are increasingly used for inference in situations in which the likelihood function is either computationally costly or intractable to evaluate. Extensions of the basic ABC rejection algorithm…
Hamiltonian Monte Carlo (HMC) algorithms are among the most widely used sampling methods in high dimensional settings, yet their convergence properties are poorly understood in divergences that quantify relative density mismatch, such as…
We consider Metropolis Hastings MCMC in cases where the log of the ratio of target distributions is replaced by an estimator. The estimator is based on m samples from an independent online Monte Carlo simulation. Under some conditions on…
We consider the problem of computing an approximation to the integral $I=\int_{[0,1]^d}f(x) dx$. Monte Carlo (MC) sampling typically attains a root mean squared error (RMSE) of $O(n^{-1/2})$ from $n$ independent random function evaluations.…
This paper addresses the problem of approximating an unknown probability distribution with density $f$ -- which can only be evaluated up to an unknown scaling factor -- with the help of a sequential algorithm that produces at each iteration…
The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…
We propose a coupled rejection-sampling method for sampling from couplings of arbitrary distributions. The method relies on accepting or rejecting coupled samples coming from dominating marginals. Contrary to existing acceptance-rejection…
In Monte-Carlo methods the Markov processes used to sample a given target distribution usually satisfy detailed balance, i.e. they are time-reversible. However, relatively recent results have demonstrated that appropriate reversible and…
Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…
We introduce a class of $\gamma$-negatively dependent random samples. We prove that this class includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin hypercube samples padded by Monte Carlo. For a…
Classification with rejection emerges as a learning paradigm which allows models to abstain from making predictions. The predominant approach is to alter the supervised learning pipeline by augmenting typical loss functions, letting model…
Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…
Hamiltonian Monte Carlo (HMC) is a state of the art method for sampling from distributions with differentiable densities, but can converge slowly when applied to challenging multimodal problems. Running HMC with a time varying Hamiltonian,…
We motive and calculate Newton--Cotes quadrature integration variance and compare it directly with Monte Carlo (MC) integration variance. We find an equivalence between deterministic quadrature sampling and random MC sampling by noting that…
The choice of transition kernel critically influences the performance of the Markov chain Monte Carlo method. Despite the importance of kernel choice, guiding principles for optimal kernels have not been established. Here, we propose a…
We sample from a given target distribution by constructing a neural network which maps samples from a simple reference, e.g. the standard normal distribution, to samples from the target. To that end, we propose using a neural network…
Bayesian data analysis is widely used across many disciplines, and representative examples in materials science include spectral analysis and sparse modeling. In such applications, the underlying models often become complex and yield…
We consider the problem of estimating the density of a random variable $X$ that can be sampled exactly by Monte Carlo (MC). We investigate the effectiveness of replacing MC by randomized quasi Monte Carlo (RQMC) or by stratified sampling…
Optimal transport has emerged as a fundamental methodology with applications spanning multiple research areas in recent years. However, the convergence rate of the empirical estimator to its population counterpart suffers from the curse of…