Related papers: On Negatively Dependent Sampling Schemes, Variance…
We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…
Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies,…
The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted $L_2$-distance between the empirical characteristic functions of…
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 two algorithms for sampling from two gamma variates possessing a negative correlation. The case of positive correlation is easily solved, so we just mention it. The main problem is the lowest value of the correlation coefficient…
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,…
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…
We derive non-asymptotic confidence regions for the mean of a random vector whose coordinates have an unknown dependence structure. The random vector is supposed to be either Gaussian or to have a symmetric bounded distribution, and we…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the…
Testing between hypotheses, when independent sampling is possible, is a well developed subject. In this paper, we propose hypothesis tests that are applicable when the samples are obtained using Markov chain Monte Carlo. These tests are…
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…
We consider a statistical test whose p-value can only be approximated using Monte Carlo simulations. We are interested in deciding whether the p-value for an observed data set lies above or below a given threshold such as 5%. We want to…
We consider the problem of deciding on sampling strategy, in particular sampling design. We propose a risk measure, whose minimizing value guides the choice. The method makes use of a superpopulation model and takes into account uncertainty…
Noise contrastive learning is a popular technique for unsupervised representation learning. In this approach, a representation is obtained via reduction to supervised learning, where given a notion of semantic similarity, the learner tries…
We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…
We analyze the Nystr\"om approximation of a positive definite kernel associated with a probability measure. We first prove an improved error bound for the conventional Nystr\"om approximation with i.i.d. sampling and singular-value…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
High-dimensional count data poses significant challenges for statistical analysis, necessitating effective methods that also preserve explainability. We focus on a low rank constrained variant of the Poisson log-normal model, which relates…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…