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An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The…
We investigate the feasibility of sample average approximation (SAA) for general stochastic optimization problems, including two-stage stochastic programming without the relatively complete recourse assumption. Instead of analyzing problems…
Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space. We provide mathematically rigorous bounds on the number of sample points required to estimate both the dimension and the tangent spaces of…
Approximate Bayesian Computation (ABC) is a powerful method for carrying out Bayesian inference when the likelihood is computationally intractable. However, a drawback of ABC is that it is an approximate method that induces a systematic…
The combination of continuum Many-Body Quantum physics and Monte Carlo methods provide a powerful and well established approach to first principles calculations for large systems. Replacing the exact solution of the problem with a…
Post-selection inference consists in providing statistical guarantees, based on a data set, that are robust to a prior model selection step on the same data set. In this paper, we address an instance of the post-selection-inference problem,…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…
In quantum metrology, one of the major applications of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram\'er-Rao bound. Yet, the latter is no longer guaranteed to carry an…
This paper studies and critically discusses the construction of nonparametric confidence regions for density level sets. Methodologies based on both vertical variation and horizontal variation are considered. The investigations provide…
We consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…
In this article we perform an asymptotic analysis of parallel Bayesian logspline density estimators. Such estimators are useful for the analysis of datasets that are partitioned into subsets and stored in separate databases without the…
We argue that measurement data in quantum physics can be rigorously interpreted only as a result of a statistical, macroscopic process, taking into account the indistinguishable character of identical particles. Quantum determinism is in…
Approximate Bayesian Computation (ABC) enables statistical inference in simulator-based models whose likelihoods are difficult to calculate but easy to simulate from. ABC constructs a kernel-type approximation to the posterior distribution…
In this paper, we propose novel, fully Bayesian non-parametric tests for one-sample and two-sample multivariate location problems. We model the underlying distribution using a Dirichlet process prior, and develop a testing procedure based…
Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist…
An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through…
Phase estimation protocols provide a fundamental benchmark for the field of quantum metrology. The latter represents one of the most relevant applications of quantum theory, potentially enabling the capability of measuring unknown physical…
A parametric theory of statistical inference is developed for the moderate deviation probability zone. The new approach to the proofs is based on the Taylor series expansion of the logarithm of the likelihood ratio based on the Hellinger…