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Galaxy cluster surveys offer great promise for measuring cosmological parameters, but survey analysis methods have not been widely studied. Using methods developed decades ago for galaxy clustering studies, it is shown that nearly exact…
We focus on the problem of estimating and quantifying uncertainties on the excursion set of a function under a limited evaluation budget. We adopt a Bayesian approach where the objective function is assumed to be a realization of a Gaussian…
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We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…
Simulation of materials at the atomistic level is an important tool in studying microscopic structure and processes. The atomic interactions necessary for the simulation are correctly described by Quantum Mechanics. However, the…
Scientific knowledge expands by observing the world, hypothesizing some theories about it, and testing them against collected data. When those theories take the form of statistical models, statistical analyses are involved in the process of…
Effective general-purpose search strategies are an important component in Constraint Programming. We introduce a new idea, namely, using correlations between variables to guide search. Variable correlations are measured and maintained by…
Upcoming surveys such as \LSST{} and \Euclid{} will significantly improve the power of weak lensing as a cosmological probe. To maximise the information that can be extracted from these surveys, it is important to explore novel statistics…
Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…
Maximising the information that can be extracted from weak lensing measurements is a key goal for upcoming surveys such as LSST and Euclid. This is typically achieved through statistics that are complementary to the cosmic shear two-point…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…
Model Predictive Control evolved as the state of the art paradigm for safety critical control tasks. Control-as-Inference approaches thereof model the constrained optimization problem as a probabilistic inference problem. The constraints…
We compute correlation functions of protected primaries on the $1/2$-BPS Wilson loop in ${\cal N}$ = 4 super Yang-Mills theory at weak coupling. We first perform direct perturbative computation at one loop in the planar limit and present…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
To estimate cosmological parameters from a given dataset, we need to construct a likelihood function, which sometimes has a complicated functional form. We introduce the copula, a mathematical tool to construct an arbitrary multivariate…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…
We consider stochastic approximations which arise from such applications as data communications and image processing. We demonstrate why constraints are needed in a stochastic approximation and how a constrained approximation can be…
We describe a Bayesian approach to estimating luminosity functions. We derive the likelihood function and posterior probability distribution for the luminosity function, given the observed data, and we compare the Bayesian approach with…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…