相关论文: Linear approximation to the statistical significan…

In high-energy physics it is a recurring challenge to efficiently and precisely (enough) calculate the global significance of, e.g., a potential new resonance. We propose a new method that models the significance in the search region as a…

Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…

Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…

This paper studies the problem of estimating a covariance matrix from correlated sub-Gaussian samples. We consider using the correlated sample covariance matrix estimator to approximate the true covariance matrix. We establish…

This paper proposes a novel profile likelihood method for estimating the covariance parameters in exploratory factor analysis of high-dimensional Gaussian datasets with fewer observations than number of variables. An implicitly restarted…

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…

Accurate assessment of systematic uncertainties is an increasingly vital task in physics studies, where large, high-dimensional datasets, like those collected at the Large Hadron Collider, hold the key to new discoveries. Common approaches…

Higher criticism is a large-scale testing procedure that can attain the optimal detection boundary for sparse and faint signals. However, there has been a lack of knowledge in most existing works about its asymptotic distribution for more…

We propose a determinant-free approach for simulation-based Bayesian inference in high-dimensional Gaussian models. We introduce auxiliary variables with covariance equal to the inverse covariance of the model. The joint probability of the…

This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…

We study the estimation of high-dimensional covariance matrices under elliptical factor models with 2 + {\epsilon}th moment. For such heavy-tailed data, robust estimators like the Huber-type estimator in Fan, Liu and Wang (2018) can not…

We study the problem of detecting a change in the mean of one-dimensional Gaussian process data. This problem is investigated in the setting of increasing domain (customarily employed in time series analysis) and in the setting of fixed…

We consider the detection problem of correlations in a $p$-dimensional Gaussian vector, when we observe $n$ independent, identically distributed random vectors, for $n$ and $p$ large. We assume that the covariance matrix varies in some…

Covariance matrix estimation concerns the problem of estimating the covariance matrix from a collection of samples, which is of extreme importance in many applications. Classical results have shown that $O(n)$ samples are sufficient to…

We discuss the use of Gaussian random fields to estimate the look-elsewhere effect correction. We show that Gaussian random fields can be used to model the null-hypothesis significance maps from a large set of statistical problems commonly…

We consider the problem of estimating the parameters of the covariance function of a Gaussian process by cross-validation. We suggest using new cross-validation criteria derived from the literature of scoring rules. We also provide an…

The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…

For systems analogous to a linear harmonic oscillator, the simplest way to characterize the state is by a covariance matrix containing the symmetrically-ordered moments of operators analogous to position and momentum. We show that using…

Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…