Related papers: Likelihood Analysis of Power Spectra and Generaliz…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
The growing scarcity of spectrum resources, wideband spectrum sensing is required to process a prohibitive volume of data at a high sampling rate. For some applications, spectrum estimation only requires second-order statistics. In this…
We tighten the Entropy Power Inequality (EPI) when one of the random summands is Gaussian. Our strengthening is closely connected to the concept of strong data processing for Gaussian channels and generalizes the (vector extension of)…
Here, we present a new method to evaluate the expectation value of the power spectrum of a time series. A statistical approach is adopted to define the method. After its demonstration, it is validated showing that it leads to the known…
We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…
Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…
A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…
We present a unified approach to the problems of reconstruction of large-scale structure distribution in the universe and determination of the underlying power spectrum. These have often been treated as two separate problems and different…
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model…
We present a method to estimate non-Gaussian power spectrum covariance matrices by directly measuring the response of the small-scale power spectrum to long-wavelength perturbations via bispectrum and trispectrum estimators. Specifically,…
Accurate predictions of inclusive scattering cross sections in the linear response regime require efficient and controllable methods to calculate the spectral density in a strongly-correlated many-body system. In this work we reformulate…
In real applications, the construction of prior and acceleration of sampling for posterior are usually two key points of Bayesian inversion algorithm for engineers. In this paper, q-analogy of Gaussian distribution, q-Gaussian distribution,…
We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we…
In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the…
We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing…
Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…
This paper investigates the problem of estimating the spectral power parameters of random analog sources using numerical measurements acquired with minimum digitization complexity. Therefore, spectral analysis has to be performed with…
We address the problem of estimating the uncertainty in the solution of power grid inverse problems within the framework of Bayesian inference. We investigate two approaches, an adjoint-based method and a stochastic spectral method. These…
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…
We study the weak convergence (in the high-frequency limit) of the parameter estimators of power spectrum coefficients associated with Gaussian, spherical and isotropic random fields. In particular, we introduce a Whittle-type approximate…