相关论文: Sparsity and the Bayesian Perspective

[Abridged]: A detection or nondetection of primordial non-Gaussianity by using the CMB data is crucial not only to discriminate inflationary models but also to test alternative scenarios. Non-Gaussianity offers, therefore, a powerful probe…

Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many…

We review some aspects of Bayesian and frequentist interval estimation, focusing first on their relative strengths and weaknesses when used in "clean" or "textbook" contexts. We then turn attention to observational-data situations which are…

This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain…

The problem of estimating cosmological parameters such as $\Omega$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of…

Upcoming stage 4 surveys, such as the Simons Observatory, LSST, and Euclid, are poised to measure weak gravitational lensing of the Cosmic Microwave Background (CMB) and galaxies with unprecedented precision. While the power spectrum is the…

Inverse problems defined naturally on the sphere are becoming increasingly of interest. In this article we provide a general framework for evaluation of inverse problems on the sphere, with a strong emphasis on flexibility and scalability.…

As confusion with lensing B-modes begins to limit experiments that search for primordial B-mode polarization, robust methods for delensing the CMB polarization sky are becoming increasingly important. We investigate in detail the…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…

We propose a novel bias-free method for reconstructing the power spectrum of the weak lensing deflection field from cosmic microwave background (CMB) observations. The proposed method is in contrast to the standard method of CMB lensing…

Handling missing data is one of the most fundamental problems in machine learning. Among many approaches, the simplest and most intuitive way is zero imputation, which treats the value of a missing entry simply as zero. However, many…

The investigation of the effects of sparsity or sparsity constraints in signal processing problems has received considerable attention recently. Sparsity constraints refer to the a priori information that the object or signal of interest…

In this paper, using a significantly improved version of the model-independent, cosmographic approach to cosmology (John, M. V. 2004, ApJ, 614, 1), we address an important question: Was there a decelerating past for the universe? To answer…

This paper addresses the sparse representation (SR) problem within a general Bayesian framework. We show that the Lagrangian formulation of the standard SR problem, i.e., $\mathbf{x}^\star=\arg\min_\mathbf{x} \lbrace \|…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

The cosmic microwave background (CMB) bispectrum is a well-known probe of the non-Gaussianity of primordial perturbations. Just as the intervening large-scale structure modifies the CMB angular power spectrum through weak gravitational…

We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…

We investigate the performance of a simple Bayesian fitting approach to correct the cosmic microwave background (CMB) B-mode polarization for gravitational lensing effects in the recovered probability distribution of the tensor-to-scalar…

Optimising the major next-generation cosmological surveys (such as {\em SNAP, KAOS etc...}) is a key problem given our ignorance of the physics underlying cosmic acceleration and the plethora of surveys planned. We propose a Bayesian design…