Related papers: On the Relation Between Field-Level Posteriors, Co…
Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…
Previous work regarding low-rank matrix recovery has concentrated on the scenarios in which the matrix is noise-free and the measurements are corrupted by noise. However, in practical application, the matrix itself is usually perturbed by…
Most parameter constraints obtained from cosmic microwave background (CMB) anisotropy data are based on power estimates and rely on approximate likelihood functions; computational difficulties generally preclude an exact analysis based on…
We present a novel Bayesian model and a corresponding robust, probabilistic calibration procedure for the CORSAIR polarimeter that can be applied to other polarimeters. Our calibration procedure combines existing Mueller matrix…
This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy observation of a permuted data set, according to which permutation was the original data sorted? The focus is on…
This work presents a formalism for deriving likelihoods of the cosmological density field directly from first principles within Perturbation Theory (PT). By assuming a perturbative expansion around the Gaussian initial density field and…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
We present a method for radical linear compression of datasets where the data are dependent on some number $M$ of parameters. We show that, if the noise in the data is independent of the parameters, we can form $M$ linear combinations of…
We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using non-rigorous but standard methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP)…
The gravitational lensing signal from the Cosmic Microwave Background is highly valuable to constrain the growth of the structures in the Universe in a clean and robust manner over a wide range of redshifts. One of the theoretical…
These lecture notes delve into field-level inference, a framework offering a robust way to extract more information and avoid biases compared to traditional methods for cosmological data analysis. The core idea is to analyse uncompressed…
Assuming a Euclid-like weak lensing data set, we compare different methods of dealing with its inherent parameter degeneracies. Including priors into a data analysis can mask the information content of a given data set alone. However, since…
We investigate the cosmological dependence and the constraining power of large-scale galaxy correlations, including all redshift-distortions, wide-angle, lensing and gravitational potential effects on linear scales. We analyze the…
The cosmological information encapsulated within a weak lensing signal can be accessed via the power spectrum of the so called convergence. We use the Fisher information matrix formalism with the convergence power spectrum as the observable…
A common approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
The backpropagation algorithm has experienced remarkable success in training large-scale artificial neural networks; however, its biological plausibility has been strongly criticized, and it remains an open question whether the brain…
The bispectrum vanishes for linear Gaussian fields and is thus a sensitive probe of non-linearities and non-Gaussianities in the cosmic density field. Hence, a detection of the bispectrum in the halo density field would enable tight…
We consider the problem of optimal weighting of tracers of structure for the purpose of constraining the non-Gaussianity parameter f_NL. We work within the Fisher matrix formalism expanded around fiducial model with f_NL=0 and make several…
An observational program focused on the high redshift ($2<z<6$) Universe has the opportunity to dramatically improve over upcoming LSS and CMB surveys on measurements of both the standard cosmological model and its extensions. Using a…