Related papers: Quantifying dimensionality: Bayesian cosmological …
In a recent article, a simple `spherical bubble' toy model for a spatially varying vacuum energy density was introduced, and type Ia supernovae data was used to constrain it. Here we generalize the model to allow for the fact that we may…
We present a Bayesian hierarchical modelling approach to infer the cosmic matter density field, and the lensing and the matter power spectra, from cosmic shear data. This method uses a physical model of cosmic structure formation to infer…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
Bayesian analysis plays a crucial role in estimating distribution of unknown parameters for given data and model. Due to the curse of dimensionality, it becomes difficult for high-dimensional problems, especially when multiple modes exist.…
We present a Bayesian analysis of large-scale structure and cosmic microwave background data to constrain the form of the primordial power spectrum. We have extended the usual presumption of a scale invariant spectrum to include: (i) a…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
This paper describes a new Bayesian interpretation of a class of skew--Student $t$ distributions. We consider a hierarchical normal model with unknown covariance matrix and show that by imposing different restrictions on the parameter…
We investigate the imprints of the Generalized Uncertainty Principle on cosmological scales by using redshift-space distortion measurements in combination with background cosmological data to determine constraints on the deformation…
Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…
We propose a new PAC-Bayesian bound and a way of constructing a hypothesis space, so that the bound is convex in the posterior distribution and also convex in a trade-off parameter between empirical performance of the posterior distribution…
In this paper, we treat estimation and prediction problems where negative multinomial variables are observed and in particular consider unbalanced settings. First, the problem of estimating multiple negative multinomial parameter vectors…
We analyze primordial tensor perturbations using the latest cosmic microwave background and gravitational waves data, focusing on the tensor-to-scalar ratio, $r$, and the tensor spectral tilt, $n_t$. Utilizing data from Planck PR4,…
In this paper we propose a Bayesian, information theoretic approach to dimensionality reduction. The approach is formulated as a variational principle on mutual information, and seamlessly addresses the notions of sufficiency, relevance,…
Bayesian model comparison requires the specification of a prior distribution on the parameter space of each candidate model. In this connection two concerns arise: on the one hand the elicitation task rapidly becomes prohibitive as the…
We present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the…
We deal with the analysis of on-off measurements designed for the confirmation of a weak source of events whose presence is hypothesized, based on former observations. The problem of a small number of source events that are masked by an…
Constraints on cosmological parameters are often distilled from sky surveys by fitting templates to summary statistics of the data that are motivated by a fiducial cosmological model. However, recent work has shown how to estimate the…
Bayesian model averaging is a procedure to obtain parameter constraints that account for the uncertainty about the correct cosmological model. We use recent cosmological observations and Bayesian model averaging to derive tight limits on…