Related papers: Getting the Measure of the Flatness Problem
Bayesian (Probabilistic) Machine Learning is used to probe the opacity of the Universe. It relies on a generative process where the model is the key object to generate the data involving the unknown parameters of the model, our prior…
We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…
We derive constraints on cosmological parameters using the power spectrum of galaxy clustering measured from the final two-degree field galaxy redshift survey (2dFGRS) and a compilation of measurements of the temperature power spectrum and…
Empirical Bayes methods are widely used for large-scale estimation and inference in the Poisson means problem. Existing results establish theoretical properties of the nonparametric maximum likelihood estimator (NPMLE) for optimal posterior…
We consider the task of forecasting an infinite sequence of future observations based on some number of past observations, where the probability measure generating the observations is "suspected" to satisfy one or more of a set of…
Applications of large language models often involve the generation of free-form responses, in which case uncertainty quantification becomes challenging. This is due to the need to identify task-specific uncertainties (e.g., about the…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
The principles of measuring the shapes of galaxies by a model-fitting approach are discussed in the context of shape-measurement for surveys of weak gravitational lensing. It is argued that such an approach should be optimal, allowing…
[Abridged] Some cosmological theories propose that the observable universe is a small part of a much larger universe in which parameters describing the low-energy laws of physics vary from region to region. How can we reasonably assess a…
Representing and quantifying uncertainty in physical parameterisations is a central challenge in weather and climate modelling, and approaches are often developed separately for different timescales. Here, we introduce a unified framework…
In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…
We are at a specific period of modern cosmology, during which the large increase of the amount of data leads to the idea that the determination of cosmological parameters has been achieved with a rather good precision. There is a large…
The paper formulates Bayesian inverse problems for inference in a topological measure space given noisy observations. Conditions for the validity of the Bayes formula and the well-posedness of the posterior measure are studied. The abstract…
The question of determining the spatial geometry of the Universe is of greater relevance than ever, as precision cosmology promises to verify inflationary predictions about the curvature of the Universe. We revisit the question of what can…
Most cosmological parameter estimations are based on the same set of observations and are therefore not independent. Here, we test the consistency of parameter estimations using a combination of large-scale structure and supernovae data,…
Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model's…
We address the problem of classification when data are collected from two samples with measurement errors. This problem turns to be an inverse problem and requires a specific treatment. In this context, we investigate the minimax rates of…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
In cosmology, we routinely choose between models to describe our data, and can incur biases due to insufficient models or lose constraining power with overly complex models. In this paper we propose an empirical approach to model selection…
In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…