Related papers: Objective Bayesian analysis of "on/off" measuremen…
In this paper the Bayesian analysis is applied to assign a probability density to the value of a quantity having a definite sign. This analysis is logically consistent with the results, positive or negative, of repeated measurements.…
The analysis of individual X-ray sources that appear in a crowded field can easily be compromised by the misallocation of recorded events to their originating sources. Even with a small number of sources, that nonetheless have overlapping…
This paper employs a recently developed asymptotic Bayesian multi-hypothesis testing (MHT) error analysis to treat the problem of superresolution imaging of a pair of closely spaced, equally bright point sources. The analysis exploits the…
This article considers the detection of point sources in two dimensional astronomical images. The detection scheme we propose is based on peak statistics. We discuss the example of the detection of far galaxies in Cosmic Microwave…
Source separation problems are ubiquitous in the physical sciences; any situation where signals are superimposed calls for source separation to estimate the original signals. In this tutorial I will discuss the Bayesian approach to the…
A flexible representation of uncertainty that remains within the standard framework of probabilistic measure theory is presented along with a study of its properties. This representation relies on a specific type of outer measure that is…
Anomaly detectors address the difficult problem of detecting automatically exceptions in an arbitrary background image. Detection methods have been proposed by the thousands because each problem requires a different background model. By…
This paper introduces the use of pseudo-filters that optimize the detection/extraction of sources on a background. We assume as a first approach that such sources are described by a spherical (central) profile and that the background is…
This paper considers the problem of making statistical inferences about a parameter when a narrow interval centred at a given value of the parameter is considered special, which is interpreted as meaning that there is a substantial degree…
We demonstrate a practical possibility of loss compensation in measured photocounting statistics in the presence of dark counts and background radiation noise. It is shown that satisfactory results are obtained even in the case of low…
Optical mixing experiments show the ability of amplifying a weak optical signal by superposing it with a stronger one. This principle has been demonstrated also for weak signals at the quantum level, down to a single photon. In the present…
In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means $\{ \mu_1, \mu_2, \mu_3\}$ through an analysis of variance…
Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…
The background method is a widely used technique to bound mean properties of turbulent flows rigorously. This work reviews recent advances in the theoretical formulation and numerical implementation of the method. First, we describe how the…
Alpha particle emission, even at extremely low levels, is a significant issue in the search for rare events (e.g., double beta decay, dark matter detection). Traditional measurement techniques require long counting times to measure low…
Counterfactual reasoning plays a crucial role in exploring hypothetical scenarios, by comparing some consequent under conditions identical except as results from a differing antecedent. David Lewis' well-known analysis evaluates…
This paper is concerned with Bayesian inference when the likelihood is analytically intractable but can be unbiasedly estimated. We propose an annealed importance sampling procedure for estimating expectations with respect to the posterior.…
We propose a novel method ($floZ$), based on normalizing flows, to estimate the Bayesian evidence (and its numerical uncertainty) from a pre-existing set of samples drawn from the unnormalized posterior distribution. We validate it on…
Photon-number measurements are a fundamental technique for the discrimination and characterization of quantum states of light. Beyond the abilities of state-of-the-art devices, we present measurements with an array of 100 avalanche…
An Earth orbiting detector sensitive to gamma ray photons will see step-like occultation features in its counting rate when a gamma ray point source crosses the Earth's limb. This is due to the change in atmospheric attenuation of the gamma…