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There has been a recent emergence of sampling-based techniques for estimating epistemic uncertainty in deep neural networks. While these methods can be applied to classification or semantic segmentation tasks by simply averaging samples,…

Time-distance helioseismology is a set of powerful tools to study features below the Sun's surface. Inverse methods are needed to interpret time-distance measurements, with many examples in the literature. However, techniques that utilize a…

An orbiting `photon clock' is proposed to test directly the relativity of simultaneity effect of special relativity. This is done by exchanging microwave signals between two satellites in low Earth orbit carrying clocks that have previously…

A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is…

The spatial distribution of galaxies we observed is subject to the given condition that we, human beings are sitting right in a galaxy -- the Milky Way. Thus the ergodicity assumption is questionable in interpretation of the observed galaxy…

Intelligent devices for supporting persons with vision impairment are becoming more widespread, but they are lacking behind the advancements in intelligent driver assistant system. To make a first step forward, this work discusses the…

Distance function to a compact set plays a central role in several areas of computational geometry. Methods that rely on it are robust to the perturbations of the data by the Hausdorff noise, but fail in the presence of outliers. The…

The flyby anomaly is the unexpected variation of the asymptotic post-encounter velocity of a spacecraft with respect to the pre-encounter velocity as it performs a slingshot manoeuvre. This effect has been detected in, at least, six flybys…

This textbook provides a systematic treatment of statistical machine learning for astronomical research through the lens of Bayesian inference, developing a unified framework that reveals connections between modern data analysis techniques…

Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…

Safety is a central requirement for automated vehicles. As such, the assessment of risk in automated driving is key in supporting both motion planning technologies and safety evaluation. In automated driving, risk is characterized by two…

We use a Bayesian approach to derive the distance probability distribution for one object from its parallax with measurement uncertainty for two spatial distribution priors, viz. a homogeneous spherical distribution and a galactocentric…

In this paper we examine the possibility of testing the equivalence principle, in its weak form, by analyzing the orbital motion of a pair of artificial satellites of different composition moving along orbits of identical shape and size in…

In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…

We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem…

Balancing a rare and serious possibility against a more common and less serious one is a familiar problem in many situations, such as the prediction of rare diseases. The relative costs of forecasting errors can be used for any prediction…

I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects (e.g., spacetimes) living in infinite-dimensional…

A classification scheme for close pairs of galaxies is proposed. The scheme is motivated by the fact that the majority of apparent close pairs are in fact wide pairs in three-dimensional space. This is demonstrated by means of numerical…

We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…

Despite centuries of close association, statistics and astronomy are surprisingly distant today. Most observational astronomical research relies on an inadequate toolbox of methodological tools. Yet the needs are substantial: astronomy…