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An overview of some recent developments in inhomogeneous models is presented. As the volume and precision of cosmological data improves, it will become more and more essential to understand the non-linear behaviour of the Einstein field…
Regression on observational data can fail to capture a causal relationship in the presence of unobserved confounding. Confounding strength measures this mismatch, but estimating it requires itself additional assumptions. A common assumption…
Astronomers are often confronted with funky populations and distributions of objects: brighter objects are more likely to be detected; targets are selected based on colour cuts; imperfect classification yields impure samples. Failing to…
The existence of incompatible measurements, epitomized by Heisenberg's uncertainty principle, is one of the distinctive features of quantum theory. So far, quantum incompatibility has been studied for measurements that test the preparation…
Recent detection of high-redshift, massive clusters through Sunyaev-Zel'dovich observations has opened up a new way to test cosmological models. It is known that detection of a single supermassive cluster at a very high redshift can rule…
In science and medicine, model interpretations may be reported as discoveries of natural phenomena or used to guide patient treatments. In such high-stakes tasks, false discoveries may lead investigators astray. These applications would…
Long-baseline interferometry at optical and near-infrared wavelengths is an emerging technology which is quickly becoming a useful tool to investigate stellar atmospheres and to compare observations with models. Stellar atmosphere models…
We propose a general and relatively simple method for the construction of goodness-of-fit tests on the sphere and the hypersphere. The method is based on the characterization of probability distributions via their characteristic function,…
In this article, we propose some two-sample tests based on ball divergence and investigate their high dimensional behavior. First, we study their behavior for High Dimension, Low Sample Size (HDLSS) data, and under appropriate regularity…
To ensure reliable causal conclusions from observational (i.e., non-randomized) studies, researchers routinely conduct sensitivity analysis to assess robustness to hidden bias due to unmeasured confounding. In matched observational studies…
Model-independent methods in cosmology has become an essential tool in order to deal with an increasing number of theoretical alternatives for explaining the late-time acceleration of the Universe. In principle, this provides a way of…
Recent galaxy redshift surveys have brought in a large amount of accurate cosmological data out to redshift 0.3, and future surveys are expected to achieve a high degree of completeness out to a redshift exceeding 1. Consequently, a…
This paper provides a nonparametric test for the identity of two multivariate continuous distribution functions (d.f.'s) when they differ in locations. The test uses Wilcoxon rank-sum statistics on distances between observations for each of…
A central problem in cognitive science and behavioural neuroscience as well as in machine learning and artificial intelligence research is to ascertain whether two or more decision makers (be they brains or algorithms) use the same…
Interpreting experimental data in high school experiments can be a difficult task for students, especially when there is large variation in the data. At the same time, calculating the standard deviation poses a challenge for students. In…
Modern astronomy has been rapidly increasing our ability to see deeper into the universe, acquiring enormous samples of cosmic populations. Gaining astrophysical insights from these datasets requires a wide range of sophisticated…
Provided that sufficient resources are deployed, we can look forward to an extraordinary future in which we will characterize potentially habitable planets. Until now, we have had to base interpretations of observations on habitability…
The properties of matter at ultra-high densities, low temperatures, and with a significant asymmetry between protons and neutrons can be studied exclusively through astrophysical observations of neutron stars. We show that measurements of…
Searches for statistically significant correlations between arrival directions of ultra-high energy cosmic rays and classes of astrophysical objects are common in astroparticle physics. We present a method to test potential correlation…
Counterfactual examples are one of the most commonly-cited methods for explaining the predictions of machine learning models in key areas such as finance and medical diagnosis. Counterfactuals are often discussed under the assumption that…