Related papers: A Mathematical Theory of Stochastic Microlensing I…
Observations of caustic-crossing galaxies at redshift $0.7<z<1$ show a wealth of transient events. Most of them are believed to be microlensing events of highly magnified stars. Earlier work predicted such events should be common near the…
In microlensing of a Galactic star by a brown dwarf or other compact object, the amplified image really consists of two unresolved images with slightly different light-travel times. The difference (of order a microsecond) is GM/c^3 times a…
The importance of alternative methods for measuring the Hubble constant, such as time-delay cosmography, is highlighted by the recent Hubble tension. It is paramount to thoroughly investigate and rule out systematic biases in all…
For a number of reasons, the properties of integrated stellar populations are distributed. Traditional synthesis models usually return the mean value of such distribution, and a perfect fitting to observational data is sought for to infer…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
In this paper, we develop the mathematical framework for filtering problems arising from biophysical applications where data is collected from confocal laser scanning microscopy recordings of the space-time evolution of intracellular wave…
We examined the anisotropic point spread function (PSF) of Suprime-Cam data utilizing dense star field data. We decomposed the PSF ellipticities into three components, the optical aberration, atmospheric turbulence, and chip-misalignment in…
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…
We summarize the first exploratory investigation into whether Machine Learning techniques can augment science strategic planning. We find that an approach based on Latent Dirichlet Allocation using abstracts drawn from high impact astronomy…
We have investigated, using both a theoretical and an empirical approach, the frequency of low redshift galaxy-galaxy lensing systems in which the signature of weak lensing might be directly detectable. We find good agreement between these…
Weak lensing leads to the non-Gaussian magnification distribution of standard candles at given redshift $z$, $p(\mu|z)$. In this paper, we give accurate and simple empirical fitting formulae of the weak lensing numerical simulation results…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
Anisoplanatic effects can cause significant systematic photometric uncertainty in the analysis of dense stellar fields observed with adaptive optics. Program packages have been developed for a spatially variable PSF, but they require that a…
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class…
Weak-scale supersymmetry is one of the most favoured theories beyond the Standard Model of particle physics that elegantly solves various theoretical and observational problems in both particle physics and cosmology. In this thesis, I…
Eldan's stochastic localization is a probabilistic construction that has proved instrumental to modern breakthroughs in high-dimensional geometry and the design of sampling algorithms. Motivated by sampling under non-Euclidean geometries…
Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment,…
The wavelength dependence of atmospheric refraction causes elongation of finite-bandwidth images along the elevation vector, which produces spurious signals in weak gravitational lensing shear measurements unless this atmospheric dispersion…
We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…