Related papers: Asymptotics of the visibility function in the Bool…
We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…
A recent development in extreme value modeling uses the geometry of the dataset to perform inference on the multivariate tail. A key quantity in this inference is the gauge function, whose values define this geometry. Methodology proposed…
In the full rectangular version of Gilbert's tessellation lines extend either horizontally (with east- and west--growing rays) or vertically (north- and south--growing rays) from seed points which form a Poisson point process, each ray…
The shortcomings of maximum likelihood estimation in the context of model-based reinforcement learning have been highlighted by an increasing number of papers. When the model class is misspecified or has a limited representational capacity,…
Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…
Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also…
Different forms of long gamma-ray bursts (GRBs) Luminosity Functions are considered on the basis of an explicit physical model. The inferred flux distributions are compared with the observed ones from two samples of GRBs, Swift and Fermi…
We introduce a novel methodology for addressing systematic uncertainties in unbinned inclusive cross-section measurements and related collider-based inference problems. Our approach incorporates known analytic dependencies on parameters of…
In a recent paper we have calculated the power density spectrum of Gamma-Ray Bursts arising from multiple shocks in a relativistic wind. The wind optical thickness is one of the factors to which the power spectrum is most sensitive,…
A new three-parameter cumulative distribution function defined on $(\alpha,\infty)$, for some $\alpha\geq0$, with asymmetric probability density function and showing exponential decays at its both tails, is introduced. The new distribution…
Bayesian decision theory advocates the Bayes classifier as the optimal approach for minimizing the risk in machine learning problems. Current deep learning algorithms usually solve for the optimal classifier by \emph{implicitly} estimating…
It is shown that a light beam in free space is representable by an integral over a vectorial angular spectrum that is expressed in terms of an extension matrix, which describes the vectorial nature of the beam. A symmetry axis of the…
Statistics of molecular random walks in a fluid is considered with the help of the Bogolyubov equation for generating functional of distribution functions. An invariance group of solutions to this equation as functions of the fluid density…
Consider a critical Galton-Watson process Z={Z_n: n=0,1,...} of index 1+alpha, alpha in (0,1]. Let S_k(j) denote the sum of the Z_n with n in the window [k,...,k+j), and M_m(j) the maximum of the S_k with k moving in [0,m-j]. We describe…
We study terrain visibility graphs, a well-known graph class closely related to polygon visibility graphs in computational geometry, for which a precise graph-theoretical characterization is still unknown. Over the last decade, terrain…
The tight-binding model of a graphene bilayer is used to find the gap between the conduction and valence bands, as a function of both the gate voltage and as the doping by donors or acceptors. The total Hartree energy is minimized and the…
Random sets with long-range dependence can be generated using a Boolean model with power-law grain sizes. We study thinnings of such Boolean models which have the hard-core property that no grains overlap in the resulting germ-grain model.…
Variational inference approximates Bayesian posterior distributions by projecting onto a tractable family of distributions. While most theoretical analyses evaluate the quality of this approximation using global divergence measures, many…
When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…
We show that the tail probability of the rough line integral $\int_{0}^{1}\phi(X_{t})dY_{t}$, where $(X,Y)$ is a 2D fractional Brownian motion with Hurst parameter $H\in(1/4,1/2)$ and $\phi$ is a $C_{b}^{\infty}$-function satisfying a mild…