Related papers: Triangle Inscribed-Triangle Picking
Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits.…
Bayesian parameter estimation on gravitational waves from compact binary coalescences (CBCs) typically requires millions of template waveform computations at different values of the parameters describing the binary. Sampling techniques such…
In this paper we give a formula for the probability that $n$ random points chosen under the uniform distribution in a disk are in convex position. While close, the formula is recursive and is totally explicit only for the first values of…
The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0,1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007)…
This paper proposes an algorithm to generate random numbers from any member of the truncated multivariate elliptical family of distributions with a strictly decreasing density generating function. Based on Neal (2003) and Ho et al. (2012),…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
The asymptotic results pertaining to the distribution of the log likelihood ratio allow for the creation of a confidence region, which is a general extension of the confidence interval. Two and three dimensional regions can be displayed…
Using a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping…
The region of attraction characterizes well-behaved and safe operation of a nonlinear system and is hence sought after for verification. In this paper, a framework for probabilistic region of attraction estimation is developed that combines…
We map the density matrix of the qubit (spin-1/2) state associated with the Bloch sphere and given in the tomographic probability representation onto vertices of a triangle determining Triada of Malevich's squares. The three triangle…
We study "tricolor percolation" on the regular tessellation of R^3 by truncated octahedra, which is the three-dimensional analog of the hexagonal tiling of the plane. We independently assign one of three colors to each cell according to a…
The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…
Selecting between different dependency structures of hidden Markov random field can be very challenging, due to the intractable normalizing constant in the likelihood. We answer this question with approximate Bayesian computation (ABC)…
We show that both aspect ratios of randomly oriented triaxial ellipsoids (representing isosurfaces of an isotropic 3D random field) can be determined from a single 2D cross-section of their sample using the probability distribution of the…
We study rectangles inscribed in lines in the plane by parametrizing these rectangles in two ways, one involving slope and the other aspect ratio. This produces two paths, one that finds rectangles with specified slope and the other…
The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types of…
In 1964 A. Bruckner observed that any bounded open set in the plane has an inscribed triangle, that is a triangle contained in the open set and with the vertices lying on the boundary. We prove that this triangle can be taken uniformly fat,…
Let $\mathcal P$ be a simple polygonal environment with $k$ vertices in the plane. Assume that a set $B$ of $b$ blue points and a set $R$ of $r$ red points are distributed in $\mathcal P$. We study the problem of computing triangles that…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
Among the topics we discuss are certain joint densities (for sides and for angles), acuteness probabilities and bivariate Rice moments.