Related papers: The Bivariate Normal Integral via Owen's T Functio…
For the extended skew-normal distribution, which represents an extension of the normal (or Gaussian) distribution, we focus on the properties of the log-likelihood function and derived quantities in the the bivariate case. Specifically, we…
This article describes an R package bqror that estimates Bayesian quantile regression for ordinal models introduced in Rahman (2016). The paper classifies ordinal models into two types and offers computationally efficient, yet simple,…
Given a density operator $\hat \rho$ the optical tomography map defines a one-parameter set of probability distributions $w_{\hat \rho}(X,\phi),\ \phi \in [0,2\pi),$ on the real line allowing to reconstruct $\hat \rho $. We introduce a dual…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
The security of the RSA cryptosystem is based on the intractability of computing Euler's totient function phi(n) for large integers n. Although deriving phi(n) deterministically remains computationally infeasible for cryptographically…
Our community has a deep and sophisticated understanding of phase transitions and their universal scaling functions. We outline and advocate an ambitious program to use this understanding as an anchor for describing the surrounding phases.…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…
In this paper, we concentrate on new methodologies for copulas introduced and developed by Joe, Cooke, Bedford, Kurowica, Daneshkhah and others on the new class of graphical models called vines as a way of constructing higher dimensional…
This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…
Let $(X_1,\ldots,X_n)$ be an i.i.d. sequence of random variables in $\mathbb{R}^d$, $d\geq 1$. We show that, for any function $\varphi :\mathbb{R}^d\rightarrow\mathbb{R}$, under regularity conditions, \[n^…
\emph{Optimal Transport} (OT) has emerged as an important computational tool in machine learning and computer vision, providing a geometrical framework for studying probability measures. OT unfortunately suffers from the curse of…
Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. A…
Algorithms are proposed for the computation of set-valued quantiles and the values of the lower cone distribution function for bivariate data sets. These new objects make data analysis possible involving an order relation for the data…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
Publication bias (PB) poses a significant threat to meta-analysis, as studies yielding notable results are more likely to be published in scientific journals. Sensitivity analysis provides a flexible method to address PB and to examine the…
We construct a Beurling generalized number system satisfying the Riemann hypothesis and whose integer counting function displays extremal oscillation in the following sense. The prime counting function of this number system satisfies…
Tang derived the exact power formulae for t tests and analysis of covariance (ANCOVA) in superiority, noninferiority and equivalence trials. The power calculation in equivalence trials can be simplified by using Owen's Q function, which is…
In our recent publication we have proposed a new methodology for determination of the two-term Machin-like formula for pi with small arguments of the arctangent function of kind $$ \frac{\pi }{4} = {2^{k - 1}}\arctan \left(…
Over four decades, the majority addresses the problem of optical flow estimation using variational methods. With the advance of machine learning, some recent works have attempted to address the problem using convolutional neural network…