Related papers: Grassmannian calculus for probability
We propose a multivariate probability distribution for categorical and ordinal random variables. To this end, we use the Grassmann distribution in conjunction with dummy encoding of categorical and ordinal variables. To realize the…
Lectures presented at the 1st CERN Asia-Europe-Pacific School of High-Energy Physics, Fukuoka, Japan, 14-27 October 2012. A pedagogical selection of topics in probability and statistics is presented. Choice and emphasis are driven by the…
The present notes provide an extended version of a small lecture course given at the Humboldt Universit\"at zu Berlin in the Winter Term 2022/23 (of 36 hours). The material starting in Section 5.4 was added afterwards. The aim of these…
The plenary lectures, parallel talks, oral presentations and panel contributions on Cosmology and Gravitation presented during the XXII Brazilian National Meeting on Particles and Fields are briefly reviewed. Some remarks on the area are…
Lecture given Thursday 22 October 1992 at a Mathematics-Computer Science Colloquium at the University of New Mexico. The lecture was videotaped; this is an edited transcript.
We begin our journey by recalling the fundamentals of Probability Theory that underlie one of its most significant applications to real-world problems: Parametric Estimation. Throughout the text, we systematically develop this theme by…
This article is geared towards theorists interested in estimating parameters of their theoretical models, and computing their own limits using available experimental data and elementary Mathematica code. The examples given can be useful…
This volume contains the papers presented at LINEARITY 2016, the Fourth International Workshop on Linearity, held on June 26, 2016 in Porto, Portugal. The workshop was a one-day satellite event of FSCD 2016, the first International…
Invitation to the statistical study of language: The topic of this presentation is the interdisciplinary nexus between linguistics and statistics. It targets linguists, for whom it may have a theoretical interest, or professionals that work…
This is an expository introduction to tropical algebraic geometry based on my lectures at the Workshop on Tropical Geometry and Integrable Systems in Glasgow, July 4-8, 2011, and at the ELGA 2011 school on Algebraic Geometry and…
These lecture notes provide an introduction to Langevin processes and briefly discuss some interesting properties and simple applications. They compile material presented at the "School of Physics and Mathematics Without Frontiers"…
This is the written version of a lecture given at the ``VI Mexican School of Gravitation and Mathematical Physics" (Nov 21-27, 2004, Playa del Carmen, Mexico), introducing the basics of Loop Quantum Geometry. The purpose of the written…
Geometrical aspects of quantum computing are reviewed elementarily for non-experts and/or graduate students who are interested in both Geometry and Quantum Computation. In the first half we show how to treat Grassmann manifolds which are…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
This is a short survey on existing upper and lower bounds on the probability of the union of a finite number of events using partial information given in terms of the individual or pairwise event probabilities (or their sums). New proofs…
Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…
A gentle introduction to Gaussian processes (GPs). The three parts of the document consider GPs for regression, classification, and dimensionality reduction.
Lecture notes given at the summer school ``Applications of random matrices to physics", Les Houches, June 2004.
This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…