Related papers: A Course on Elementary Probability Theory
The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crosswords between possibility and probability theories. Such confidence relations between events are commonly found in monotonic…
We report on a course project in which students submit weekly probabilistic forecasts of two weather variables and one financial variable. This real-time format allows students to engage in practical forecasting, which requires a diverse…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
The main goal of statistical learning theory is to provide a fundamental framework for the problem of decision making and model construction based on sets of data. Here, we present a brief introduction to the fundamentals of statistical…
This is a replacement paper. There are 6 chapters. The first two chapters are introductory. The third chapter is on extremal graph theory. The fourth chapter is about algebra in graph theory. The fifth chapter is focused on algorithms. The…
The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of…
I am presenting a first-ever scientific collection of short sayings on probability and statistics expressed by most various men of science, many classics included, from antiquity to Kepler to our time. Quite understandably, the reader will…
We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…
The prime number problem falls within the realm of number theory, specifically elementary number theory. Current research approaches have unnecessarily complicated this matter. In contrast to more advanced mathematical tools, the methods of…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
Probability theory is far from being the most general mathematical theory of uncertainty. A number of arguments point at its inability to describe second-order ('Knightian') uncertainty. In response, a wide array of theories of uncertainty…
We provide a systematic, thorough treatment of the foundations of probability theory and stochastic processes along the lines of E. Bishop's constructive analysis. Every existence result presented shall be a construction; and the input…
According to the probability ranking principle, the document set with the highest values of probability of relevance optimizes information retrieval effectiveness given the probabilities are estimated as accurately as possible. The key…
How should social scientists understand and communicate the uncertainty of statistically estimated causal effects? I propose we utilize the posterior distribution of a causal effect and present the probability of the effect being greater…
We give a survey of the foundations of statistical queries and their many applications to other areas. We introduce the model, give the main definitions, and we explore the fundamental theory statistical queries and how how it connects to…
The goal of this thesis is twofold; introduce the fundamentals of Bayesian inference and computation focusing on astronomical and cosmological applications, and present recent advances in probabilistic computational methods developed by the…
This survey paper is an expanded version of lectures given at the Clay Mathematics Academy ; see http://www.claymath.org/programs/outreach/academy/colloquium2005.php These lectures were intended to very young (and motivated) college…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…