Etemadi's inequality is a result in probability theory that provides a bound on the tail probabilities of a non-negative, integrable random variable. Specifically, it is used to give a probabilistic estimate concerning the sum of independent random variables, especially in the context of martingales and stopping times. The inequality states that if \( X \) is a non-negative random variable that is integrable (i.e.

QuantLib is an open-source library for quantitative finance, primarily used for modeling, trading, and risk management in financial markets. It is written in C++ and provides a comprehensive suite of tools for quantitative analysis, including: - **Interest rate models**: Facilities for modeling and analyzing interest rate derivatives. - **Options pricing models**: Various methodologies for pricing different types of options, including European, American, and exotic options.

Gauss's inequality, also known as the Gaussian inequality, is a result in probability theory and statistics that provides a bound on the tail probabilities of a normal distribution. Specifically, it states that for a standard normal variable \( Z \) (mean 0 and variance 1), the probability that \( Z \) deviates from its mean by more than a certain threshold can be bounded.

Hoeffding's inequality is a fundamental result in probability theory and statistics that provides a bound on the probability that the sum of bounded independent random variables deviates from its expected value. It is particularly useful in the context of statistical learning and empirical process theory.

The Janson inequality is a result in probability theory, particularly in the context of the study of random variables and dependent events. It provides a bound on the probability that a sum of random variables exceeds its expected value. Specifically, it is often used when dealing with random variables that exhibit some form of dependence.

The title "University Professor of Natural Philosophy" at Dublin typically refers to a prestigious academic position at Trinity College Dublin. Historically, "natural philosophy" is the term that was used before the modern sciences were fully articulated, encompassing topics like physics, astronomy, and other sciences that study the natural world. The role of the University Professor of Natural Philosophy would generally involve teaching, conducting research, and contributing to the academic community in areas related to the natural sciences.

Multidimensional Chebyshev's inequality is an extension of the classical Chebyshev's inequality to the context of multivariate distributions. The classical Chebyshev's inequality provides a probabilistic bound on how far a random variable can deviate from its mean.

The Van den Berg–Kesten inequality is a result in the field of probability theory, particularly in the study of dependent random variables. It provides a way to compare the probabilities of certain events that are dependent on each other under specific conditions. In a more formal context, the inequality deals with events in a finite set, where these events are allowed to be dependent, and it provides a bound on the probability of the union of these events.

Ville's inequality is a result in probability theory that provides an upper bound on the probability of a certain event involving a martingale. Specifically, it deals with the behavior of a non-negative submartingale and relates to stopping times.

Vitale's random Brunn–Minkowski inequality is a result in the field of geometric probability, particularly in the study of random convex bodies. It generalizes the classical Brunn–Minkowski inequality, which is a fundamental result in the theory of convex sets in Euclidean space, relating the volume of convex bodies to the volumes of their convex combinations.

P-boxes (probability boxes) and probability bounds analysis are powerful tools in the field of uncertainty quantification and risk assessment. They provide a systematic way to characterize and handle uncertainties in various applications, particularly when precise probability distributions are difficult to obtain.

An "appeal to probability" is a type of logical fallacy that occurs when someone assumes that because something is possible or likely, it must be true or will happen. This fallacy involves an unwarranted conclusion based on the probability of an event, rather than on solid evidence or deductive reasoning. For example, someone might argue, "It's likely that it will rain tomorrow, so it will rain.

The Law of Averages is a principle that suggests that over a large enough sample size, events will statistically tend to average out. In other words, it implies that if something happens with a certain probability, over time and numerous trials, the outcomes will reflect that probability.

Gambler's ruin is a concept from probability theory and statistics that models a gambling scenario where a gambler continues to gamble until either they lose all their money or reach a predetermined target amount. It is often used to illustrate the principles of random walks and the behavior of stochastic processes. In a typical setup, a gambler starts with a certain amount of capital and bets on a game with a fixed probability of winning or losing.

The Pill Puzzle is a logical reasoning problem often presented as a brain teaser or puzzle. It typically involves a scenario where you have a certain number of pills, some of which are good (safe to take) and some of which are bad (harmful or lethal). The challenge often centers around identifying the good pills from the bad ones using a limited number of tests or a specific set of rules. Here's a common formulation of the Pill Puzzle: - You have a number of pills, say 12.

Béla Krekó is a Hungarian political scientist and expert in the fields of foreign policy, international relations, and political psychology. He is recognized for his work on topics related to Central and Eastern Europe, nationalism, and the impact of public opinion on foreign policy decisions. Krekó may also be involved in academic research, public discourse, and policy analysis.

The Erasmus Smith's Professor of Mathematics is a prestigious academic position at Trinity College Dublin, the University of Dublin, Ireland. Established in 1752 through a bequest from Erasmus Smith, a wealthy merchant and philanthropist, the role is typically filled by a leading mathematician and involves both teaching and research responsibilities. The position is known for its contributions to mathematical sciences and its influence on mathematical education in Ireland.

Projective polyhedra are a class of geometric structures in the field of topology and geometry. More specifically, a projective polyhedron is a polyhedron that has been associated with the projective space, particularly projective 3-space. In topology, projective geometry can be understood as the study of geometric properties that are invariant under projective transformations.