Bayesian epistemologyBayesian epistemology is a formal approach to various topics in epistemology that has its roots in Thomas Bayes' work in the field of probability theory. One advantage of its formal method in contrast to traditional epistemology is that its concepts and theorems can be defined with a high degree of precision. It is based on the idea that beliefs can be interpreted as subjective probabilities. As such, they are subject to the laws of probability theory, which act as the norms of rationality.
Agent-based computational economicsAgent-based computational economics (ACE) is the area of computational economics that studies economic processes, including whole economies, as dynamic systems of interacting agents. As such, it falls in the paradigm of complex adaptive systems. In corresponding agent-based models, the "agents" are "computational objects modeled as interacting according to rules" over space and time, not real people. The rules are formulated to model behavior and social interactions based on incentives and information.
Convergence of random variablesIn probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied.
Bayesian inferenceBayesian inference (ˈbeɪziən or ˈbeɪʒən ) is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law.
Computational physicsComputational physics is the study and implementation of numerical analysis to solve problems in physics. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science. It is sometimes regarded as a subdiscipline (or offshoot) of theoretical physics, but others consider it an intermediate branch between theoretical and experimental physics - an area of study which supplements both theory and experiment.
Dynamical systems theoryDynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle.
Prior probabilityA prior probability distribution of an uncertain quantity, often simply called the prior, is its assumed probability distribution before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable.
Computational scienceComputational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science that uses advanced computing capabilities to understand and solve complex physical problems. This includes Algorithms (numerical and non-numerical): mathematical models, computational models, and computer simulations developed to solve sciences (e.
Convex preferencesIn economics, convex preferences are an individual's ordering of various outcomes, typically with regard to the amounts of various goods consumed, with the property that, roughly speaking, "averages are better than the extremes". The concept roughly corresponds to the concept of diminishing marginal utility without requiring utility functions. Comparable to the greater-than-or-equal-to ordering relation for real numbers, the notation below can be translated as: 'is at least as good as' (in preference satisfaction).
Dynamical billiardsA dynamical billiard is a dynamical system in which a particle alternates between free motion (typically as a straight line) and specular reflections from a boundary. When the particle hits the boundary it reflects from it without loss of speed (i.e. elastic collisions). Billiards are Hamiltonian idealizations of the game of billiards, but where the region contained by the boundary can have shapes other than rectangular and even be multidimensional.
