Bayesian probabilityBayesian probability (ˈbeɪziən or ˈbeɪʒən ) is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown.
ApproximationAn approximation is anything that is intentionally similar but not exactly equal to something else. The word approximation is derived from Latin approximatus, from proximus meaning very near and the prefix ad- (ad- before p becomes ap- by assimilation) meaning to. Words like approximate, approximately and approximation are used especially in technical or scientific contexts. In everyday English, words such as roughly or around are used with a similar meaning. It is often found abbreviated as approx.
Effective methodIn logic, mathematics and computer science, especially metalogic and computability theory, an effective method or effective procedure is a procedure for solving a problem by any intuitively 'effective' means from a specific class. An effective method is sometimes also called a mechanical method or procedure. The definition of an effective method involves more than the method itself. In order for a method to be called effective, it must be considered with respect to a class of problems.
Ricci calculusIn mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern name for what used to be called the absolute differential calculus (the foundation of tensor calculus), developed by Gregorio Ricci-Curbastro in 1887–1896, and subsequently popularized in a paper written with his pupil Tullio Levi-Civita in 1900.
ComputabilityComputability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem. The most widely studied models of computability are the Turing-computable and μ-recursive functions, and the lambda calculus, all of which have computationally equivalent power.
Tensor calculusIn mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime). Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita, it was used by Albert Einstein to develop his general theory of relativity. Unlike the infinitesimal calculus, tensor calculus allows presentation of physics equations in a form that is independent of the choice of coordinates on the manifold.
Total variation distance of probability measuresIn probability theory, the total variation distance is a distance measure for probability distributions. It is an example of a statistical distance metric, and is sometimes called the statistical distance, statistical difference or variational distance. Consider a measurable space and probability measures and defined on . The total variation distance between and is defined as: Informally, this is the largest possible difference between the probabilities that the two probability distributions can assign to the same event.
Elliptic complexIn mathematics, in particular in partial differential equations and differential geometry, an elliptic complex generalizes the notion of an elliptic operator to sequences. Elliptic complexes isolate those features common to the de Rham complex and the Dolbeault complex which are essential for performing Hodge theory. They also arise in connection with the Atiyah-Singer index theorem and Atiyah-Bott fixed point theorem. If E0, E1, ...
