Plurisubharmonic functionIn mathematics, plurisubharmonic functions (sometimes abbreviated as psh, plsh, or plush functions) form an important class of functions used in complex analysis. On a Kähler manifold, plurisubharmonic functions form a subset of the subharmonic functions. However, unlike subharmonic functions (which are defined on a Riemannian manifold) plurisubharmonic functions can be defined in full generality on complex analytic spaces.
Locally convex topological vector spaceIn functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They can be defined as topological vector spaces whose topology is generated by translations of balanced, absorbent, convex sets. Alternatively they can be defined as a vector space with a family of seminorms, and a topology can be defined in terms of that family.
Maximum spacing estimationIn statistics, maximum spacing estimation (MSE or MSP), or maximum product of spacing estimation (MPS), is a method for estimating the parameters of a univariate statistical model. The method requires maximization of the geometric mean of spacings in the data, which are the differences between the values of the cumulative distribution function at neighbouring data points.
Maximum a posteriori estimationIn Bayesian statistics, a maximum a posteriori probability (MAP) estimate is an estimate of an unknown quantity, that equals the mode of the posterior distribution. The MAP can be used to obtain a point estimate of an unobserved quantity on the basis of empirical data. It is closely related to the method of maximum likelihood (ML) estimation, but employs an augmented optimization objective which incorporates a prior distribution (that quantifies the additional information available through prior knowledge of a related event) over the quantity one wants to estimate.
Laplace's methodIn mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form where is a twice-differentiable function, M is a large number, and the endpoints a and b could possibly be infinite. This technique was originally presented in . In Bayesian statistics, Laplace's approximation can refer to either approximating the posterior normalizing constant with Laplace's method or approximating the posterior distribution with a Gaussian centered at the maximum a posteriori estimate.
Distribution (mathematics)Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. Distributions are widely used in the theory of partial differential equations, where it may be easier to establish the existence of distributional solutions (weak solutions) than classical solutions, or where appropriate classical solutions may not exist.
Spanish fluThe 1918-20 flu pandemic, also known as the Great Influenza epidemic or by the common misnomer of the Spanish flu, was an exceptionally deadly global influenza pandemic caused by the H1N1 influenza A virus. The earliest documented case was March 1918 in the state of Kansas in the United States, with further cases recorded in France, Germany and the United Kingdom in April. Two years later, nearly a third of the global population, or an estimated 500 million people, had been infected in four successive waves.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Pierre-Simon LaplacePierre-Simon, Marquis de Laplace (ləˈplɑ:s; pjɛʁ simɔ̃ laplas; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and extended the work of his predecessors in his five-volume Mécanique céleste (Celestial Mechanics) (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems.
2009 swine flu pandemicThe 2009 swine flu pandemic, caused by the H1N1/swine flu/influenza virus and declared by the World Health Organization (WHO) from June 2009 to August 2010, is the third recent flu pandemic involving the H1N1 virus (the first being the 1918–1920 Spanish flu pandemic and the second being the 1977 Russian flu). The first two cases were discovered independently in the United States in April 2009. The virus appeared to be a new strain of H1N1 that resulted from a previous triple reassortment of bird, swine, and human flu viruses which further combined with a Eurasian pig flu virus, leading to the term "swine flu".
Hong Kong fluThe Hong Kong flu, also known as the 1968 flu pandemic, was a flu pandemic whose outbreak in 1968 and 1969 killed between one and four million people globally. It is among the deadliest pandemics in history, and was caused by an H3N2 strain of the influenza A virus. The virus was descended from H2N2 (which caused the Asian flu pandemic in 1957–1958) through antigenic shift, a genetic process in which genes from multiple subtypes are reassorted to form a new virus.
Likelihood functionIn statistical inference, the likelihood function quantifies the plausibility of parameter values characterizing a statistical model in light of observed data. Its most typical usage is to compare possible parameter values (under a fixed set of observations and a particular model), where higher values of likelihood are preferred because they correspond to more probable parameter values.
