|
Vecchia Approximation
Vecchia approximation is a Gaussian processes approximation technique originally developed by Aldo Vecchia, a statistician at United States Geological Survey. It is one of the earliest attempts to use Gaussian processes in high-dimensional settings. It has since been extensively generalized giving rise to many contemporary approximations. Intuition A joint probability distribution for events A, B, and C, denoted P(A,B,C), can be expressed as : P(A,B,C) = P(A) P(B , A) P(C , A,B) Vecchia's approximation takes the form, for example, : P(A,B,C) \approx P(A) P(B , A) P(C , A ) and is accurate when events B and C are close to conditionally independent given knowledge of A. Of course one could have alternatively chosen the approximation : P(A,B,C) \approx P(A) P(B, A) P(C , B) and so use of the approximation requires some knowledge of which events are close to conditionally independent given others. Moreover, we could have chosen a different ordering, for example : P(A,B,C) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Process
In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random variables, and as such, it is a distribution over functions with a continuous domain, e.g. time or space. The concept of Gaussian processes is named after Carl Friedrich Gauss because it is based on the notion of the Gaussian distribution (normal distribution). Gaussian processes can be seen as an infinite-dimensional generalization of multivariate normal distributions. Gaussian processes are useful in statistical modelling, benefiting from properties inherited from the normal distribution. For example, if a random process is modelled as a Gaussian process, the distribution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Process Approximations
In statistics and machine learning, Gaussian process approximation is a computational method that accelerates inference tasks in the context of a Gaussian process model, most commonly likelihood evaluation and prediction. Like approximations of other models, they can often be expressed as additional assumptions imposed on the model, which do not correspond to any actual feature, but which retain its key properties while simplifying calculations. Many of these approximation methods can be expressed in purely linear algebraic or functional analytic terms as matrix or function approximations. Others are purely algorithmic and cannot easily be rephrased as a modification of a statistical model. Basic ideas In statistical modeling, it is often convenient to assume that y \in \mathcal, the phenomenon under investigation is a Gaussian process indexed by X \in \mathcal = \mathcal_1 \times \mathcal_2 \dots \mathcal_d which has mean function \mu: \mathcal \rightarrow \mathcal and covar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aldo Vecchia , a town in Argentina
{{disambiguation ...
Aldo may refer to: * Aldo (given name), male given name ** Aldo (footballer, born 1977) ** Aldo (footballer, born 1988) * Aldo Group, a worldwide chain of shoe stores * Aldosterone in shorthand * Aldo Bonzi Aldo Bonzi is a town in La Matanza Partido, Buenos Aires Province, Argentina. It is located within the Greater Buenos Aires metro area. The town owes its name to Turin-born businessman Dr. Aldo Bonzi (1852–1935), who arrived in Argentina in 18 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States Geological Survey
The United States Geological Survey (USGS), formerly simply known as the Geological Survey, is a scientific agency of the United States government. The scientists of the USGS study the landscape of the United States, its natural resources, and the natural hazards that threaten it. The organization's work spans the disciplines of biology, geography, geology, and hydrology. The USGS is a fact-finding research organization with no regulatory responsibility. The agency was founded on March 3, 1879. The USGS is a bureau of the United States Department of the Interior; it is that department's sole scientific agency. The USGS employs approximately 8,670 people and is headquartered in Reston, Virginia. The USGS also has major offices near Lakewood, Colorado, at the Denver Federal Center, and Menlo Park, California. The current motto of the USGS, in use since August 1997, is "science for a changing world". The agency's previous slogan, adopted on the occasion of its hundredt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cholesky Decomposition
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced ) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices, and posthumously published in 1924. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations. Statement The Cholesky decomposition of a Hermitian positive-definite matrix A, is a decomposition of the form : \mathbf = \mathbf^*, where L is a lower triangular matrix with real and positive diagonal entries, and L* denotes the conjugate transpose of L. Every Hermitian positive-definite matrix (and thus also every real-valued symmetric positive-definite matrix) has a unique Cholesky decomposition. The converse holds trivially: if A can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moral Graph
In graph theory, a moral graph is used to find the equivalent undirected form of a directed acyclic graph. It is a key step of the junction tree algorithm, used in belief propagation on graphical models. The moralized counterpart of a directed acyclic graph is formed by adding edges between all pairs of non-adjacent nodes that have a common child, and then making all edges in the graph undirected. Equivalently, a moral graph of a directed acyclic graph is an undirected graph in which each node of the original is now connected to its Markov blanket. The name stems from the fact that, in a moral graph, two nodes that have a common child are required to be ''married'' by sharing an edge. Moralization may also be applied to mixed graphs, called in this context "chain graphs". In a chain graph, a connected component of the undirected subgraph is called a chain. Moralization adds an undirected edge between any two vertices that both have outgoing edges to the same chain, and then forge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sparse Matrix
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.g., ''m'' × ''n'' for an ''m'' × ''n'' matrix) is sometimes referred to as the sparsity of the matrix. Conceptually, sparsity corresponds to systems with few pairwise interactions. For example, consider a line of balls connected by springs from one to the next: this is a sparse system as only adjacent balls are coupled. By contrast, if the same line of balls were to have springs connecting each ball to all other balls, the system would correspond to a dense matrix. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CRAN (R Programming Language)
R packages are extensions to the R statistical programming language. R packages contain code, data, and documentation in a standardised collection format that can be installed by users of R, typically via a centralised software repository such as CRAN (the Comprehensive R Archive Network). The large number of packages available for R, and the ease of installing and using them, has been cited as a major factor driving the widespread adoption of the language in data science. Compared to libraries in other programming language, R packages must conform to a relatively strict specification. The ''Writing R Extensions'' manual specifies a standard directory structure for R source code, data, documentation, and package metadata, which enables them to be installed and loaded using R's in-built package management tools. Packages distributed on CRAN must meet additional standards. According to John Chambers, whilst these requirements "impose considerable demands" on package developers, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PyPI
The Python Package Index, abbreviated as PyPI () and also known as the Cheese Shop (a reference to the ''Monty Python's Flying Circus'' sketch " Cheese Shop"), is the official third-party software repository for Python. It is analogous to the CPAN repository for Perl and to the CRAN repository for R. PyPI is run by the Python Software Foundation, a charity. Some package managers, including pip, use PyPI as the default source for packages and their dependencies. more than 350,000 Python packages can be accessed through PyPI. PyPI primarily hosts Python packages in the form of archives called (source distributions) or precompiled "wheels." PyPI as an index allows users to search for packages by keywords or by filters against their metadata, such as free software license or compatibility with POSIX. A single entry on PyPI is able to store, aside from just a package and its metadata, previous releases of the package, precompiled wheels (e.g. containing DLLs on Windows), as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geostatistics
Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geometallurgy, geography, forestry, environmental control, landscape ecology, soil science, and agriculture (esp. in precision farming). Geostatistics is applied in varied branches of geography, particularly those involving the spread of diseases (epidemiology), the practice of commerce and military planning (logistics), and the development of efficient spatial networks. Geostatistical algorithms are incorporated in many places, including geographic information systems (GIS). Background Geostatistics is intimately related to interpolation methods, but extends far beyond simple interpolation problems. Geostatistical techniques rely on statistical models that are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Science
Computational science, also known as scientific computing or scientific computation (SC), is a field in mathematics that uses advanced computing capabilities to understand and solve complex problems. It is an area of science that spans many disciplines, but at its core, it involves the development of models and simulations to understand natural systems. * Algorithms ( numerical and non-numerical): mathematical models, computational models, and computer simulations developed to solve science (e.g., biological, physical, and social), engineering, and humanities problems * Computer hardware that develops and optimizes the advanced system hardware, firmware, networking, and data management components needed to solve computationally demanding problems * The computing infrastructure that supports both the science and engineering problem solving and the developmental computer and information science In practical use, it is typically the application of computer simulation and other fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Statistics
Computational statistics, or statistical computing, is the bond between statistics and computer science. It means statistical methods that are enabled by using computational methods. It is the area of computational science (or scientific computing) specific to the mathematical science of statistics. This area is also developing rapidly, leading to calls that a broader concept of computing should be taught as part of general statistical education. As in traditional statistics the goal is to transform raw data into knowledge, Wegman, Edward J. Computational Statistics: A New Agenda for Statistical Theory and Practice. Journal of the Washington Academy of Sciences', vol. 78, no. 4, 1988, pp. 310–322. ''JSTOR'' but the focus lies on computer intensive statistical methods, such as cases with very large sample size and non-homogeneous data sets. The terms 'computational statistics' and 'statistical computing' are often used interchangeably, although Carlo Lauro (a former presid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
