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Bayesian Inference Using Gibbs Sampling
Bayesian inference using Gibbs sampling (BUGS) is a statistical software for performing Bayesian inference using Markov chain Monte Carlo (MCMC) methods. It was developed by David Spiegelhalter at the Medical Research Council Biostatistics Unit in University of Cambridge, Cambridge in 1989 and released as free software in 1991. The BUGS project has evolved through four main versions: ClassicBUGS, WinBUGS, OpenBUGS anMultiBUGS MultiBUGS is built on the existing algorithms and tools in OpenBUGS and WinBUGS, which are no longer developed, and implements Parallel computing, parallelization to speed up computation. Several R (programming language), R packages are availableR2MultiBUGSacts as an interface to MultiBUGS, whilNimbleis an extension of the BUGS language. Alternative implementations of the BUGS language include Just another Gibbs sampler, JAGS and Stan (software), Stan. See also * Spike and slab variable selection * Bayesian structural time series References External l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Software
The following is a list of statistical software. Open-source * ADaMSoft – a generalized statistical software with data mining algorithms and methods for data management * ADMB – a software suite for non-linear statistical modeling based on C++ which uses automatic differentiation * Chronux – for neurobiological time series data * DAP (software), DAP – free replacement for SAS * Environment for DeveLoping KDD-Applications Supported by Index-Structures (ELKI) a software framework for developing data mining algorithms in Java (programming language), Java * Epi Info – List of statistical packages, statistical software for epidemiology developed by Centers for Disease Control and Prevention (CDC). Apache 2 licensed * Fityk – nonlinear regression software (GUI and command line) * GNU Octave – programming language very similar to MATLAB with statistical features * gretl – gnu regression, econometrics and time-series library * intrinsic Noise Analyzer (iNA) – For analyzin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Inference
Bayesian inference ( or ) is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available. Fundamentally, Bayesian inference uses a prior distribution to estimate posterior probabilities. 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. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". Introduction to Bayes' rule Formal explanation Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Chain Monte Carlo
In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it – that is, the Markov chain's Discrete-time Markov chain#Stationary distributions, equilibrium distribution matches the target distribution. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Markov chain Monte Carlo methods are used to study probability distributions that are too complex or too highly N-dimensional space, dimensional to study with analytic techniques alone. Various algorithms exist for constructing such Markov chains, including the Metropolis–Hastings algorithm. General explanation Markov chain Monte Carlo methods create samples from a continuous random variable, with probability density proportional to a known function. These samples can be used to e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Spiegelhalter
Sir David John Spiegelhalter (born 16 August 1953) is a British statistician and a Fellow of Churchill College, Cambridge. From 2007 to 2018 he was Winton Professorship of the Public Understanding of Risk, Winton Professor of the Public Understanding of Risk in the Faculty of Mathematics, University of Cambridge, Statistical Laboratory at the University of Cambridge. Spiegelhalter is an ISI highly cited researcher. He is currently Chair of the Winton Centre for Risk and Evidence Communication in the Centre for Mathematical Sciences (Cambridge), Centre for Mathematical Sciences at Cambridge. On 27 May 2020 he joined the UK Statistics Authority#Current board members, board of the UK Statistics Authority as a non-executive director for a period of three years, a term which was extended through to 2026. Early life and education Spiegelhalter was born on 16 August 1953. He was educated at Barnstaple Grammar School, a State school, state grammar school in Barnstaple, Devon, from 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Cambridge
The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, world's third-oldest university in continuous operation. The university's founding followed the arrival of scholars who left the University of Oxford for Cambridge after a dispute with local townspeople. The two ancient university, ancient English universities, although sometimes described as rivals, share many common features and are often jointly referred to as Oxbridge. In 1231, 22 years after its founding, the university was recognised with a royal charter, granted by Henry III of England, King Henry III. The University of Cambridge includes colleges of the University of Cambridge, 31 semi-autonomous constituent colleges and List of institutions of the University of Cambridge#Schools, Faculties, and Departments, over 150 academic departm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yale University Press
Yale University Press is the university press of Yale University. It was founded in 1908 by George Parmly Day and Clarence Day, grandsons of Benjamin Day, and became a department of Yale University in 1961, but it remains financially and operationally autonomous. , Yale University Press publishes approximately 300 new hardcover A hardcover, hard cover, or hardback (also known as hardbound, and sometimes as casebound (At p. 247.)) book is one bookbinding, bound with rigid protective covers (typically of binder's board or heavy paperboard covered with buckram or other clo ... and 150 new paperback books annually and has a backlist of about 5,000 books in print. Its books have won five National Book Awards, two National Book Critics Circle Awards and eight Pulitzer Prizes. The press maintains offices in New Haven, Connecticut and London, England. Yale is the only American university press with a full-scale publishing operation in Europe. It was a co-founder of the dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
WinBUGS
WinBUGS is statistical software for Bayesian analysis using Markov chain Monte Carlo (MCMC) methods. It is based on the BUGS ( Bayesian inference Using Gibbs Sampling) project started in 1989. It runs under Microsoft Windows, though it can also be run on Linux or Mac using Wine. It was developed by the BUGS Project, a team of British researchers at the MRC Biostatistics Unit, Cambridge, and Imperial College School of Medicine, London. Originally intended to solve problems encountered in medical statistics, it soon became widely used in other disciplines, such as ecology, sociology, and geology. The last version of WinBUGS was version 1.4.3, released in August 2007. Development is now focused on OpenBUGS, an open-source Open source is source code that is made freely available for possible modification and redistribution. Products include permission to use and view the source code, design documents, or content of the product. The open source model is a decentrali ... version ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OpenBUGS
OpenBUGS is a software application for the Bayesian analysis of complex statistical models using Markov chain Monte Carlo (MCMC) methods. OpenBUGS is the open source variant of WinBUGS (Bayesian inference Using Gibbs Sampling). It runs under Microsoft Windows and Linux, as well as from inside the R statistical package. Versions from v3.0.7 onwards have been designed to be at least as efficient and reliable as WinBUGS over a range of test applications. Differences from WinBUGS In addition to the different licence and greater range of operating systems, a fundamental difference between OpenBUGS and WinBUGS is the way in which the expert system selects the updating algorithm to use for the class of full conditional distribution of each node. While WinBUGS defines one algorithm for each possible class, there is no limit to the number of algorithms that OpenBUGS can use, allowing greater flexibility and extensibility. The user can select the updater to be used for each node after com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Computing
Parallel computing is a type of computing, computation in which many calculations or Process (computing), processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different forms of parallel computing: Bit-level parallelism, bit-level, Instruction-level parallelism, instruction-level, Data parallelism, data, and task parallelism. Parallelism has long been employed in high-performance computing, but has gained broader interest due to the physical constraints preventing frequency scaling.S.V. Adve ''et al.'' (November 2008)"Parallel Computing Research at Illinois: The UPCRC Agenda" (PDF). Parallel@Illinois, University of Illinois at Urbana-Champaign. "The main techniques for these performance benefits—increased clock frequency and smarter but increasingly complex architectures—are now hitting the so-called power wall. The computer industry has accepted that future performance inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R (programming Language)
R is a programming language for statistical computing and Data and information visualization, data visualization. It has been widely adopted in the fields of data mining, bioinformatics, data analysis, and data science. The core R language is extended by a large number of R package, software packages, which contain Reusability, reusable code, documentation, and sample data. Some of the most popular R packages are in the tidyverse collection, which enhances functionality for visualizing, transforming, and modelling data, as well as improves the ease of programming (according to the authors and users). R is free and open-source software distributed under the GNU General Public License. The language is implemented primarily in C (programming language), C, Fortran, and Self-hosting (compilers), R itself. Preprocessor, Precompiled executables are available for the major operating systems (including Linux, MacOS, and Microsoft Windows). Its core is an interpreted language with a na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Just Another Gibbs Sampler
Just another Gibbs sampler (JAGS) is a program for simulation from Bayesian hierarchical models using Markov chain Monte Carlo (MCMC), developed by Martyn Plummer. JAGS has been employed for statistical work in many fields, for example ecology, management, and genetics. JAGS aims for compatibility with WinBUGS/ OpenBUGS through the use of a dialect of the same modeling language (informally, BUGS), but it provides no GUI for model building and MCMC sample postprocessing, which must therefore be treated in a separate program (for example calling JAGS from R through a library such as rjags and post-processing MCMC output in R).Martyn Plummer (2003)JAGS: A Program for Analysis of Bayesian Graphical Models Using Gibbs Sampling Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003), March 20–22, Vienna, Austria. ISSN 1609-395X. The main advantage of JAGS in comparison to the members of the original BUGS family ( WinBUGS and OpenBUGS) is its p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stan (software)
Stan is a probabilistic programming language for statistical inference written in C++.Stan Development Team. 2015Stan Modeling Language User's Guide and Reference Manual, Version 2.9.0/ref> The Stan language is used to specify a (Bayesian) statistical model with an imperative program calculating the log probability density function. Stan is licensed under the New BSD License. Stan is named in honour of Stanislaw Ulam, pioneer of the Monte Carlo method. Stan was created by a development team consisting of 52 members that includes Andrew Gelman, Bob Carpenter, Daniel Lee, Ben Goodrich, and others. Example A simple linear regression model can be described as y_n = \alpha + \beta x_n + \epsilon_n, where \epsilon_n \sim \text (0, \sigma). This can also be expressed as y_n \sim \text(\alpha + \beta X_n, \sigma). The latter form can be written in Stan as the following: data parameters model Interfaces The Stan language itself can be accessed through several interfaces: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
