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Particle Filter
Particle filters, or sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to solve filtering problems arising in signal processing and Bayesian statistical inference. The filtering problem consists of estimating the internal states in dynamical systems when partial observations are made and random perturbations are present in the sensors as well as in the dynamical system. The objective is to compute the posterior distributions of the states of a Markov process, given the noisy and partial observations. The term "particle filters" was first coined in 1996 by Del Moral about mean-field interacting particle methods used in fluid mechanics since the beginning of the 1960s. The term "Sequential Monte Carlo" was coined by Liu and Chen in 1998. Particle filtering uses a set of particles (also called samples) to represent the posterior distribution of a stochastic process given the noisy and/or partial observations. The state-space model can be nonlinear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of ris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Physics
Computational physics is the study and implementation of numerical analysis to solve problems in physics for which a quantitative theory already exists. 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. Overview In physics, different theories based on mathematical models provide very precise predictions on how systems behave. Unfortunately, it is often the case that solving the mathematical model for a particular system in order to produce a useful prediction is not feasible. This can occur, for instance, when the solution does not have a closed-form expression, or is too complicated. In such cases, numerical approximations are required. Computational phy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extended Kalman Filter
In estimation theory, the extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about an estimate of the current mean and covariance. In the case of well defined transition models, the EKF has been considered the ''de facto'' standard in the theory of nonlinear state estimation, navigation systems and GPS. History The papers establishing the mathematical foundations of Kalman type filters were published between 1959 and 1961. The Kalman filter is the optimal linear estimator for ''linear'' system models with additive independent white noise in both the transition and the measurement systems. Unfortunately, in engineering, most systems are ''nonlinear'', so attempts were made to apply this filtering method to nonlinear systems; most of this work was done at NASA Ames. The EKF adapted techniques from calculus, namely multivariate Taylor series expansions, to linearize a model about a working point. If the system model (as described below) is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Chain Monte Carlo
In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by recording states from the chain. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Various algorithms exist for constructing chains, including the Metropolis–Hastings algorithm. Application domains MCMC methods are primarily used for calculating numerical approximations of multi-dimensional integrals, for example in Bayesian statistics, computational physics, computational biology and computational linguistics. In Bayesian statistics, the recent development of MCMC methods has made it possible to compute large hierarchical models that require integrations over hundreds to thousands of unknown parameters. In rare e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kalman Filter
For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, who was one of the primary developers of its theory. This digital filter is sometimes termed the ''Stratonovich–Kalman–Bucy filter'' because it is a special case of a more general, nonlinear filter developed somewhat earlier by the Soviet mathematician Ruslan Stratonovich. In fact, some of the special case linear filter's equations appeared in papers by Stratonovich that were published before summer 1960, when Kalman met with Stratonovich during a conference in Moscow. Kalman filtering has numerous te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Filter
In signal processing, a nonlinear (or non-linear) filter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals ''R'' and ''S'' for two input signals ''r'' and ''s'' separately, but does not always output ''αR'' + ''βS'' when the input is a linear combination ''αr'' + ''βs''. Both continuous-domain and discrete-domain filters may be nonlinear. A simple example of the former would be an electrical device whose output voltage ''R''(''t'') at any moment is the square of the input voltage ''r''(''t''); or which is the input clipped to a fixed range 'a'',''b'' namely ''R''(''t'') = max(''a'', min(''b'', ''r''(''t''))). An important example of the latter is the running-median filter, such that every output sample ''R''''i'' is the median of the last three input samples ''r''''i'', ''r''''i''−1, ''r''''i''−2. Like linear filters, nonlinear filters may be shift invariant or not. Non-linear filters hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hidden Markov Model
A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process — call it X — with unobservable ("''hidden''") states. As part of the definition, HMM requires that there be an observable process Y whose outcomes are "influenced" by the outcomes of X in a known way. Since X cannot be observed directly, the goal is to learn about X by observing Y. HMM has an additional requirement that the outcome of Y at time t=t_0 must be "influenced" exclusively by the outcome of X at t=t_0 and that the outcomes of X and Y at t handwriting recognition, handwriting, gesture recognition, part-of-speech tagging, musical score following, partial discharges and bioinformatics. Definition Let X_n and Y_n be discrete-time stochastic processes and n\geq 1. The pair (X_n,Y_n) is a ''hidden Markov model'' if * X_n is a Markov process whose behavior is not directly observable ("hidden"); * \operatorname\bigl(Y_n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolutionary Computation
In computer science, evolutionary computation is a family of algorithms for global optimization inspired by biological evolution, and the subfield of artificial intelligence and soft computing studying these algorithms. In technical terms, they are a family of population-based trial and error problem solvers with a metaheuristic or stochastic optimization character. In evolutionary computation, an initial set of candidate solutions is generated and iteratively updated. Each new generation is produced by stochastically removing less desired solutions, and introducing small random changes. In biological terminology, a population of solutions is subjected to natural selection (or artificial selection) and mutation. As a result, the population will gradually evolve to increase in fitness, in this case the chosen fitness function of the algorithm. Evolutionary computation techniques can produce highly optimized solutions in a wide range of problem settings, making them popula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Algorithm
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation, crossover and selection. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, etc. Methodology Optimization problems In a genetic algorithm, a population of candidate solutions (called individuals, creatures, organisms, or phenotypes) to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its chromosomes or genotype) which can be mutated and altered; traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusion Monte Carlo
Diffusion Monte Carlo (DMC) or diffusion quantum Monte Carlo is a quantum Monte Carlo method that uses a Green's function to solve the Schrödinger equation. DMC is potentially numerically exact, meaning that it can find the exact ground state energy within a given error for any quantum system. When actually attempting the calculation, one finds that for bosons, the algorithm scales as a polynomial with the system size, but for fermions, DMC scales exponentially with the system size. This makes exact large-scale DMC simulations for fermions impossible; however, DMC employing a clever approximation known as the fixed-node approximation can still yield very accurate results. The projector method To motivate the algorithm, let's look at the Schrödinger equation for a particle in some potential in one dimension: :i\frac=-\frac\frac + V(x)\Psi(x,t). We can condense the notation a bit by writing it in terms of an '' operator'' equation, with :H=-\frac\frac + V(x). So then we have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Monte Carlo
Quantum Monte Carlo encompasses a large family of computational methods whose common aim is the study of complex quantum systems. One of the major goals of these approaches is to provide a reliable solution (or an accurate approximation) of the quantum many-body problem. The diverse flavors of quantum Monte Carlo approaches all share the common use of the Monte Carlo method to handle the multi-dimensional integrals that arise in the different formulations of the many-body problem. Quantum Monte Carlo methods allow for a direct treatment and description of complex many-body effects encoded in the wave function, going beyond mean-field theory. In particular, there exist numerically exact and polynomially-scaling algorithms to exactly study static properties of boson systems without geometrical frustration. For fermions, there exist very good approximations to their static properties and numerically exact exponentially scaling quantum Monte Carlo algorithms, but none that ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arianna W
Arianna may refer to: * Ariana (name), a given name Opera * '' L'Arianna'', (English: ''Arianna''), by Monteverdi, first performed 1608 * ''Arianna'' (Marcello), by Benedetto Marcello, first concert performance 1727 * '' Arianna in Creta'', by Handel, first performed 1734 * ''Arianna'' (Goehr), by Alexander Goehr, first performed 1995 Other uses * ''Arianna'' (film), 2015 * ARIANNA Experiment, a proposed neutrino detector at the Ross Ice Shelf, Antarctica * Arianna (yacht), a 2012 luxury megayacht See also * Ariana (other) * Ariane (other) *Ariadne (other) *Aria (region) Aria ( el, ''Ar(e)ía'', آريا; Latin ''Aria'', representing Old Persian. 𐏃𐎼𐎡𐎺 ''Haraiva'', Avestan 𐬵𐬀𐬭𐬋𐬌𐬬𐬀 ''Harōiva'') was an Achaemenid region centered on the city of Herat in present-day western Afgha ..., sometimes confused with Ariana * Aryana (TV series) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
