|
Sequential Monte Carlo
Particle filters, also known as sequential Monte Carlo methods, are a set of Monte Carlo method, Monte Carlo algorithms used to find approximate solutions for Filtering problem (stochastic processes), filtering problems for nonlinear state-space systems, such as signal processing and Bayesian inference, Bayesian statistical inference. The Filtering problem (stochastic processes), 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 probability, 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 Pierre Del Moral about mean-field particle methods, mean-field interacting particle methods used in fluid mechanics since the beginning of the 1960s. The term "Sequential Monte Carlo" was coined ... [...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. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, mathematician Stanisław Ulam, was inspired by his uncle's gambling habits. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant failure. Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically. Monte Carlo methods are widely used in va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during reactions with other substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology. It is sometimes called the central science because it provides a foundation for understanding both basic and applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth (botany), the formation of igneous rocks (geology), how atmospheric ozone is formed and how environmental pollutants are degraded (ecology), the properties of the soil on the Moon ( cosmochemistry), how medications work (pharmacology), ... [...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] |
Kalman Filter
In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those based on a single measurement, by estimating a joint probability distribution over the variables for each time-step. The filter is constructed as a mean squared error minimiser, but an alternative derivation of the filter is also provided showing how the filter relates to maximum likelihood statistics. The filter is named after Rudolf E. Kálmán. Kalman filtering has numerous technological applications. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and ships Dynamic positioning, positioned dynamically. Furthermore, Kalman filtering is much applied in time series analysis tasks such as signal processing and econometrics. K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Filter
In signal processing, a nonlinear filter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals and for two input signals and separately, but does not always output when the input is a linear combination . Both continuous-domain and discrete-domain filters may be nonlinear. A simple example of the former would be an electrical device whose output voltage at any moment is the square of the input voltage ; or which is the input clipped to a fixed range , namely . An important example of the latter is the running-median filter, such that every output sample is the median of the last three input samples . Like linear filters, nonlinear filters may be shift invariant or not. Non-linear filters have many applications, especially in the removal of certain types of noise that are not additive. For example, the median filter is widely used to remove spike noise — that affects only a small percentage of the samples, possibly b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hidden Markov Model
A hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent (or ''hidden'') Markov process (referred to as X). An HMM requires that there be an observable process Y whose outcomes depend on the outcomes of X in a known way. Since X cannot be observed directly, the goal is to learn about state of X by observing Y. By definition of being a Markov model, an 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 < t_0 must be conditionally independent of at given at time . Estimation of the parameters in an HMM can be performed using maximum likelihood estimation. For linear chain HMMs, the Baum–Welch algorithm can be used to estimate parameters. Hidden Markov models are known for their applications to thermodynamics, statistical mechanics, physics, chem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolutionary Computation
Evolutionary computation from computer science 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 as well as, depending on the method, mixing parental information. In biological terminology, a population of solutions is subjected to natural selection (or artificial selection), mutation and possibly recombination. As a result, the population will gradually evolve to increase in fitness, in this case the chosen fitness function of the algorithm. Evolutionary computation techni ... [...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 via biologically inspired operators such as selection, crossover, and mutation. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, and causal inference. 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 encod ... [...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 calculate low-lying energies of a quantum many-body Hamiltonian. Introduction and motivation of the algorithm Diffusion Monte Carlo has the potential to be numerically exact, meaning that it can find the exact ground state energy for any quantum system within a given error, but approximations must often be made and their impact must be assessed in particular cases. 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. To motivate the algorithm, let's look at the Schrödinger equation for a particle in some potential in one dimensi ... [...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 are b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arianna W
{{disambig ...
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), sometimes confused with Ariana *Aryana (TV series) ''Aryana'' is a Philippine television drama fantasy series broadcast by ABS-CBN. Directed by Erick C. Salud, Lino Cayetano, Lino S. Cayetano and Darnel Joy R. Villaflor. it stars Ella Cruz, Francis Magundayao, Paul Salas, Dominic Roque and Miche ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marshall Rosenbluth
Marshall Nicholas Rosenbluth (5 February 1927 – 28 September 2003) was an American plasma physicist and member of the National Academy of Sciences, and member of the American Philosophical Society. In 1997 he was awarded the National Medal of Science for discoveries in controlled thermonuclear fusion, contributions to plasma physics, and work in computational statistical mechanics. He was also a recipient of the E.O. Lawrence Prize (1964), the Albert Einstein Award (1967), the James Clerk Maxwell Prize for Plasma Physics (1976), the Enrico Fermi Award (1985), and the Hannes Alfvén Prize (2002). Early life and education Rosenbluth was born into a Jewish family and graduated from Stuyvesant High School in 1942. He did his undergraduate study at Harvard, graduating in 1946 (B.S., Phi Beta Kappa), while also serving in the U.S. Navy (1944–46). He received his Ph.D. in 1949 from the University of Chicago. Career During his first post-doctoral position at Stanford Univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
