query: named_after hidden markov model
supports: In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process. It is named after the Russian mathematician Andrey Markov. A Dynamic Bayesian Network (DBN) is a Bayesian network which relates variables to each other over adjacent time steps. This is often called a "Two-Timeslice" BN (2TBN) because it says that at any point in time T, the value of a variable can be calculated from the internal regressors and the immediate prior value (time T-1). DBNs were developed by Paul Dagum in the early 1990s when he led research funded by two National Science Foundation grants at Stanford University's Section on Medical Informatics. Dagum developed DBNs to unify and extend traditional linear state-space models such as Kalman filters, linear and normal forecasting models such as ARMA and simple dependency models such as hidden Markov models into a general probabilistic representation and inference mechanism for arbitrary nonlinear and non-normal time-dependent domains. Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. The National Science Foundation (NSF) is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health. With an annual budget of about US$7.0 billion (fiscal year 2012), the NSF funds approximately 24% of all federally supported basic research conducted by the United States' colleges and universities. In some fields, such as mathematics, computer science, economics, and the social sciences, the NSF is the major source of federal backing. A hidden Markov model ( HMM ) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved ( hidden ) states . A HMM can be presented as the simplest dynamic Bayesian network . The mathematics behind the HMM were developed by L. E. Baum and coworkers . It is closely related to an earlier work on the optimal nonlinear filtering problem by Ruslan L. Stratonovich , who was the first to describe the forward - backward procedure . In simpler Markov models ( like a Markov chain ) , the state is directly visible to the observer , and therefore the state transition probabilities are the only parameters . In a hidden Markov model , the state is not directly visible , but the output , dependent on the state , is visible . Each state has a probability distribution over the possible output tokens . Therefore the sequence of tokens generated by an HMM gives some information about the sequence of states . The adjective ' hidden ' refers to the state sequence through which the model passes , not to the parameters of the model ; the model is still referred to as a ' hidden ' Markov model even if these parameters are known exactly . Hidden Markov models are especially known for their application in temporal pattern recognition such as speech , handwriting , gesture recognition , part - of - speech tagging , musical score following , partial discharges and bioinformatics . A hidden Markov model can be considered a generalization of a mixture model where the hidden variables ( or latent variables ) , which control the mixture component to be selected for each observation , are related through a Markov process rather than independent of each other . Recently , hidden Markov models have been generalized to pairwise Markov models and triplet Markov models which allow consideration of more complex data structures and the modelling of nonstationary data . In probability theory, a Markov model is a stochastic model used to model randomly changing systems where it is assumed that future states depend only on the current state not on the events that occurred before it (that is, it assumes the Markov property). Generally, this assumption enables reasoning and computation with the model that would otherwise be intractable. For this reason, in the fields of predictive modelling and probabilistic forecasting, it is desirable for a given model to exhibit the Markov property.
  Introduction.
  There are four common Markov models used in different situations, depending on whether every sequential state is observable or not, and whether the system is to be adjusted on the basis of observations made: Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more precise than those based on a single measurement alone, by using Bayesian inference and estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, one of the primary developers of its theory. Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California, adjacent to Palo Alto and between San Jose and San Francisco. Its campus is one of the largest in the United States. Stanford also has land and facilities elsewhere.
candidates: 2012 7 andrey markov california central leland stanford mathematics russian san francisco time
answer: andrey markov