named_after hidden markov model
Kalman filtering , also known as linear quadratic estimation ( LQE ), is an algorithm that uses a series of measurements observed over ___MASK47___ , 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 . A Dynamic Bayesian Network ( DBN ) is a Bayesian network which relates variables to each other over adjacent ___MASK47___ steps . This is often called a " Two - Timeslice " BN ( 2TBN ) because it says that at any point in ___MASK47___ T , the value of a variable can be calculated from the internal regressors and the immediate prior value ( ___MASK47___ 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 ___MASK47___ - dependent domains . In probability theory and statistics , the term Markov property refers to the memoryless property of a stochastic process . It is named after the ___MASK53___ mathematician ___MASK56___ . 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 ___MASK58___ 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 . Stanford University , officially ___MASK40___ Junior University , is a private research university in Stanford , California , adjacent to Palo Alto and between ___MASK9___ and San Francisco . Its campus is one of the largest in the United States . Stanford also has land and facilities elsewhere . 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 $ ___MASK98___ . 0 billion ( fiscal year ___MASK66___ ), 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 . Probability theory is the branch of ___MASK58___ 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 ___MASK47___ in an apparently random fashion . 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 :