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Hidden Semi-Markov Model
A hidden semi-Markov model (HSMM) is a statistical model with the same structure as a hidden Markov model except that the unobservable process is semi-Markov rather than Markov Markov ( Bulgarian, russian: Марков), Markova, and Markoff are common surnames used in Russia and Bulgaria. Notable people with the name include: Academics *Ivana Markova (born 1938), Czechoslovak-British emeritus professor of psychology at .... This means that the probability of there being a change in the hidden state depends on the amount of time that has elapsed since entry into the current state. This is in contrast to hidden Markov models where there is a constant probability of changing state given survival in the state up to that time. For instance modelled daily rainfall using a hidden semi-Markov model. If the underlying process (e.g. weather system) does not have a geometrically distributed duration, an HSMM may be more appropriate. Hidden semi-Markov models can be used in implementati ... [...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 \i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semi-Markov Process
In probability and statistics, a Markov renewal process (MRP) is a random process that generalizes the notion of Markov jump processes. Other random processes like Markov chains, Poisson processes and renewal processes can be derived as special cases of MRP's. Definition Consider a state space \mathrm. Consider a set of random variables (X_n,T_n), where T_n are the jump times and X_n are the associated states in the Markov chain (see Figure). Let the inter-arrival time, \tau_n=T_n-T_. Then the sequence (X_n,T_n) is called a Markov renewal process if : \begin & \Pr(\tau_\le t, X_=j\mid(X_0, T_0), (X_1, T_1),\ldots, (X_n=i, T_n)) \\ pt= & \Pr(\tau_\le t, X_=j\mid X_n=i)\, \forall n \ge1,t\ge0, i,j \in \mathrm \end Relation to other stochastic processes # If we define a new stochastic process Y_t:=X_n for t \in _n,T_), then the process Y_t is called a semi-Markov process. Note the main difference between an MRP and a semi-Markov process is that the former is defined as a two- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Process
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs ''now''." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). It is named after the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes, such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, currency exchange rates and animal population dynamics. Markov processes are the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability distr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Distribution
In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: * The probability distribution of the number ''X'' of Bernoulli trials needed to get one success, supported on the set \; * The probability distribution of the number ''Y'' = ''X'' − 1 of failures before the first success, supported on the set \. Which of these is called the geometric distribution is a matter of convention and convenience. These two different geometric distributions should not be confused with each other. Often, the name ''shifted'' geometric distribution is adopted for the former one (distribution of the number ''X''); however, to avoid ambiguity, it is considered wise to indicate which is intended, by mentioning the support explicitly. The geometric distribution gives the probability that the first occurrence of success requires ''k'' independent trials, each with success probability ''p''. If the probability of succe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speech Synthesis
Speech synthesis is the artificial production of human speech. A computer system used for this purpose is called a speech synthesizer, and can be implemented in software or hardware products. A text-to-speech (TTS) system converts normal language text into speech; other systems render symbolic linguistic representations like phonetic transcriptions into speech. The reverse process is speech recognition. Synthesized speech can be created by concatenating pieces of recorded speech that are stored in a database. Systems differ in the size of the stored speech units; a system that stores phones or diphones provides the largest output range, but may lack clarity. For specific usage domains, the storage of entire words or sentences allows for high-quality output. Alternatively, a synthesizer can incorporate a model of the vocal tract and other human voice characteristics to create a completely "synthetic" voice output. The quality of a speech synthesizer is judged by its similarity to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Neural Network
Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons. An artificial neuron receives signals then processes them and can signal neurons connected to it. The "signal" at a connection is a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs. The connections are called ''edges''. Neurons and edges typically have a ''weight'' that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Neurons may have a threshold such that a signal is sent only if the aggregate signal crosses that threshold. Typically ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonard E
Leonard or ''Leo'' is a common English masculine given name and a surname. The given name and surname originate from the Old High German ''Leonhard'' containing the prefix ''levon'' ("lion") from the Greek Λέων ("lion") through the Latin '' Leo,'' and the suffix ''hardu'' ("brave" or "hardy"). The name has come to mean "lion strength", "lion-strong", or "lion-hearted". Leonard was the name of a Saint in the Middle Ages period, known as the patron saint of prisoners. Leonard is also an Irish origin surname, from the Gaelic ''O'Leannain'' also found as O'Leonard, but often was anglicised to just Leonard, consisting of the prefix ''O'' ("descendant of") and the suffix ''Leannan'' ("lover"). The oldest public records of the surname appear in 1272 in Huntingdonshire, England, and in 1479 in Ulm, Germany. Variations The name has variants in other languages: * Leen, Leendert, Lenard (Dutch) * Lehnertz, Lehnert (Luxembourgish) * Len (English) * :hu:Lénárd (Hungarian) * Len ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Renewal Process
In probability and statistics, a Markov renewal process (MRP) is a random process that generalizes the notion of Markov jump processes. Other random processes like Markov chains, Poisson processes and renewal processes can be derived as special cases of MRP's. Definition Consider a state space \mathrm. Consider a set of random variables (X_n,T_n), where T_n are the jump times and X_n are the associated states in the Markov chain (see Figure). Let the inter-arrival time, \tau_n=T_n-T_. Then the sequence (X_n,T_n) is called a Markov renewal process if : \begin & \Pr(\tau_\le t, X_=j\mid(X_0, T_0), (X_1, T_1),\ldots, (X_n=i, T_n)) \\ pt= & \Pr(\tau_\le t, X_=j\mid X_n=i)\, \forall n \ge1,t\ge0, i,j \in \mathrm \end Relation to other stochastic processes # If we define a new stochastic process Y_t:=X_n for t \in _n,T_), then the process Y_t is called a semi-Markov process. Note the main difference between an MRP and a semi-Markov process is that the former is defined as a two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Computational And Graphical Statistics
The ''Journal of Computational and Graphical Statistics'' is a quarterly peer-reviewed scientific journal published by Taylor & Francis on behalf of the American Statistical Association. Established in 1992, the journal covers the use of computational and graphical methods in statistics and data analysis, including numerical methods, graphical displays and methods, and perception. It is published jointly with the Institute of Mathematical Statistics and the Interface Foundation of North America. According to the ''Journal Citation Reports'', the journal has a 2021 impact factor of 1.884. See also *List of statistics journals This is a list of scientific journals published in the field of statistics. Introductory and outreach *''The American Statistician'' *'' Significance'' General theory and methodology *''Annals of the Institute of Statistical Mathematics'' *''An ... References External links * {{DEFAULTSORT:Journal of Computational and Graphical Statistics Ame ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
