|
Variable-order Markov Model
In the mathematical theory of stochastic processes, variable-order Markov (VOM) models are an important class of models that extend the well known Markov chain models. In contrast to the Markov chain models, where each random variable in a sequence with a Markov property depends on a fixed number of random variables, in VOM models this number of conditioning random variables may vary based on the specific observed realization. This realization sequence is often called the ''context''; therefore the VOM models are also called ''context trees''. VOM models are nicely rendered by colorized probabilistic suffix trees (PST). The flexibility in the number of conditioning random variables turns out to be of real advantage for many applications, such as statistical analysis, classification and prediction. Example Consider for example a sequence of random variables, each of which takes a value from the ternary alphabet . Specifically, consider the string constructed from infinite concatena ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
 |
Stochastic Processes
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
Code
In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication channel or storage in a storage medium. An early example is an invention of language, which enabled a person, through speech, to communicate what they thought, saw, heard, or felt to others. But speech limits the range of communication to the distance a voice can carry and limits the audience to those present when the speech is uttered. The invention of writing, which converted spoken language into visual symbols, extended the range of communication across space and time. The process of encoding converts information from a source into symbols for communication or storage. Decoding is the reverse process, converting code symbols back into a form that the recipient understands, such as English, Spanish, etc. One reason for coding is ... [...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] |
 |
Markov Process
In probability theory and statistics, a Markov chain or Markov process is a stochastic process 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). Markov processes are named in honor of the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes. They provide the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability distributions, and have found application in areas including Bayesian statistics, biology, chemistry, economics, finance, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
Variable Order Bayesian Network
Variable-order Bayesian network (VOBN) models provide an important extension of both the Bayesian network models and the variable-order Markov models. VOBN models are used in machine learning in general and have shown great potential in bioinformatics applications. These models extend the widely used position weight matrix (PWM) models, Markov models, and Bayesian network (BN) models. In contrast to the BN models, where each random variable depends on a fixed subset of random variables, in VOBN models these subsets may vary based on the specific realization of observed variables. The observed realizations are often called the context and, hence, VOBN models are also known as context-specific Bayesian networks.{{cite conference , title=Context-specific independence in Bayesian networks , last1=Boutilier , first1=C. , last2=Friedman , first2=N. , author-link2=Nir Friedman , last3=Goldszmidt , first3=M. , last4=Koller , first4=D., author-link4=Daphne Koller , date=1996 , publisher= , b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
|
Examples Of Markov Chains
Example may refer to: * ''exempli gratia'' (e.g.), usually read out in English as "for example" * .example, reserved as a domain name that may not be installed as a top-level domain of the Internet ** example.com, example.net, example.org, and example.edu: second-level domain names reserved for use in documentation as examples * HMS ''Example'' (P165), an Archer-class patrol and training vessel of the Royal Navy Arts * ''The Example'', a 1634 play by James Shirley * ''The Example'' (comics), a 2009 graphic novel by Tom Taylor and Colin Wilson * Example (musician), the British dance musician Elliot John Gleave (born 1982) * ''Example'' (album), a 1995 album by American rock band For Squirrels See also * Exemplar (other), a prototype or model which others can use to understand a topic better * Exemplum An exemplum (Latin for "example", exempla, ''exempli gratia'' = "for example", abbr.: ''e.g.'') is a moral anecdote, brief or extended, real or fictitious, us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
|
Stochastic Chains With Memory Of Variable Length
Stochastic chains with memory of variable length are a family of stochastic chains of finite order in a finite alphabet, such as, for every time pass, only one finite suffix of the past, called context, is necessary to predict the next symbol. These models were introduced in the information theory literature by Jorma Rissanen in 1983, as a universal tool to data compression, but recently have been used to model data in different areas such as biology, linguistics and music. Definition A stochastic chain with memory of variable length is a stochastic chain (X_n)_, taking values in a finite alphabet A, and characterized by a probabilistic context tree (\tau,p), so that *\tau is the group of all contexts. A context X_,\ldots,X_, being l the size of the context, is a finite portion of the past X_,\ldots,X_, which is relevant to predict the next symbol X_; *p is a family of transition probabilities associated with each context. History The class of stochastic chains with memory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
 |
Sequence Analysis In Social Sciences
In social sciences, sequence analysis (SA) is concerned with the analysis of sets of categorical sequences that typically describe longitudinal data. Analyzed sequences are encoded representations of, for example, individual life trajectories such as family formation, school to work transitions, working careers, but they may also describe daily or weekly time use or represent the evolution of observed or self-reported health, of political behaviors, or the development stages of organizations. Such sequences are chronologically ordered unlike words or DNA sequences for example. SA is a longitudinal analysis approach that is holistic in the sense that it considers each sequence as a whole. SA is essentially exploratory. Broadly, SA provides a comprehensible overall picture of sets of sequences with the objective of characterizing the structure of the set of sequences, finding the salient characteristics of groups, identifying typical paths, comparing groups, and more generally study ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
Sharon R
Sharon ( 'plain'), also spelled Saron, is a given name as well as a Hebrew name. In English-speaking areas, Sharon is now predominantly a feminine given name, but historically it was also used as a masculine given name. In Israel, it is used as both. Etymology The Hebrew word simply means "plain", as in a flat area of land. But in the Hebrew Bible, is the name specifically given to the fertile plain between the Samarian Hills and the coast, known (tautologically) as Sharon plain in English. The phrase "rose of Sharon" (חבצלת השרון ''ḥăḇaṣṣeleṯ ha-sharon'') occurs in the KJV translation of the Song of Songs ("I am the rose of Sharon, the lily of the valley"), and has since been used in reference to a number of flowering plants. Unlike other unisex names that have come to be used almost exclusively as feminine (e.g. Evelyn), ''Sharon'' was never predominantly a masculine name. Usage before 1925 is very rare and was apparently inspired either by the Biblica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
|
Haplotyping
A haplotype (haploid genotype) is a group of alleles in an organism that are inherited together from a single parent. Many organisms contain genetic material (DNA) which is inherited from two parents. Normally these organisms have their DNA organized in two sets of pairwise similar chromosomes. The offspring gets one chromosome in each pair from each parent. A set of pairs of chromosomes is called diploid and a set of only one half of each pair is called haploid. The haploid genotype (haplotype) is a genotype that considers the singular chromosomes rather than the pairs of chromosomes. It can be all the chromosomes from one of the parents or a minor part of a chromosome, for example a sequence of 9000 base pairs or a small set of alleles. Specific contiguous parts of the chromosome are likely to be inherited together and not be split by chromosomal crossover, a phenomenon called genetic linkage. As a result, identifying these statistical associations and a few alleles of a specif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
|
|
Spam Filtering
Spam most often refers to: * Spam (food), a consumer brand product of canned processed pork of the Hormel Foods Corporation * Spamming, unsolicited or undesired electronic messages ** Email spam, unsolicited, undesired, or illegal email messages ** Messaging spam, spam targeting users of instant messaging (IM) services, SMS or private messages within websites Art and entertainment * Spam (gaming), the repetition of an in-game action * Spam (Monty Python sketch), "Spam" (Monty Python sketch), a comedy sketch * "Spam", a song on the album ''It Means Everything'' (1997), by Save Ferris * "Spam", a song by "Weird Al" Yankovic on the album ''UHF – Original Motion Picture Soundtrack and Other Stuff'' * Spam Museum, a museum in Austin, Minnesota, US dedicated to the canned pork meat product Other uses * Smooth-particle applied mechanics, the use of smoothed-particle hydrodynamics computation to study impact fractures in solids * SPAM, a Bacterial phyla#Uncultivated Phyla and metag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |