Markov modelIn probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. 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.
Mixture modelIn statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to the mixture distribution that represents the probability distribution of observations in the overall population.
Marginal likelihoodA marginal likelihood is a likelihood function that has been integrated over the parameter space. In Bayesian statistics, it represents the probability of generating the observed sample from a prior and is therefore often referred to as model evidence or simply evidence. Given a set of independent identically distributed data points where according to some probability distribution parameterized by , where itself is a random variable described by a distribution, i.e.
Gibbs' inequalityIn information theory, Gibbs' inequality is a statement about the information entropy of a discrete probability distribution. Several other bounds on the entropy of probability distributions are derived from Gibbs' inequality, including Fano's inequality. It was first presented by J. Willard Gibbs in the 19th century. Suppose that is a discrete probability distribution. Then for any other probability distribution the following inequality between positive quantities (since pi and qi are between zero and one) holds: with equality if and only if for all i.
Cosine similarityIn data analysis, cosine similarity is a measure of similarity between two non-zero vectors defined in an inner product space. Cosine similarity is the cosine of the angle between the vectors; that is, it is the dot product of the vectors divided by the product of their lengths. It follows that the cosine similarity does not depend on the magnitudes of the vectors, but only on their angle. The cosine similarity always belongs to the interval For example, two proportional vectors have a cosine similarity of 1, two orthogonal vectors have a similarity of 0, and two opposite vectors have a similarity of -1.
Wilks' theoremIn statistics Wilks' theorem offers an asymptotic distribution of the log-likelihood ratio statistic, which can be used to produce confidence intervals for maximum-likelihood estimates or as a test statistic for performing the likelihood-ratio test. Statistical tests (such as hypothesis testing) generally require knowledge of the probability distribution of the test statistic. This is often a problem for likelihood ratios, where the probability distribution can be very difficult to determine.
Multinomial probitIn statistics and econometrics, the multinomial probit model is a generalization of the probit model used when there are several possible categories that the dependent variable can fall into. As such, it is an alternative to the multinomial logit model as one method of multiclass classification. It is not to be confused with the multivariate probit model, which is used to model correlated binary outcomes for more than one independent variable. It is assumed that we have a series of observations Yi, for i = 1.
Spoken languageA spoken language is a language produced by articulate sounds or (depending on one's definition) manual gestures, as opposed to a written language. An oral language or vocal language is a language produced with the vocal tract in contrast with a sign language, which is produced with the body and hands. The term "spoken language" is sometimes used to mean only oral languages, especially by linguists, excluding sign languages and making the terms 'spoken', 'oral', 'vocal language' synonymous.
TongueThe tongue is a muscular organ in the mouth of a typical tetrapod. It manipulates food for chewing and swallowing as part of the digestive process, and is the primary organ of taste. The tongue's upper surface (dorsum) is covered by taste buds housed in numerous lingual papillae. It is sensitive and kept moist by saliva and is richly supplied with nerves and blood vessels. The tongue also serves as a natural means of cleaning the teeth. A major function of the tongue is the enabling of speech in humans and vocalization in other animals.
Emotional prosodyEmotional prosody or affective prosody is the various non-verbal aspects of language that allow people to convey or understand emotion. It includes an individual's tone of voice in speech that is conveyed through changes in pitch, loudness, timbre, speech rate, and pauses. It can be isolated from semantic information, and interacts with verbal content (e.g. sarcasm). Emotional prosody in speech is perceived or decoded slightly worse than facial expressions but accuracy varies with emotions.
