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Causality is an influence by which one event, process, state, or object (acause) contributes to the production of another event, process, state, or object (an effect) where the cause is at least partly responsible for the effect, and the effect is at least partly dependent on the cause. The cause of something may also be described as the reason for the event or process.
A hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent Markov process. An HMM requires that there be an observable process whose outcomes depend on the outcomes of in a known way. Since cannot be observed directly, the goal is to learn about state of by observing . By definition of being a Markov model, an HMM has an additional requirement that the outcome of at time must be "influenced" exclusively by the outcome of at and that the outcomes of and at must be conditionally independent of at given at time . Estimation of the parameters in an HMM can be performed using maximum likelihood estimation. For linear chain HMMs, the Baum–Welch algorithm can be used to estimate parameters.
Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics. It is generally, but not universally, called relevant logic by British and, especially, Australian logicians, and relevance logic by American logicians.
A Bayesian network is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one of several forms of causal notation, causal networks are special cases of Bayesian networks. Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases.
In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process, which means that its future evolution is independent of its history. It is named after the Russian mathematician Andrey Markov. The term strong Markov property is similar to the Markov property, except that the meaning of "present" is defined in terms of a random variable known as a stopping time.
A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics—particularly Bayesian statistics—and machine learning.
Counterfactual conditionals are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted with indicatives, which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use of fake tense morphology, which some languages use in combination with other kinds of morphology including aspect and mood.
In econometrics, the autoregressive conditional heteroskedasticity (ARCH) model is a statistical model for time series data that describes the variance of the current error term or innovation as a function of the actual sizes of the previous time periods' error terms; often the variance is related to the squares of the previous innovations. The ARCH model is appropriate when the error variance in a time series follows an autoregressive (AR) model; if an autoregressive moving average (ARMA) model is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH) model.
The material conditional is an operation commonly used in logic. When the conditional symbol is interpreted as material implication, a formula is true unless is true and is false. Material implication can also be characterized inferentially by modus ponens, modus tollens, conditional proof, and classical reductio ad absurdum.
A mental model is an internal representation of external reality: that is, a way of representing reality within one's mind. Such models are hypothesized to play a major role in cognition, reasoning and decision-making. The term for this concept was coined in 1943 by Kenneth Craik, who suggested that the mind constructs "small-scale models" of reality that it uses to anticipate events. Mental models can help shape behaviour, including approaches to solving problems and performing tasks.
In statistical classification, two main approaches are called the generative approach and the discriminative approach. These compute classifiers by different approaches, differing in the degree of statistical modelling. Terminology is inconsistent, but three major types can be distinguished, following Jebara (2004):
- A generative model is a statistical model of the joint probability distribution on a given observable variable X and target variable Y; A generative model can be used to "generate" random instances (outcomes) of an observation x.
- A discriminative model is a model of the conditional probability of the target Y, given an observation x. It can be used to "discriminate" the value of the target variable Y, given an observation x.
- Classifiers computed without using a probability model are also referred to loosely as "discriminative".
The Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another, first proposed in 1969. Ordinarily, regressions reflect "mere" correlations, but Clive Granger argued that causality in economics could be tested for by measuring the ability to predict the future values of a time series using prior values of another time series. Since the question of "true causality" is deeply philosophical, and because of the post hoc ergo propter hoc fallacy of assuming that one thing preceding another can be used as a proof of causation, econometricians assert that the Granger test finds only "predictive causality". Using the term "causality" alone is a misnomer, as Granger-causality is better described as "precedence", or, as Granger himself later claimed in 1977, "temporally related". Rather than testing whether Xcauses Y, the Granger causality tests whether X forecastsY.
Dreambox is a series of Linux-powered DVB satellite, terrestrial and cable digital television receivers, produced by German multimedia vendor Dream Multimedia.
Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without considering "neighbouring" samples, a CRF can take context into account. To do so, the predictions are modelled as a graphical model, which represents the presence of dependencies between the predictions. The kind of graph used depends on the application. For example, in natural language processing, "linear chain" CRFs are popular, for which each prediction is dependent only on its immediate neighbours. In image processing, the graph typically connects locations to nearby and/or similar locations to enforce that they receive similar predictions.
Predictive analytics encompasses a variety of statistical techniques from data mining, predictive modeling, and machine learning that analyze current and historical facts to make predictions about future or otherwise unknown events.
Discriminative models, also referred to as conditional models, are a class of models frequently used for classification. They are typically used to solve binary classification problems, i.e. assign labels, such as pass/fail, win/lose, alive/dead or healthy/sick, to existing datapoints.
Mixed logit is a fully general statistical model for examining discrete choices. It overcomes three important limitations of the standard logit model by allowing for random taste variation across choosers, unrestricted substitution patterns across choices, and correlation in unobserved factors over time. Mixed logit can choose any distribution for the random coefficients, unlike probit which is limited to the normal distribution. It is called "mixed logit" because the choice probability is a mixture of logits, with as the mixing distribution. It has been shown that a mixed logit model can approximate to any degree of accuracy any true random utility model of discrete choice, given appropriate specification of variables and the coefficient distribution.
Structured prediction or structured output learning is an umbrella term for supervised machine learning techniques that involves predicting structured objects, rather than discrete or real values.
In statistics, linear regression is a model that estimates the linear relationship between a scalar response and one or more explanatory variables. A model with exactly one explanatory variable is a simple linear regression; a model with two or more explanatory variables is a multiple linear regression. This term is distinct from multivariate linear regression, which predicts multiple correlated dependent variables rather than a single dependent variable.
In statistics, a sequence of random variables is homoscedastic if all its random variables have the same finite variance; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity, also known as heterogeneity of variance. The spellings homoskedasticity and heteroskedasticity are also frequently used. “Skedasticity” comes from the Ancient Greek word “skedánnymi”, meaning “to scatter”. Assuming a variable is homoscedastic when in reality it is heteroscedastic results in unbiased but inefficient point estimates and in biased estimates of standard errors, and may result in overestimating the goodness of fit as measured by the Pearson coefficient.
References
- Plewis, I. (1985). Analysing Change: Measurement and Explanation Using Longitudinal Data. Wiley. ISBN 0-471-10444-2.
- Aickin, M. (2009). "Dealing With Change: Using the Conditional Change Model for Clinical Research". The Permanente Journal. 13 (2): 80–84. doi:10.7812/TPP/08-070. PMC 3034438 . PMID 21373237.
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