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Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms .
A statistical model represents, often in considerably idealized form, the data-generating process. [1] When referring specifically to probabilities, the corresponding term is probabilistic model. All statistical hypothesis tests and all statistical estimators are derived via statistical models.
For the "linear probability model", this relationship is a particularly simple one, and allows the model to be fitted by linear regression. The model assumes that, for a binary outcome ( Bernoulli trial ), Y {\displaystyle Y} , and its associated vector of explanatory variables, X {\displaystyle X} , [ 1 ]
A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability distribution is known as probability mass function.
The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. [1] These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. [2] There are several other (equivalent) approaches to formalising ...
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.
Binary probabilistic classifiers are also called binary regression models in statistics. In econometrics , probabilistic classification in general is called discrete choice . Some classification models, such as naive Bayes , logistic regression and multilayer perceptrons (when trained under an appropriate loss function ) are naturally ...
In statistics, a parametric model or parametric family or finite-dimensional model is a particular class of statistical models. Specifically, a parametric model is a family of probability distributions that has a finite number of parameters.
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