Likelihood function, the Glossary

Table of Contents

1. 153 relations: A. W. F. Edwards, Akaike information criterion, Almost all, Almost surely, Annals of Statistics, Arg max, Base rate fallacy, Bayes factor, Bayes' theorem, Bayesian inference, Bayesian probability, Bayesian statistics, Biometrika, Boundary (topology), Cambridge University Press, Change of basis, Chapman & Hall, Compact space, Computational complexity, Concave function, Conditional entropy, Conditional probability, Conditional probability distribution, Confidence interval, Confidence region, Connected space, Consistent estimator, Continuous function, Continuous or discrete variable, Contour line, Counting measure, Coverage probability, Credible interval, D. Reidel, Derivative, Design matrix, Differential calculus, Elsevier, Empirical likelihood, Estimating equations, Euclidean space, Event (probability theory), Evidence-based medicine, Exponential family, Exponentiation, Extreme value theorem, Fair coin, Fisher information, Fisher's exact test, Foundations of statistics, ... Expand index (103 more) »

2. Likelihood

A. W. F. Edwards

Anthony William Fairbank Edwards, FRS One or more of the preceding sentences incorporates text from the royalsociety.org website where: (born 1935) is a British statistician, geneticist and evolutionary biologist.

See Likelihood function and A. W. F. Edwards

Akaike information criterion

The Akaike information criterion (AIC) is an estimator of prediction error and thereby relative quality of statistical models for a given set of data.

See Likelihood function and Akaike information criterion

Almost all

In mathematics, the term "almost all" means "all but a negligible quantity".

See Likelihood function and Almost all

Almost surely

In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (with respect to the probability measure).

See Likelihood function and Almost surely

Annals of Statistics

The Annals of Statistics is a peer-reviewed statistics journal published by the Institute of Mathematical Statistics.

See Likelihood function and Annals of Statistics

Arg max

In mathematics, the arguments of the maxima (abbreviated arg max or argmax) and arguments of the minima (abbreviated arg min or argmin) are the input points at which a function output value is maximized and minimized, respectively.

See Likelihood function and Arg max

Base rate fallacy

The base rate fallacy, also called base rate neglect or base rate bias, is a type of fallacy in which people tend to ignore the base rate (e.g., general prevalence) in favor of the individuating information (i.e., information pertaining only to a specific case).

See Likelihood function and Base rate fallacy

Bayes factor

The Bayes factor is a ratio of two competing statistical models represented by their evidence, and is used to quantify the support for one model over the other.

See Likelihood function and Bayes factor

Bayes' theorem

Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting conditional probabilities, allowing us to find the probability of a cause given its effect. Likelihood function and Bayes' theorem are Bayesian statistics.

See Likelihood function and Bayes' theorem

Bayesian inference

Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Likelihood function and Bayesian inference are Bayesian statistics.

See Likelihood function and Bayesian inference

Bayesian probability

Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. Likelihood function and Bayesian probability are Bayesian statistics.

See Likelihood function and Bayesian probability

Bayesian statistics

Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability, where probability expresses a degree of belief in an event.

See Likelihood function and Bayesian statistics

Biometrika

Biometrika is a peer-reviewed scientific journal published by Oxford University Press for the.

See Likelihood function and Biometrika

Boundary (topology)

In topology and mathematics in general, the boundary of a subset of a topological space is the set of points in the closure of not belonging to the interior of.

See Likelihood function and Boundary (topology)

Cambridge University Press

Cambridge University Press is the university press of the University of Cambridge.

See Likelihood function and Cambridge University Press

Change of basis

In mathematics, an ordered basis of a vector space of finite dimension allows representing uniquely any element of the vector space by a coordinate vector, which is a sequence of scalars called coordinates.

See Likelihood function and Change of basis

Chapman & Hall

Chapman & Hall is an imprint owned by CRC Press, originally founded as a British publishing house in London in the first half of the 19th century by Edward Chapman and William Hall.

See Likelihood function and Chapman & Hall

Compact space

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space.

See Likelihood function and Compact space

Computational complexity

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it.

See Likelihood function and Computational complexity

Concave function

In mathematics, a concave function is one for which the value at any convex combination of elements in the domain is greater than or equal to the convex combination of the values at the endpoints.

See Likelihood function and Concave function

Conditional entropy

In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable Y given that the value of another random variable X is known.

See Likelihood function and Conditional entropy

Conditional probability

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred.

See Likelihood function and Conditional probability

Conditional probability distribution

In probability theory and statistics, the conditional probability distribution is a probability distribution that describes the probability of an outcome given the occurrence of a particular event.

See Likelihood function and Conditional probability distribution

Confidence interval

Informally, in frequentist statistics, a confidence interval (CI) is an interval which is expected to typically contain the parameter being estimated.

See Likelihood function and Confidence interval

Confidence region

In statistics, a confidence region is a multi-dimensional generalization of a confidence interval.

See Likelihood function and Confidence region

Connected space

In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets.

See Likelihood function and Connected space

Consistent estimator

In statistics, a consistent estimator or asymptotically consistent estimator is an estimator—a rule for computing estimates of a parameter θ0—having the property that as the number of data points used increases indefinitely, the resulting sequence of estimates converges in probability to θ0.

See Likelihood function and Consistent estimator

Continuous function

In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function.

See Likelihood function and Continuous function

Continuous or discrete variable

In mathematics and statistics, a quantitative variable may be continuous or discrete if they are typically obtained by measuring or counting, respectively.

See Likelihood function and Continuous or discrete variable

Contour line

A contour line (also isoline, isopleth, isoquant or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value.

See Likelihood function and Contour line

Counting measure

In mathematics, specifically measure theory, the counting measure is an intuitive way to put a measure on any set – the "size" of a subset is taken to be the number of elements in the subset if the subset has finitely many elements, and infinity \infty if the subset is infinite.

See Likelihood function and Counting measure

Coverage probability

In statistical estimation theory, the coverage probability, or coverage for short, is the probability that a confidence interval or confidence region will include the true value (parameter) of interest.

See Likelihood function and Coverage probability

Credible interval

In Bayesian statistics, a credible interval is an interval used to characterize a probability distribution.

See Likelihood function and Credible interval

D. Reidel

D.

See Likelihood function and D. Reidel

Derivative

The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function's output with respect to its input.

See Likelihood function and Derivative

Design matrix

In statistics and in particular in regression analysis, a design matrix, also known as model matrix or regressor matrix and often denoted by X, is a matrix of values of explanatory variables of a set of objects.

See Likelihood function and Design matrix

Differential calculus

In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change.

See Likelihood function and Differential calculus

Elsevier

Elsevier is a Dutch academic publishing company specializing in scientific, technical, and medical content.

See Likelihood function and Elsevier

Empirical likelihood

In probability theory and statistics, empirical likelihood (EL) is a nonparametric method for estimating the parameters of statistical models.

See Likelihood function and Empirical likelihood

Estimating equations

In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimated.

See Likelihood function and Estimating equations

Euclidean space

Euclidean space is the fundamental space of geometry, intended to represent physical space.

See Likelihood function and Euclidean space

Event (probability theory)

In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.

See Likelihood function and Event (probability theory)

Evidence-based medicine

Evidence-based medicine (EBM) is "the conscientious, explicit and judicious use of current best evidence in making decisions about the care of individual patients.

See Likelihood function and Evidence-based medicine

Exponential family

In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below.

See Likelihood function and Exponential family

Exponentiation

In mathematics, exponentiation is an operation involving two numbers: the base and the exponent or power.

See Likelihood function and Exponentiation

Extreme value theorem

In calculus, the extreme value theorem states that if a real-valued function f is continuous on the closed and bounded interval, then f must attain a maximum and a minimum, each at least once.

See Likelihood function and Extreme value theorem

Fair coin

In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin.

See Likelihood function and Fair coin

Fisher information

In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information.

See Likelihood function and Fisher information

Fisher's exact test

Fisher's exact test is a statistical significance test used in the analysis of contingency tables.

See Likelihood function and Fisher's exact test

Foundations of statistics

The foundations of statistics consist of the mathematical and philosophical basis for arguments and inferences made using statistics.

See Likelihood function and Foundations of statistics

Frequency (statistics)

In statistics, the frequency or absolute frequency of an event i is the number n_i of times the observation has occurred/recorded in an experiment or study.

See Likelihood function and Frequency (statistics)

Frequentist inference

Frequentist inference is a type of statistical inference based in frequentist probability, which treats “probability” in equivalent terms to “frequency” and draws conclusions from sample-data by means of emphasizing the frequency or proportion of findings in the data.

See Likelihood function and Frequentist inference

Frequentist probability

Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability as the limit of its relative frequency in many trials (the long-run probability).

See Likelihood function and Frequentist probability

Frisch–Waugh–Lovell theorem

In econometrics, the Frisch–Waugh–Lovell (FWL) theorem is named after the econometricians Ragnar Frisch, Frederick V. Waugh, and Michael C. Lovell.

See Likelihood function and Frisch–Waugh–Lovell theorem

Function (mathematics)

In mathematics, a function from a set to a set assigns to each element of exactly one element of.

See Likelihood function and Function (mathematics)

Fundamental theorem of calculus

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions).

See Likelihood function and Fundamental theorem of calculus

Gamma distribution

In probability theory and statistics, the gamma distribution is a versatile two-parameter family of continuous probability distributions.

See Likelihood function and Gamma distribution

Gradient

In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p gives the direction and the rate of fastest increase.

See Likelihood function and Gradient

Graph of a function

In mathematics, the graph of a function f is the set of ordered pairs (x, y), where f(x).

See Likelihood function and Graph of a function

Hessian matrix

In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field.

See Likelihood function and Hessian matrix

Hypergeometric distribution

In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k successes (random draws for which the object drawn has a specified feature) in n draws, without replacement, from a finite population of size N that contains exactly K objects with that feature, wherein each draw is either a success or a failure.

See Likelihood function and Hypergeometric distribution

Independence (probability theory)

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.

See Likelihood function and Independence (probability theory)

Independent and identically distributed random variables

In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent.

See Likelihood function and Independent and identically distributed random variables

Informant (statistics)

In statistics, the score (or informant) is the gradient of the log-likelihood function with respect to the parameter vector.

See Likelihood function and Informant (statistics)

Information content

In information theory, the information content, self-information, surprisal, or Shannon information is a basic quantity derived from the probability of a particular event occurring from a random variable.

See Likelihood function and Information content

Information theory

Information theory is the mathematical study of the quantification, storage, and communication of information.

See Likelihood function and Information theory

Inner product space

In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product.

See Likelihood function and Inner product space

Interval (mathematics)

In mathematics, a (real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps".

See Likelihood function and Interval (mathematics)

Interval estimation

In statistics, interval estimation is the use of sample data to estimate an interval of possible values of a parameter of interest.

See Likelihood function and Interval estimation

Inverse function

In mathematics, the inverse function of a function (also called the inverse of) is a function that undoes the operation of.

See Likelihood function and Inverse function

Inverse function theorem

In mathematics, specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood of a point in its domain: namely, that its derivative is continuous and non-zero at the point.

See Likelihood function and Inverse function theorem

Inverse probability

In probability theory, inverse probability is an old term for the probability distribution of an unobserved variable. Likelihood function and inverse probability are Bayesian statistics.

See Likelihood function and Inverse probability

Johns Hopkins University Press

Johns Hopkins University Press (also referred to as JHU Press or JHUP) is the publishing division of Johns Hopkins University.

See Likelihood function and Johns Hopkins University Press

Joint probability distribution

Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs.

See Likelihood function and Joint probability distribution

Journal of the American Statistical Association

The Journal of the American Statistical Association (JASA) is the primary journal published by the American Statistical Association, the main professional body for statisticians in the United States.

See Likelihood function and Journal of the American Statistical Association

Journal of the Royal Statistical Society

The Journal of the Royal Statistical Society is a peer-reviewed scientific journal of statistics.

See Likelihood function and Journal of the Royal Statistical Society

Laplace's approximation

Laplace's approximation provides an analytical expression for a posterior probability distribution by fitting a Gaussian distribution with a mean equal to the MAP solution and precision equal to the observed Fisher information.

See Likelihood function and Laplace's approximation

Leibniz integral rule

In calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form \int_^ f(x,t)\,dt, where -\infty and the integrands are functions dependent on x, the derivative of this integral is expressible as \begin & \frac \left (\int_^ f(x,t)\,dt \right) \\ &.

See Likelihood function and Leibniz integral rule

Likelihood principle

In statistics, the likelihood principle is the proposition that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. Likelihood function and likelihood principle are likelihood.

See Likelihood function and Likelihood principle

Likelihood ratios in diagnostic testing

In evidence-based medicine, likelihood ratios are used for assessing the value of performing a diagnostic test.

See Likelihood function and Likelihood ratios in diagnostic testing

Likelihood-ratio test

In statistics, the likelihood-ratio test is a hypothesis test that involves comparing the goodness of fit of two competing statistical models, typically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods.

See Likelihood function and Likelihood-ratio test

Likelihoodist statistics

Likelihoodist statistics or likelihoodism is an approach to statistics that exclusively or primarily uses the likelihood function. Likelihood function and likelihoodist statistics are likelihood.

See Likelihood function and Likelihoodist statistics

Linear regression

In statistics, linear regression is a statistical model which estimates the linear relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables).

See Likelihood function and Linear regression

Log probability

In probability theory and computer science, a log probability is simply a logarithm of a probability.

See Likelihood function and Log probability

Logarithmically concave function

In convex analysis, a non-negative function is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality for all and.

See Likelihood function and Logarithmically concave function

Loss function

In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event.

See Likelihood function and Loss function

Marginal likelihood

A marginal likelihood is a likelihood function that has been integrated over the parameter space. Likelihood function and marginal likelihood are Bayesian statistics.

See Likelihood function and Marginal likelihood

Mathematical optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives.

See Likelihood function and Mathematical optimization

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. Likelihood function and maximum likelihood estimation are likelihood.

See Likelihood function and Maximum likelihood estimation

Medical test

A medical test is a medical procedure performed to detect, diagnose, or monitor diseases, disease processes, susceptibility, or to determine a course of treatment.

See Likelihood function and Medical test

Middle English

Middle English (abbreviated to ME) is a form of the English language that was spoken after the Norman Conquest of 1066, until the late 15th century.

See Likelihood function and Middle English

Mixed model

A mixed model, mixed-effects model or mixed error-component model is a statistical model containing both fixed effects and random effects.

See Likelihood function and Mixed model

Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

See Likelihood function and Monotonic function

Morse theory

In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold.

See Likelihood function and Morse theory

Mountain pass theorem

The mountain pass theorem is an existence theorem from the calculus of variations, originally due to Antonio Ambrosetti and Paul Rabinowitz.

See Likelihood function and Mountain pass theorem

Negative definiteness

In mathematics, negative definiteness is a property of any object to which a bilinear form may be naturally associated, which is negative-definite.

See Likelihood function and Negative definiteness

Neighbourhood (mathematics)

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.

See Likelihood function and Neighbourhood (mathematics)

Neyman–Pearson lemma

In statistics, the Neyman–Pearson lemma describes the existence and uniqueness of the likelihood ratio as a uniformly most powerful test in certain contexts.

See Likelihood function and Neyman–Pearson lemma

Nuisance parameter

In statistics, a nuisance parameter is any parameter which is unspecified but which must be accounted for in the hypothesis testing of the parameters which are of interest.

See Likelihood function and Nuisance parameter

Odds

In probability theory, odds provide a measure of the probability of a particular outcome.

See Likelihood function and Odds

Open set

In mathematics, an open set is a generalization of an open interval in the real line.

See Likelihood function and Open set

Outcome (probability)

In probability theory, an outcome is a possible result of an experiment or trial.

See Likelihood function and Outcome (probability)

Oxford University Press

Oxford University Press (OUP) is the publishing house of the University of Oxford.

See Likelihood function and Oxford University Press

Parameter space

The parameter space is the space of possible parameter values that define a particular mathematical model.

See Likelihood function and Parameter space

Parametric model

In statistics, a parametric model or parametric family or finite-dimensional model is a particular class of statistical models.

See Likelihood function and Parametric model

Partial derivative

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).

See Likelihood function and Partial derivative

Partition of a set

In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset.

See Likelihood function and Partition of a set

Phylogenetics

In biology, phylogenetics is the study of the evolutionary history and relationships among or within groups of organisms.

See Likelihood function and Phylogenetics

Point estimation

In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population mean).

See Likelihood function and Point estimation

Positive definiteness

In mathematics, positive definiteness is a property of any object to which a bilinear form or a sesquilinear form may be naturally associated, which is positive-definite.

See Likelihood function and Positive definiteness

Posterior probability

The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood via an application of Bayes' rule. Likelihood function and posterior probability are Bayesian statistics.

See Likelihood function and Posterior probability

Power (statistics)

In frequentist statistics, power is a measure of the ability of an experimental design and hypothesis testing setup to detect a particular effect if it is truly present.

See Likelihood function and Power (statistics)

Precision (statistics)

In statistics, the precision matrix or concentration matrix is the matrix inverse of the covariance matrix or dispersion matrix, P. Likelihood function and precision (statistics) are Bayesian statistics.

See Likelihood function and Precision (statistics)

Princeton University Press

Princeton University Press is an independent publisher with close connections to Princeton University.

See Likelihood function and Princeton University Press

Principle of maximum entropy

The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge about a system is the one with largest entropy, in the context of precisely stated prior data (such as a proposition that expresses testable information). Likelihood function and principle of maximum entropy are Bayesian statistics.

See Likelihood function and Principle of maximum entropy

Prior probability

A prior probability distribution of an uncertain quantity, often simply called the prior, is its assumed probability distribution before some evidence is taken into account. Likelihood function and prior probability are Bayesian statistics.

See Likelihood function and Prior probability

Probability density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.

See Likelihood function and Probability density function

Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment.

See Likelihood function and Probability distribution

Probability mass function

In probability and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the probability that a discrete random variable is exactly equal to some value.

See Likelihood function and Probability mass function

Product rule

In calculus, the product rule (or Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions.

See Likelihood function and Product rule

Projection matrix

In statistics, the projection matrix (\mathbf), sometimes also called the influence matrix or hat matrix (\mathbf), maps the vector of response values (dependent variable values) to the vector of fitted values (or predicted values).

See Likelihood function and Projection matrix

Proportional hazards model

Proportional hazards models are a class of survival models in statistics.

See Likelihood function and Proportional hazards model

Pseudolikelihood

In statistical theory, a pseudolikelihood is an approximation to the joint probability distribution of a collection of random variables.

See Likelihood function and Pseudolikelihood

Radon–Nikodym theorem

In mathematics, the Radon–Nikodym theorem is a result in measure theory that expresses the relationship between two measures defined on the same measurable space.

See Likelihood function and Radon–Nikodym theorem

Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.

See Likelihood function and Random variable

Realization (probability)

In probability and statistics, a realization, observation, or observed value, of a random variable is the value that is actually observed (what actually happened).

See Likelihood function and Realization (probability)

Restricted maximum likelihood

In statistics, the restricted (or residual, or reduced) maximum likelihood (REML) approach is a particular form of maximum likelihood estimation that does not base estimates on a maximum likelihood fit of all the information, but instead uses a likelihood function calculated from a transformed set of data, so that nuisance parameters have no effect.

See Likelihood function and Restricted maximum likelihood

Rolle's theorem

In calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct points must have at least one point, somewhere between them, at which the slope of the tangent line is zero.

See Likelihood function and Rolle's theorem

Ronald Fisher

Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic.

See Likelihood function and Ronald Fisher

Sample mean and covariance

The sample mean (sample average) or empirical mean (empirical average), and the sample covariance or empirical covariance are statistics computed from a sample of data on one or more random variables.

See Likelihood function and Sample mean and covariance

Shorter Oxford English Dictionary

The Shorter Oxford English Dictionary (SOED) is an English language dictionary published by the Oxford University Press.

See Likelihood function and Shorter Oxford English Dictionary

Simple random sample

In statistics, a simple random sample (or SRS) is a subset of individuals (a sample) chosen from a larger set (a population) in which a subset of individuals are chosen randomly, all with the same probability.

See Likelihood function and Simple random sample

Smoothness

In mathematical analysis, the smoothness of a function is a property measured by the number, called differentiability class, of continuous derivatives it has over its domain.

See Likelihood function and Smoothness

Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

See Likelihood function and Springer Science+Business Media

Stack Exchange

Stack Exchange is a network of question-and-answer (Q&A) websites on topics in diverse fields, each site covering a specific topic, where questions, answers, and users are subject to a reputation award process.

See Likelihood function and Stack Exchange

Standard error

The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation.

See Likelihood function and Standard error

Stationary point

In mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero.

See Likelihood function and Stationary point

Statistic

A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose.

See Likelihood function and Statistic

Statistical hypothesis test

A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently support a particular hypothesis.

See Likelihood function and Statistical hypothesis test

Statistical model

A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population).

See Likelihood function and Statistical model

Statistical parameter

In statistics, as opposed to its general use in mathematics, a parameter is any quantity of a statistical population that summarizes or describes an aspect of the population, such as a mean or a standard deviation.

See Likelihood function and Statistical parameter

Statistical Science

Statistical Science is a review journal published by the Institute of Mathematical Statistics.

See Likelihood function and Statistical Science

Statistical significance

In statistical hypothesis testing, a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true.

See Likelihood function and Statistical significance

Sufficient statistic

In statistics, sufficiency is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset.

See Likelihood function and Sufficient statistic

Taylor series

In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.

See Likelihood function and Taylor series

Test statistic

Test statistic is a quantity derived from the sample for statistical hypothesis testing.

See Likelihood function and Test statistic

The American Statistician

The American Statistician is a quarterly peer-reviewed scientific journal covering statistics published by Taylor & Francis on behalf of the American Statistical Association.

See Likelihood function and The American Statistician

Topographic profile

A topographic profile or topographic cut or elevation profile is a representation of the relief of the terrain that is obtained by cutting transversely the lines of a topographic map.

See Likelihood function and Topographic profile

Tunghai University

Tunghai University (THU;; lit. East Sea University) is a private university in Taiwan, established in 1955.

See Likelihood function and Tunghai University

Univariate

In mathematics, a univariate object is an expression, equation, function or polynomial involving only one variable.

See Likelihood function and Univariate

Well-defined expression

In mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value.

See Likelihood function and Well-defined expression

Wiley (publisher)

John Wiley & Sons, Inc., commonly known as Wiley, is an American multinational publishing company that focuses on academic publishing and instructional materials.

See Likelihood function and Wiley (publisher)

Wilks' theorem

In statistics, Wilks' theorem states that the log-likelihood ratio is asymptotically normal.

See Likelihood function and Wilks' theorem

See also

Likelihood

• Likelihood function
• Likelihood principle
• Likelihoodist statistics
• Maximum likelihood estimation
• Method of support
• Quasi-likelihood
• Relative likelihood

References

[1] https://en.wikipedia.org/wiki/Likelihood_function

Also known as Concentrated likelihood, Concentrated likelihood function, Conditional likelihood, Likelihood, Likelihood (statistics), Likelihood density function, Likelihood equations, Likelihood functions, Likelihood ratio, Likelihood-ratio, Likelihoods, Log likelihood, Log-likelihood, Log-likelihood function, Loglikelihood, Profile likelihood, Profile-likelihood function, Support curve.

, Frequency (statistics), Frequentist inference, Frequentist probability, Frisch–Waugh–Lovell theorem, Function (mathematics), Fundamental theorem of calculus, Gamma distribution, Gradient, Graph of a function, Hessian matrix, Hypergeometric distribution, Independence (probability theory), Independent and identically distributed random variables, Informant (statistics), Information content, Information theory, Inner product space, Interval (mathematics), Interval estimation, Inverse function, Inverse function theorem, Inverse probability, Johns Hopkins University Press, Joint probability distribution, Journal of the American Statistical Association, Journal of the Royal Statistical Society, Laplace's approximation, Leibniz integral rule, Likelihood principle, Likelihood ratios in diagnostic testing, Likelihood-ratio test, Likelihoodist statistics, Linear regression, Log probability, Logarithmically concave function, Loss function, Marginal likelihood, Mathematical optimization, Maximum likelihood estimation, Medical test, Middle English, Mixed model, Monotonic function, Morse theory, Mountain pass theorem, Negative definiteness, Neighbourhood (mathematics), Neyman–Pearson lemma, Nuisance parameter, Odds, Open set, Outcome (probability), Oxford University Press, Parameter space, Parametric model, Partial derivative, Partition of a set, Phylogenetics, Point estimation, Positive definiteness, Posterior probability, Power (statistics), Precision (statistics), Princeton University Press, Principle of maximum entropy, Prior probability, Probability density function, Probability distribution, Probability mass function, Product rule, Projection matrix, Proportional hazards model, Pseudolikelihood, Radon–Nikodym theorem, Random variable, Realization (probability), Restricted maximum likelihood, Rolle's theorem, Ronald Fisher, Sample mean and covariance, Shorter Oxford English Dictionary, Simple random sample, Smoothness, Springer Science+Business Media, Stack Exchange, Standard error, Stationary point, Statistic, Statistical hypothesis test, Statistical model, Statistical parameter, Statistical Science, Statistical significance, Sufficient statistic, Taylor series, Test statistic, The American Statistician, Topographic profile, Tunghai University, Univariate, Well-defined expression, Wiley (publisher), Wilks' theorem.