Likelihood function | EPFL Graph Search

Are you an EPFL student looking for a semester project?

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

In statistical inference, the likelihood function quantifies the plausibility of parameter values characterizing a statistical model in light of observed data. Its most typical usage is to compare possible parameter values (under a fixed set of observations and a particular model), where higher values of likelihood are preferred because they correspond to more probable parameter values. While it is derived from the joint probability distribution on the observed data, it is not necessarily a measure of probability because it can return values larger than 1, especially when considering statistical models involving continuous random variables. Since it can be used to choose parameter values, it is a common utility function in situations that consider randomness. In maximum likelihood estimation, the arg max (over the parameter ) of the likelihood function serves as a point estimate for , while the Fisher information (often approximated by the likelihood's Hessian matrix) indicates the estimate's precision. Meanwhile in Bayesian statistics, parameter estimates are derived from the converse of the likelihood, the so-called posterior probability, which is calculated via Bayes' rule. The likelihood function, parameterized by a (possibly multivariate) parameter , is usually defined differently for discrete and continuous probability distributions (a more general definition is discussed below). Given a probability density or mass function where is a realization of the random variable , the likelihood function is often written In other words, when is viewed as a function of with fixed, it is a probability density function, and when viewed as a function of with fixed, it is a likelihood function. The likelihood function does not specify the probability that is the truth, given the observed sample . Such an interpretation is a common error, with potentially disastrous consequences (see prosecutor's fallacy). Let be a discrete random variable with probability mass function depending on a parameter .

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (26)

Related people (18)

Related concepts (90)

Related courses (71)

Related lectures (646)

Related MOOCs (10)

MATH-442: Statistical theory

The course aims at developing certain key aspects of the theory of statistics, providing a common general framework for statistical methodology. While the main emphasis will be on the mathematical asp

MATH-234(d): Probability and statistics

Ce cours enseigne les notions élémentaires de la théorie de probabilité et de la statistique, tels que l'inférence, les tests et la régression.

MATH-413: Statistics for data science

Statistics lies at the foundation of data science, providing a unifying theoretical and methodological backbone for the diverse tasks enountered in this emerging field. This course rigorously develops

The activity of neurons in the brain and the code used by these neurons is described by mathematical neuron models at different levels of detail.

Basic signal processing concepts, Fourier analysis and filters. This module can be used as a starting point or a basic refresher in elementary DSP

The Debiased Spatial Whittle likelihood

Sofia Charlotta Olhede

We provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our propo

WILEY2022

Fitting summary statistics of neural data with a differentiable spiking network simulator

Wulfram Gerstner, Johanni Michael Brea, Alireza Modirshanechi, Shuqi Wang

Fitting network models to neural activity is an important tool in neuroscience. A popular approach is to model a brain area with a probabilistic recurrent spiking network whose parameters maximize the

2021

Automatic L2 Regularization for Multiple Generalized Additive Models

Yousra El Bachir

Multiple generalized additive models are a class of statistical regression models wherein parameters of probability distributions incorporate information through additive smooth functions of predictor

EPFL2019

Likelihood function

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. A likelihood function arises from a probability density function considered as a function of its distributional parameterization argument.

Bayesian inference

Bayesian inference (ˈbeɪziən or ˈbeɪʒən ) 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. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law.

Inference Problems & Spin Glass Game

Covers inference problems related to the Spin Glass Game and the challenges of making mistakes with preb P.

Maximum Likelihood Decision

Explains decision by maximum likelihood and the use of logarithms.

Classification Detection

Covers binary hypothesis testing and decision functions in specific scenarios.