Likelihood function (Likelihood-Funktion)
Definition: x und des Parameters theta vertauscht werden, so dass die Wahrscheinlichkeit als eine Funktion von theta für spezifische Daten x betrachtet werden kann. In diesem Fall würde die Likelihood-Funktion eine Kurve oder Hyperfläche beschreiben, deren Spitze, falls vorhanden, die Kombination von Modellparameterwerten darstellt, die die Wahrscheinlichkeit der Ziehung der erhaltenen Stichprobe maximiert.
Verwandte Begriffe: Bayes factor, Bayesian inference, Bayesian parameter estimation, Posterior distribution, Prior distribution Alternative definition: For a more statistically-informed definition, given a parametric model specified by a probability (density) function f(x|theta), a likelihood for a statistical model is defined by the same formula as the density except that the roles of the data x and the parameter theta are interchanged, and thus the likelihood can be considered a function of theta for fixed data x. Here, then, the likelihood function would describe a curve or hypersurface whose peak, if it exists, represents the combination of model parameter values that maximize the probability of drawing the sample obtained. Alternative definition: For a more statistically-informed definition, given a parametric model specified by a probability (density) function f(x|theta), a likelihood for a statistical model is defined by the same formula as the density except that the roles of the data x and the parameter theta are interchanged, and thus the likelihood can be considered a function of theta for fixed data x . Here, then, the likelihood function would describe a curve or hypersurface whose peak, if it exists, represents the combination of model parameter values that maximize the probability of drawing the sample obtained.
Referenz: Dienes (2008); Hogg et al. (2010); van de Schoot et al. (2021); Geyer (2003); Geyer (2007); https://blog.stata.com/2016/11/01/introduction-to-bayesian-statistics-part-1-the-basic-concepts/
Verfasst und Überprüft von: Alaa AlDoh, Dominik Kiersz, Graham Reid, Sam Parsons, Flávio Azevedo