Alternative definition: For a more statistically-informed definition, given a parametric model specified by a probability (densidity) 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.
References: 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/
Drafted and Reviewed by: Alaa AlDoh, Dominik Kiersz, Graham Reid, Sam Parsons, Flávio Azevedo