Likelihoodfunktio

The likelihood function, often denoted as L(θ | x), is a fundamental concept in statistical inference. It quantifies the probability of observing a particular dataset (x) given a specific set of parameters (θ) for a statistical model. In essence, it tells us how "likely" a particular set of parameter values is to have produced the observed data.

The likelihood function is not a probability distribution of the parameters themselves. Instead, it is a function of the parameters, with the data treated as fixed. The goal in many statistical problems is to find the parameter values that maximize the likelihood function. This is known as maximum likelihood estimation (MLE). The parameter values that yield the highest likelihood are considered the best estimates for the true, unknown parameters of the underlying distribution.

The concept of likelihood is crucial in Bayesian statistics as well, where it forms a key component in Bayes' theorem. Bayes' theorem combines the prior beliefs about the parameters with the information from the data (expressed through the likelihood function) to produce posterior beliefs about the parameters. The likelihood function is therefore a bridge between the data and our understanding of the model's parameters.