Kredibilitetsintervall

Kredibilitetsintervall, also known as a credible interval, is a concept used in Bayesian statistics to represent a range of values within which an unknown parameter is believed to lie with a certain probability. Unlike frequentist confidence intervals, which are derived from the properties of repeated sampling, credible intervals are probabilistic statements about the parameter itself, based on the observed data and prior beliefs.

In Bayesian analysis, the credible interval is determined from the posterior distribution of the parameter. Given a prior distribution and the likelihood function based on observed data, Bayes' theorem updates the prior to produce the posterior distribution. The credible interval is then obtained by identifying the interval within the posterior distribution that contains a specified probability, often 95%. This means there is a 95% probability that the parameter falls within this interval, conditional on the observed data and the prior assumptions.

Credible intervals can be constructed in various ways, such as equal-tailed intervals or highest posterior density (HPD) intervals. The equal-tailed interval includes the lower and upper bounds such that the probability of the parameter being below or above these bounds is equal. The HPD interval, on the other hand, is the shortest interval containing the specified probability and typically provides a more precise estimate of the parameter.

The interpretation of a kredibilitetsintervall differs from classical confidence intervals, as it directly relates to the probability distribution of the parameter itself rather than the long-term frequency properties of the interval estimation procedure. Credible intervals are widely used in Bayesian inference for their intuitive probabilistic interpretation and flexibility.

Overall, the kredibilitetsintervall is a fundamental concept in Bayesian statistics, providing a probabilistic measure of uncertainty about an unknown parameter based on the available data and prior information.