Posteriorintervall

Posteriorintervall is a term used in statistics and Bayesian inference to describe the range of plausible values for an unknown parameter after considering observed data. It is the Bayesian counterpart to the confidence interval in frequentist statistics. A posterior interval is constructed from the posterior distribution of a parameter, which is the probability distribution of that parameter after it has been updated with evidence from the data.

To construct a posterior interval, one first defines a prior distribution representing beliefs about the parameter before observing any data. Then, using Bayes' theorem, this prior distribution is combined with the likelihood function derived from the observed data to obtain the posterior distribution. The posterior interval is then typically defined as a range that contains a certain probability mass of the posterior distribution, for example, a 95% posterior interval would contain 95% of the posterior probability. Common types of posterior intervals include credible intervals and highest posterior density (HPD) intervals.

Credible intervals are symmetric around the posterior median or mean and are defined by the quantiles of the posterior distribution. A 95% credible interval, for instance, would be the interval between the 2.5th and 97.5th percentiles of the posterior distribution. HPD intervals, on the other hand, are the narrowest interval that contains a specified probability mass. They are characterized by having the highest probability density within their range. The interpretation of a posterior interval is direct: there is a specified probability (e.g., 95%) that the true value of the parameter lies within the calculated interval.