Uskomusväliarviot

Uskomusväliarviot, known in English as credibility intervals or belief intervals, are a key concept in Bayesian statistics. They represent a range of plausible values for an unknown parameter, reflecting the degree of belief or uncertainty about that parameter's true value. Unlike frequentist confidence intervals, which are interpreted based on repeated sampling, credibility intervals are directly interpreted in terms of probability. If a 95% credibility interval for a parameter is [2.5, 4.0], it means there is a 95% probability that the true value of the parameter lies within this range, given the observed data and the prior beliefs.

The construction of credibility intervals is based on the posterior distribution of the parameter. After a Bayesian analysis, the parameter is no longer treated as fixed but unknown, but rather as a random variable with a probability distribution that summarizes all available information, including prior knowledge and data. The credibility interval is derived from this posterior distribution. Common types include the highest posterior density (HPD) interval, which is the narrowest interval containing a specified mass of probability, and the equal-tailed interval, which is defined by quantiles of the posterior distribution. The choice between these can depend on the specific application and the shape of the posterior. Credibility intervals provide a more intuitive interpretation of uncertainty for many practitioners compared to their frequentist counterparts.