sannsynlighetsskattning

Probability estimation, also known as sannsynlighetsskattning in Norwegian contexts, is the statistical task of inferring probabilities or probability distributions from observed data. It covers estimating the probability of events, parameters of probabilistic models, and whole distributional shapes.

In frequentist approaches, estimation aims to produce point estimates and interval estimates that reflect sampling variability. Common methods include maximum likelihood estimation (MLE), which selects parameters that maximize the probability of observed data, and the method of moments, which matches sample moments to theoretical moments. For binary or count data, estimators of p in a Bernoulli/binomial model are central, with confidence intervals derived from asymptotic theory or exact methods. Model validation and calibration are important, with scoring rules such as log loss and the Brier score used to assess probabilistic predictions.

In Bayesian inference, estimation uses prior information combined with data to form a posterior distribution over parameters. This yields posterior point estimates, credible intervals, and, in hierarchical models, sharing information across groups. Bayesian methods naturally handle uncertainty and can accommodate small samples through prior regularization.

Key considerations include bias, variance, consistency, and efficiency, as well as model misspecification and overfitting. Computational tools such as optimization routines, Markov chain Monte Carlo, and variational methods enable estimation in complex models.

Applications span finance, meteorology, medicine, engineering, and machine learning. Sannsynlighetsskattning provides the quantitative basis for decision-making under uncertainty, prediction, and risk assessment.