Confidence distributions can be seen as a frequentist alternative to Bayesian posteriors for summarizing the knowledge available for an unknown quantity based on the observed data and a model, but without the need for a Bayesian prior. A confidence distribution is defined by two equally important parts: (i) A distribution estimator. (ii) A matching family of confidence-credibility regions. This is illustrated by examples for two-dimensional parameters, but also for one-dimensional parameters. The main tools for construction is given by (a) Data generating equations, (b) Pivotal quantities, and (c) p-value functions. Presently, confidence distributions are in practice not anywhere near the success of Bayesian posteriors due to a lack of general available software and a lack of a fully developed theory. This can be changed.
Gunnar Taraldsen: Multivariate Confidence Distributions
Gunnar Taraldsen is professor at Department of Mathematical Sciences, NTNU. His current research interest focusses on the foundational principles of statistical inference including quantum probability, artificial intelligence, and machine learning. The aim is to bridge foundations for statistical inferences, to facilitate objective and replicable scientific learning, and to develop analytic and computing methodologies for data analysis.
Earlier research includes quantum mechanics, mathematical physics, measure theory, probability, medical ultrasound, non-linear wave propagation, numerical acoustics, medical statistics, outdoors sound propagation, community noise annoyance, acoustic noise mapping, underwater localization, underwater wave propagation, and spherical microphone arrays.
