We characterize those coherent design criteria which depend only on the dispersion matrix (assumed proper and nonsingular) of the "state of nature," which may be a parameter-vector or a set of future observables, and describe the associated decision problems. Connections are established with the classical approach to optimal design theory for the normal linear model, based on concave functions of the information matrix. Implications of the theory for more general models are also considered.

Proper scoring rules are methods for encouraging honest assessment of probability distributions. Just like likelihood, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory of such equations can be applied to understand the properties of the associated estimator. In this paper we develop some basic scoring rule estimation theory, and explore robustness and interval estimation preoperties by means of theory and simulations.

Expert Opinions, Coherence, Compatibility, Combining Opinions, Linear Opinion Pool, Logarithmic Opinion Pool, Harmonic Opinion Pool,

We give an overview of some uses of proper scoring rules in statistical inference, including frequentist estimation theory and Bayesian model selection with improper priors.

No abstract