Well-calibrated, coherent forecasting systems

This paper introduces a definition of predictive inference based on sequential observations in the light of de Finetti's principle of coherence. It includes characterizations of coherent predictive inferences and of strategic predictive inferences. It thoroughly analyzes the concepts of well calibrated and finitarily well calibrated forecasting systems. Apropos to this subject, some new laws of large numbers are assessed with reference to finitarily additive probability distributions. These results are then used to critically confute some objections raised against the coherence principle.