Do We Need Higher-Order Probabilities and, If So, What Do They Mean?
This addresses a foundational issue in probability theory and AI, clarifying notation for researchers, but is incremental as it refutes the need for new formalisms.
The paper tackles the problem of distinguishing uncertainty about truths from uncertainty about probabilistic assessments, showing that classical probabilistic models already provide this distinction, making specialized notations unnecessary.
The apparent failure of individual probabilistic expressions to distinguish uncertainty about truths from uncertainty about probabilistic assessments have prompted researchers to seek formalisms where the two types of uncertainties are given notational distinction. This paper demonstrates that the desired distinction is already a built-in feature of classical probabilistic models, thus, specialized notations are unnecessary.