Do We Need Higher-Order Probabilities and, If So, What Do They Mean?

TL;DR

This paper argues that classical probabilistic models inherently distinguish between uncertainty about truths and about assessments, negating the need for higher-order probabilities or specialized notation.

Contribution

It shows that the distinction sought by researchers is already embedded in traditional probabilistic frameworks, challenging the necessity of higher-order probabilities.

Findings

Classical models inherently distinguish types of uncertainty

Specialized notations for higher-order probabilities are unnecessary

Clarifies the conceptual understanding of probabilistic uncertainty

Abstract

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.