This discussion addresses the equivalence of marginal constraints to linear constraints within the context of probability distributions on a product space. Specifically, it explores whether a set of probability distributions constrained by marginal conditions can be expressed as a linear family of distributions, defined by the expectation of functions E_P[f_i] equating to constants a_i. The consensus indicates that while marginal constraints can often be represented linearly, the specific conditions and functions involved play a crucial role in determining this equivalence.
PREREQUISITESMathematicians, statisticians, and researchers in probability theory who are exploring the relationships between different types of constraints in probability distributions.