Finite Exchangeability

• a finite set {𝑦₁, 𝑦₂, ..., 𝑦_𝑛} is exchangeable if the joint probability 𝐏(𝑦₁, 𝑦₂, ..., 𝑦_𝑛) is invariant under permutations of the indices
• that is, for every permutation (𝜔₁, 𝜔₂, ..., 𝜔_𝑛) of {𝑦₁, 𝑦₂, ..., 𝑦_𝑛}; 𝐏(𝑦₁, 𝑦₂, ..., 𝑦_𝑛) = 𝐏(𝜔₁, 𝜔₂, ..., 𝜔_𝑛)

Infinite Exchangeability

• is the property that every finite subset of an infinite sequence {𝑦₁, 𝑦₂, ...} is exchangeable

Subpages

• Exchangeable/Exchangeability vs Independent and Identically Distributed (IID)