  We derive a formula for non-Archimedean Monge-Amp\`{e}re measures of big
models. As applications, we derive a positive intersection formula for
non-Archimedean Mabuchi functional, and further reduce the uniform
Yau-Tian-Donaldson conjecture for polarized manifolds to a conjecture about the
existence of approximate Zariski decompositions that satisfy some asymptotic
vanishing condition.
