Definition: A sequence $\epsilon_n$ is a posterior contraction rate at the parameter $θ_0$ if $$\Pi_n(θ: d(θ, θ_0) ≥ M_n \epsilon_n| X^{(n)}) → 0$$ in $P^{(n)}_{θ_0}$-probability, for every $M_n → ∞$.
I am studying the subject of posterior consistency. While this subject seems straight forward there are few keywords used which I can't find any definition for. Most of these terms are used in the literature and published papers where the author assumes prior knowledge of this subject by the reader. From farther reading, it seems that these "rates" are related to the contraction rate and seem to originate from the Minimax theory/criterion however I still haven't found any definition for them or their relationship to the contraction rate $\epsilon_n$.
Could you please provide me with any helpful definition for these terms or direct me to a source where they are explained?
Some papers:
https://arxiv.org/pdf/1712.08964.pdf