$$
\newcommand{\ts}{\theta^{\star}}
\newcommand{\tss}{\theta^{\star\star}}
\newcommand{\qf}[1]{q_{f}(#1|\ts)}
\newcommand{\qb}[1]{q_{b}(#1|\tss)}
\newcommand{\thresh}{\rho(X,Y) \leq \epsilon_{0}}
\newcommand{\Normal}{\mathcal{N}}
\newcommand{\R}{\mathbb{R}}
$$