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Table 2 Examples of test function η t (z,d) for different update rules (recall that \(d=d_{t}(z)=|q_{t}(z|\mathcal {S}_{t})-\pi (z)|\))

From: Adaptive independent sticky MCMC algorithms

Rule 1 η t (d)=1−eβd
Rule 2 \(\eta _{t}(d)=\left \{ \begin {array}{ll} 1, \text {if} ~d> \varepsilon _{t},\\ 0, \text {if}~ d\leq \varepsilon _{t} \end {array} \right.\)
Rule 3 \(\eta _{t}(z,d)=\frac {d}{\max \{\pi (z),q_{t}(z|\mathcal {S}_{t})\}}\)
  1. In the first and second cases, we have η t (z,d)=η t (d)