Optimize SIS graph-vertex-rate parameters for autocorrelation reduction

Identify parameter choices for the SIS conditional-path Monte Carlo graph vertex sets E2 and E3—including the parameters \(\psi\), \(\phi\), and \(q\)—that minimize autocorrelation times in the trajectory Markov chain.

Background

Conditional-path Monte Carlo constructs intermediate graph configurations whose vertex rates determine both the computational cost of an update and the mobility of the resulting spacetime clusters. For SIS dynamics, the E2 and E3 edge-vertex sets contain adjustable parameters such as ψ\psi, ϕ\phi, and qq, which control features including upstream and downstream flexibility and the handling of asymmetric infection rates.

Although the paper derives the admissible solution spaces for these rates and discusses pragmatic choices, the optimal parameter values depend on the network structure and model details. The unresolved problem is therefore to determine model-dependent parameter choices that minimize autocorrelation times rather than merely minimizing the cost of individual cluster updates.

References

Finally, while we have derived the solution space for vertex rates in suitable SIS graph vertex sets (e.g., the parameters \psi, \phi, and q in the E2 and E3 edge sets), the identification of (model-dependent) parameter choices that minimize autocorrelation times remains an open optimization problem.

— Conditional-path Monte Carlo for rare stochastic dynamics on networks: Details and derivations  (2608.17511 - Barthel et al., 18 Aug 2026) in Section Discussion, subsection “Future directions”