Efficient computational strategies for doubly intractable problems with applications to Bayesian social networks

摘要

Powerful ideas recently appeared in the literature are adjusted and combinedto design improved samplers for Bayesian exponential random graph models.Different forms of adaptive Metropolis-Hastings proposals (vertical, horizontaland rectangular) are tested and combined with the Delayed rejection (DR)strategy with the aim of reducing the variance of the resulting Markov chainMonte Carlo estimators for a given computational time. In the examples treatedin this paper the best combination, namely horizontal adaptation with delayedrejection, leads to a variance reduction that varies between 92% and 144%relative to the adaptive direction sampling approximate exchange algorithm ofCaimo and Friel (2011). These results correspond to an increased performancewhich varies from 10% to 94% if we take simulation time into account. Thehighest improvements are obtained when highly correlated posteriordistributions are considered.