Hierarchical Bayesian adaptive lasso methods on exponential random graph models

Applied Network Science

Table 5 Results of simulating 100 graphs and comparing results for BERGM and BALERGM using means as the estimates of \(\varvec{\theta }\)

Mean of the MCMC output as the estimate for \({\theta }\)
		True Value \(^{a}\)	Estimate \(^{b}\)	Quantiles\(^{c}\)
				2.5%	25%	50%	75%	97.5%
BERGM	\(\theta _{1}\)	−4.800	−5.3470	−5.607	−5.456	−5.349	−5.253	−5.031
BERGM	\(\theta _{2}\)	2.300	5.2656	4.455	5.026	5.251	5.543	6.185
BALERGM	\(\theta _{1}\)	−4.800	−4.9444	−5.172	−5.018	−4.938	−4.871	−4.739
BALERGM	\(\theta _{2}\)	2.300	2.8550	2.496	2.680	2.824	2.996	3.304
Median of the MCMC output as the estimate for \(\varvec{\theta }\)
		True Value	Estimate \(^{d}\)	Quantiles
		True Value	Estimate \(^{d}\)	2.5%	25%	50%	75%	97.5%
BERGM	\(\theta _{1}\)	−4.800	−5.1367	−5.386	−5.235	−5.137	−5.045	−4.874
BERGM	\(\theta _{2}\)	2.300	4.6296	3.903	4.397	4.632	4.822	5.355
BALERGM	\(\theta _{1}\)	−4.800	−4.8778	−5.077	−4.949	−4.873	−4.806	−4.682
BALERGM	\(\theta _{2}\)	2.300	2.6131	2.398	2.501	2.595	2.713	2.918