Bergm (version 4.2.0)

evidence_CJ: Evidence estimation via Chib and Jeliazkov's method

Description

Function to estimate the evidence (marginal likelihood) with Chib and Jeliazkov's method, based on the adjusted pseudolikelihood function.

Usage

evidence_CJ(formula, prior.mean, prior.sigma, nits, burnin, thin = 1,
  num.samples = 5000, tunePL = 2, seed = NA, info.adjustPL = NULL)

Arguments

formula

formula; an ergm formula object, of the form <network> ~ <model terms> where <network> is a network object and <model terms> are ergm-terms.

prior.mean

vector; Prior means.

prior.sigma

matrix; Prior covariance matrix.

nits

count; Number of MCMC iterations after burn-in for the adjusted pseudo-posterior estimation.

burnin

count; Number of burn-in iterations at the beginning of an MCMC run for the adjusted pseudo-posterior estimation.

thin

count; Thinning interval used in the simulation for the adjusted pseudo-posterior estimation. The number of MCMC iterations must be divisible by this value.

num.samples

integer; number of samples used in the marginal likelihood estimate. Must be <=(nits-burnin).

tunePL

count; Tuning parameter for the Metropolis sampling for the pseudo-posterior estimation.

seed

The seed for the random number generator. See MCMCmetrop1R.

info.adjustPL

Transformation parameters for adjusting the pseudolikelihood function adjustPL.

References

Caimo, A., & Friel, N. (2013). Bayesian model selection for exponential random graph models. Social Networks, 35(1), 11-24. https://arxiv.org/abs/1201.2337

Bouranis, L., Friel, N., & Maire, F. (2018). Bayesian model selection for exponential random graph models via adjusted pseudolikelihoods. Journal of Computational and Graphical Statistics, 1-13. https://arxiv.org/abs/1706.06344

Examples

# NOT RUN {
# Load the florentine marriage network:
data(florentine)

flo.formula <- flomarriage ~ edges + kstar(2)

info.adjustPL <- adjustPL(formula = flo.formula,
                          aux.iters    = 100, 
                          noisy.nsim   = 50,   
                          noisy.thin   = 50,   
                          ladder       = 30,   
                          estimate     = "MLE",
                          control      = control.ergm(MCMC.samplesize=2000))

# Specify a prior distribution: 
mean.priors  <- rep(0, 2)
sigma.priors <- diag(5, 2)          
                                                
# MCMC sampling and evidence estimation:
Chib.est.evidence <- evidence_CJ(formula      = flo.formula,
                                 prior.mean   = mean.priors,   
                                 prior.sigma  = sigma.priors,
                                 nits         = 30000,
                                 burnin       = 5000,
                                 thin         = 1,
                                 num.samples  = 25000,
                                 tunePL       = 2,
                                 info.adjustPL = info.adjustPL)                         
                                   
# MCMC diagnostics and posterior summaries:
bergm.output(Chib.est.evidence)
  
# Log-marginal likelihood estimate:             
Chib.est.evidence$log.evidence
# }
# NOT RUN {
# }