Bergm (version 4.2.0)

evidence_PP: Evidence estimation via power posteriors

Description

Function to estimate the evidence (marginal likelihood) with Power posteriors, based on the adjusted pseudolikelihood function.

Usage

evidence_PP(formula, prior.mean, prior.sigma, nits, burnin, thin = 1,
  tunePL = 2, seed = 1, temps = seq(0, 1, length.out = 50)^5,
  info.adjustPL)

Arguments

formula

formula; an R 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.

tunePL

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

seed

The seed for the random number generator. See MCMCmetrop1R.

temps

numeric vector; Inverse temperature ladder, \(t\in[0,1]\).

info.adjustPL

Transformation parameters for adjusting the pseudolikelihood function adjustPL.

References

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 location and shape of prior distribution: 
prior.mean  <- rep(0, 2)
prior.sigma <- diag(5, 2)   

pp.est.evidence <- evidence_PP(formula = flo.formula,
                               prior.mean = prior.mean,   
                               prior.sigma = prior.sigma,
                               nits = 10000,
                               burnin = 2000,
                               temps = seq(0, 1, length.out = 20)^5,
                               info.adjustPL = info.adjustPL)
                                   
# MCMC diagnostics and posterior summaries:
bergm.output(pp.est.evidence)
  
# Log-marginal likelihood estimate:             
pp.est.evidence$log.evidence
# }
# NOT RUN {
# }