evidenceCJ {Bergm}

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

evidenceCJ(
  formula,
  prior.mean = NULL,
  prior.sigma = NULL,
  aux.iters = 1000,
  n.aux.draws = 5,
  aux.thin = 50,
  ladder = 30,
  main.iters = 30000,
  burn.in = 5000,
  thin = 1,
  V.proposal = 1.5,
  num.samples = 25000,
  seed = 1,
  estimate = c("MLE", "CD"),
  ...
)

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; mean vector of the multivariate Normal prior. By default set to a vector of 0's.

prior.sigma

square matrix; variance/covariance matrix for the multivariate Normal prior. By default set to a diagonal matrix with every diagonal entry equal to 100.

aux.iters

count; number of auxiliary iterations used for drawing the first network from the ERGM likelihood. See control.simulate.formula and ergmAPL.

n.aux.draws

count; number of auxiliary networks drawn from the ERGM likelihood. See control.simulate.formula and ergmAPL.

aux.thin

count; number of auxiliary iterations between network draws after the first network is drawn. See control.simulate.formula and ergmAPL.

ladder

count; length of temperature ladder (>=3). See ergmAPL.

main.iters

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

burn.in

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.

V.proposal

count; diagonal entry for the multivariate Normal proposal. By default set to 1.5.

num.samples

integer; number of samples used in the marginal likelihood estimate. Must be lower than main.iters - burnin.

seed

integer; seed for the random number generator. See set.seed and MCMCmetrop1R.

estimate

If "MLE" (the default), then an approximate maximum likelihood estimator is returned. If "CD" , the Monte-Carlo contrastive divergence estimate is returned. See ergm.

...

additional arguments, to be passed to the ergm function. See ergm and ergmAPL.

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, 27(3), 516-528. https://arxiv.org/abs/1706.06344

Examples

## Not run: 
# Load the florentine marriage network:
data(florentine)
                                                
# MCMC sampling and evidence estimation:
CJE <- evidenceCJ(flomarriage ~ edges + kstar(2),
                  main.iters  = 2000,
                  burn.in     = 200,
                  aux.iters   = 500,
                  num.samples = 25000,
                  V.proposal  = 2.5)
                                   
# Posterior summaries:
summary(CJE)

# MCMC diagnostics plots:
plot(CJE)
    
# Log-evidence (marginal likelihood) estimate:
CJE$log.evidence

## End(Not run)