evidenceCJ {Bergm} R Documentation

## 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,
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 ~ where is a network object and 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)



[Package Bergm version 5.0.7 Index]