Bergm: evidenceCJ – R documentation

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evidenceCJ

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)

Bergm

Bayesian Exponential Random Graph Models

v5.0.2

GPL (>= 2)

Authors

Alberto Caimo [aut, cre], Lampros Bouranis [aut], Robert Krause [aut] Nial Friel [ctb]

Initial release

2020-11-12