Bergm: evidencePP – R documentation

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evidencePP

Evidence estimation via power posteriors

Description

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

Usage

evidencePP(
  formula,
  prior.mean = NULL,
  prior.sigma = NULL,
  aux.iters = 1000,
  n.aux.draws = 50,
  aux.thin = 50,
  ladder = 30,
  main.iters = 20000,
  burn.in = 5000,
  thin = 1,
  V.proposal = 1.5,
  seed = 1,
  temps = NULL,
  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.
`seed`	integer; seed for the random number generator. See `set.seed` and `MCMCmetrop1R`.
`temps`	numeric vector; inverse temperature ladder, t \in [0,1].
`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

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)

PPE <- evidencePP(flomarriage ~ edges + kstar(2),
                  aux.iters   = 500, 
                  noisy.nsim  = 50,   
                  aux.thin    = 50,   
                  main.iters  = 2000,
                  burn.in     = 100,
                  V.proposal  = 2.5)
                                   
# Posterior summaries:
summary(PPE)

# MCMC diagnostics plots:
plot(PPE)
  
# Log-evidence (marginal likelihood) estimate:             
PPE$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