32,378 research outputs found
Bayesian model selection for exponential random graph models via adjusted pseudolikelihoods
Models with intractable likelihood functions arise in areas including network
analysis and spatial statistics, especially those involving Gibbs random
fields. Posterior parameter es timation in these settings is termed a
doubly-intractable problem because both the likelihood function and the
posterior distribution are intractable. The comparison of Bayesian models is
often based on the statistical evidence, the integral of the un-normalised
posterior distribution over the model parameters which is rarely available in
closed form. For doubly-intractable models, estimating the evidence adds
another layer of difficulty. Consequently, the selection of the model that best
describes an observed network among a collection of exponential random graph
models for network analysis is a daunting task. Pseudolikelihoods offer a
tractable approximation to the likelihood but should be treated with caution
because they can lead to an unreasonable inference. This paper specifies a
method to adjust pseudolikelihoods in order to obtain a reasonable, yet
tractable, approximation to the likelihood. This allows implementation of
widely used computational methods for evidence estimation and pursuit of
Bayesian model selection of exponential random graph models for the analysis of
social networks. Empirical comparisons to existing methods show that our
procedure yields similar evidence estimates, but at a lower computational cost.Comment: Supplementary material attached. To view attachments, please download
and extract the gzzipped source file listed under "Other formats
Penalized Bayesian exponential random graph models.
Networks have the critical ability to represent the complex interconnectedness of social relationships, biological processes, and the spread of diseases and information. Exponential random graph models (ERGM) are one of the popular statistical methods for analyzing network data. ERGM, however, struggle with computational challenges and degeneracy issues, further exacerbated by their inability to handle high-dimensional network data. Bayesian techniques provide a promising avenue to overcome these two problems. This paper considers penalized Bayesian exponential random graph models with adaptive lasso and adaptive ridge penalties to perform variable selection and reduce multicollinearity on a variety of networks. The experimental results demonstrate their effectiveness in variable selection and reduction of multicollinearity across diverse networks, outperforming the widely used Bayesian exponential random graph model proposed by Caimo et al., which lacks regularization capabilities. This paper presents a valuable extension to network models for large-scale high-dimensional data and offers opportunities for advancing research in diverse fields
Bayesian Exponential Random Graph Models with Nodal Random Effects
We extend the well-known and widely used Exponential Random Graph Model
(ERGM) by including nodal random effects to compensate for heterogeneity in the
nodes of a network. The Bayesian framework for ERGMs proposed by Caimo and
Friel (2011) yields the basis of our modelling algorithm. A central question in
network models is the question of model selection and following the Bayesian
paradigm we focus on estimating Bayes factors. To do so we develop an
approximate but feasible calculation of the Bayes factor which allows one to
pursue model selection. Two data examples and a small simulation study
illustrate our mixed model approach and the corresponding model selection.Comment: 23 pages, 9 figures, 3 table
Statistical Network Analysis with Bergm
Recent advances in computational methods for intractable models have made
network data increasingly amenable to statistical analysis. Exponential random
graph models (ERGMs) emerged as one of the main families of models capable of
capturing the complex dependence structure of network data in a wide range of
applied contexts. The Bergm package for R has become a popular package to carry
out Bayesian parameter inference, missing data imputation, model selection and
goodness-of-fit diagnostics for ERGMs. Over the last few years, the package has
been considerably improved in terms of efficiency by adopting some of the
state-of-the-art Bayesian computational methods for doubly-intractable
distributions. Recently, version 5 of the package has been made available on
CRAN having undergone a substantial makeover, which has made it more accessible
and easy to use for practitioners. New functions include data augmentation
procedures based on the approximate exchange algorithm for dealing with missing
data, adjusted pseudo-likelihood and pseudo-posterior procedures, which allow
for fast approximate inference of the ERGM parameter posterior and model
evidence for networks on several thousands nodes.Comment: 22 pages, 5 figure
Non-parametric Bayesian modeling of complex networks
Modeling structure in complex networks using Bayesian non-parametrics makes
it possible to specify flexible model structures and infer the adequate model
complexity from the observed data. This paper provides a gentle introduction to
non-parametric Bayesian modeling of complex networks: Using an infinite mixture
model as running example we go through the steps of deriving the model as an
infinite limit of a finite parametric model, inferring the model parameters by
Markov chain Monte Carlo, and checking the model's fit and predictive
performance. We explain how advanced non-parametric models for complex networks
can be derived and point out relevant literature
- …