Bayesian analysis for exponential random graph models using the adaptive exchange sampler

Simulating from distributions with intractable normalizing constants has been a long-standing problem in machine learning. In this letter, we propose a new algorithm, the Monte Carlo Metropolis-Hastings (MCMH) algorithm, for tackling this problem. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. It replaces the unknown normalizing constant ratio by a Monte Carlo estimate in simulations, while still converges, as shown in the letter, to the desired target distribution under mild conditions. The MCMH algorithm is illustrated with spatial autologistic models and exponential random graph models. Unlike other auxiliary variable Markov chain Monte Carlo (MCMC) algorithms, such as the Møller and exchange algorithms, the MCMH algorithm avoids the requirement for perfect sampling, and thus can be applied to many statistical models for which perfect sampling is not available or very expensive. The MCMH algorithm can also be applied to Bayesian inference for random effect models and missing data problems that involve simulations from a distribution with intractable integrals.

Advances in exponential random graph ( p*) models applied to a large social network

A number of discrete exponential family models for dependent data, first and foremost relational data, have turned out to be near-degenerate and problematic in terms of Markov chain Monte Carlo (MCMC) simulation and statistical inference. I introduce the notion of instability with an eye to characterize, detect, and penalize discrete exponential family models that are near-degenerate and problematic in terms of MCMC simulation and statistical inference. I show that unstable discrete exponential family models are characterized by excessive sensitivity and near-degeneracy. In special cases, the subset of the natural parameter space corresponding to nondegenerate distributions and mean-value parameters far from the boundary of the mean-value parameter space turns out to be a lower-dimensional subspace of the natural parameter space. These characteristics of unstable discrete exponential family models tend to obstruct MCMC simulation and statistical inference. In applications to relational data, I show that discrete exponential family models with Markov dependence tend to be unstable, and that the parameter space of some curved exponential families contains unstable subsets.

Millions of users follow each other on Twitter and form a large and complex network. The size of the network creates statistical and computational challenges on exploring and examining individual behavior on Twitter. Using a sample of 697,628 Korean Twitter users and 34 million relations, this study investigates the patterns of unfollow behavior on Twitter, i.e. people removing others from their Twitter follow lists. We use Exponential Random Graph Models (p*/ERGMs) and Statnet in R to examine the impacts of reciprocity, status, embeddedness, homophily, and informativeness on tie dissolution. We perform data processing, statistics calculation, network sampling, and Markov chain Monte Carlo (MCMC) simulation on Gordon, a unique supercomputer at the San Diego Supercomputer Center (SDSC). The process demonstrates the role of advanced computing technologies in social science studies.

Social network analysis has typically concerned analysis of one type of tie connecting nodes of the same type. It has however been recognised that people are connected through multiple types of ties and that people in addition are affiliated with multiple types of non-people nodes. Exponential random graph models (ERGM) is a family of statistical models for social networks that at this point allows for a number of different types of network data, including one-mode networks, bipartite networks, multiplex data, as well as multilevel network data. Multilevel networks have been proposed as a joint representation of associations between multiple types of entities or nodes, such as people and organization, where two types of nodes gives rise to three distinct types of ties. The typical roster data collection method may be impractical or infeasible when the node sets are hard to detect or define or because of the cognitive demands on respondents. Multilevel multilayered networks allow us to consider a multitude of different sources of data and to sample on different types of nodes and relations. We consider modelling multilevel multilayered networks using exponential random graph models and extend a recently developed Bayesian data-augmentation scheme to allow for partially missing data. We illustrate the proposed inference procedures for the case of multilevel snowball sampling and sampling with error based on the Noordin Top network.

Social network analysis is a suite of approaches for exploring relational data. Two approaches commonly used to analyze animal social network data are permutation-based tests of significance and exponential random graph models. However, the performance of these approaches when analyzing different types of network data has not been simultaneously evaluated. Here we test both approaches to determine their performance when analyzing a range of biologically realistic simulated animal social networks. We examined the false positive and false negative error rate of an effect of a two-level explanatory variable (e.g., sex) on the number and combined strength of an individual’s network connections. We measured error rates for two types of simulated data collection methods in a range of network structures, and with/without a confounding effect and missing observations. Both methods performed consistently well in networks of dyadic interactions, and worse on networks constructed using observations of individuals in groups. Exponential random graph models had a marginally lower rate of false positives than permutations in most cases. Phenotypic assortativity had a large influence on the false positive rate, and a smaller effect on the false negative rate for both methods in all network types. Aspects of within- and between-group network structure influenced error rates, but not to the same extent. In "grouping event-based" networks, increased sampling effort marginally decreased rates of false negatives, but increased rates of false positives for both analysis methods. These results provide guidelines for biologists analyzing and interpreting their own network data using these methods.

An introduction of Markov chain Monte Carlo method to geochemical inverse problems: Reading melting parameters from REE abundances in abyssal peridotites

Since the 1970s, communication researchers have utilized social network analysis to understand mass, health, organizational, and interpersonal communication. This article introduces communication researchers to a new class of social network analysis methods, exponential random graph (p*) models. This new method represents the latest advancement in social network methodology and will enhance the trajectory of social network research in the communication discipline. The benefits of this class of models include allowing for the simultaneous estimation of attribute and structural parameters, accounting for the interdependent nature of network data, and retaining the complexity of network observations throughout the analysis. An example analysis using data from Shumate, Fulk, and Monge (2005) is provided to illustrate the potentials of exponential random graph modeling. Five different social network software programs capable of the analysis discussed in this article are introduced with regard to their respective benefits. Finally, a brief tutorial based on data from Palazzolo (2005) is given on how to conduct an ERGM analysis using the PNET software program.

A new method is proposed based on the finite difference method (FDM), differential evolution algorithm and Markov Chain Monte Carlo (MCMC) simulation to identify water quality model parameters of an open channel in a long distance water transfer project. Firstly, this parameter identification problem is considered as a Bayesian estimation problem and the forward numerical model is solved by FDM, and the posterior probability density function of the parameters is deduced. Then these parameters are estimated using a sampling method with differential evolution algorithm and MCMC simulation. Finally this proposed method is compared with FDM-MCMC by a twin experiment. The results show that the proposed method can be used to identify water quality model parameters of an open channel in a long distance water transfer project under different scenarios better with fewer iterations, higher reliability and anti-noise capability compared with FDM-MCMC. Therefore, it provides a new idea and method to solve the traceability problem in sudden water pollution accidents.

Despite the importance of social network analysis (SNA) in public administration, comprehensive reviews on this topic are rare. This study aims to fill this gap by focusing on the application of SNA in network research within public administration. This research analyzes 144 empirical papers from top public administration journals (January 1997–January 2022), utilizing bibliometric and content analyses. The study identifies social capital, the Advocacy Coalition Framework (ACF), the ecology of games framework, and resource dependence theory as the predominant theoretical foundations of SNA. The primary focus of these works is on collective action problems and public service delivery, with a trend towards the integration and comparison of theories. Through content analysis, we find a notable shift in SNA application from descriptive analysis to network inference, predominantly using Exponential Random Graph Models (ERGMs). It also reveals the growing significance of network visualization in SNA. The study concludes with potential future directions for SNA in public administration, highlighting its evolving role and significance.

The exponential random graph model (ERGM) is a popular model for social networks, which is known to have an intractable likelihood function. Sampling from the posterior for such a model is a long-standing problem in statistical research. We analyze the performance of the stochastic gradient Langevin dynamics (SGLD) algorithm (also known as noisy Longevin Monte Carlo) in tackling this problem, where the stochastic gradient is calculated via running a short Markov chain (the so-called inner Markov chain in this paper) at each iteration. We show that if the model size grows with the network size slowly enough, then SGLD converges to the true posterior in 2-Wasserstein distance as the network size and iteration number become large regardless of the length of the inner Markov chain performed at each iteration. Our study provides a scalable algorithm for analyzing large-scale social networks with possibly high-dimensional ERGMs.

Fortran code for SU(3) lattice gauge theory with and without MPI checkerboard parallelization

Accident risk assessment in marine transportation via Markov modelling and Markov Chain Monte Carlo simulation

Tropical cyclone (TC) is one of the most devastating weather systems that causes enormous loss of life and property in the coastal regions of Bay of Bengal (BoB). Statistical forecasting of TC occurrence can help decision-makers and inhabitants in shoreline zones to take necessary planning and actions in advance. In this study, we have investigated the impact of El Nino–Southern Oscillation (ENSO) on the frequency of TC over the BoB by using 100 years TC and Southern Oscillation Index data. The frequency of TC is approximated through observation and Markov Chain Monte Carlo (MCMC) simulation. Two-sample Student’s t test has been applied for examining the statistical significance where the results are significant at 5% level for all cyclonic disturbances. The monthly and seasonal distribution show this feature more distinctly. The total annual frequency of depressions and cyclonic storms in El Nino and La Nina conditions does not differ much, but the monthly/seasonal distribution shows high differences for certain months and seasons. The simulated frequency of TC landfall using MCMC matches well with the observation. The proposed methodology is illustrated through a case study in BoB rim countries-Bangladesh, India, Sri Lanka and Myanmar. Poisson and Bayesian regression have also been used to predict the probabilities of TC frequency over the BoB. Both the regression approaches show 10 and 32% improvement than climatology for the forecast and cross-validation skill respectively. We have also analyzed TC impact over Bangladesh as a case study. Possible links of the variation of TC activities with the largescale geographical distribution of sea surface temperature, vertical wind shear, vorticity, moisture and relative humidity are also explored.

This study presented a Bayesian logistic model to evaluate the failure probability of asphalt pavement preventive treatments. The Markov Chain Monte Carlo (MCMC) simulation using Metropolis...