Efficient computational strategies for doubly intractable problems with applications to Bayesian social networks

Powerful ideas recently appeared in the literature are adjusted and combined to design improved samplers for Bayesian exponential random graph models. Different forms of adaptive Metropolis-Hastings proposals (vertical, horizontal and rectangular) are tested and combined with the Delayed rejection (DR) strategy with the aim of reducing the variance of the resulting Markov chain Monte Carlo estimators for a given computational time. In the examples treated in this paper the best combination, namely horizontal adaptation with delayed rejection, leads to a variance reduction that varies between 92% and 144% relative to the adaptive direction sampling approximate exchange algorithm of Caimo and Friel (2011). These results correspond to an increased performance which varies from 10% to 94% if we take simulation time into account. The highest improvements are obtained when highly correlated posterior distributions are considered.Comment: 23 pages, 8 figures. Accepted to appear in Statistics and Computin

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

Bayesian exponential random graph modelling of interhospital patient referral networks

Using original data that we have collected on referral relations between 110 hospitals serving a large regional community, we show how recently derived Bayesian exponential random graph models may be adopted to illuminate core empirical issues in research on relational coordination among health care organisations. We show how a rigorous Bayesian computation approach supports a fully probabilistic analytical framework that alleviates well-known problems in the estimation of model parameters of exponential random graph models. We also show how the main structural features of interhospital patient referral networks that prior studies have described, can be reproduced with accuracy by specifying the system of local dependencies that produce – but at the same time are induced by – decentralised collaborative arrangements between hospitals

Missing Data Augmentation for Bayesian Multiplex ERGMs

In this paper we present an estimation algorithm for Bayesian multiplex exponential random graphs (BmERGMs) under missing net- work data. Social actors are often connected with more than one type of relation, thus forming a multiplex network. It is important to consider these multiplex structures simultaneously when analyzing a multiplex network. The importance of proper models of multiplex network structures is even more pronounced under the issue of missing network data. The proposed algorithm is able to estimate BmERGMs under missing data and can be used to obtain proper multiple imputations for multiplex network structures. It is an extension of Bayesian exponential random graphs (BERGMs) as implemented in the Bergm package in R. We demonstrate the algorithm on a well known example, with and without artificially simulated missing data

Knowledge sharing in organizations: A Bayesian analysis of the role of reciprocity and formal structure

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordWe examine the conditions under which knowledge embedded in advice relations is likely to reach across intraorganizational boundaries and be shared between distant organizational members. We emphasize boundary-crossing relations because activities of knowledge transfer and sharing across subunit boundaries are systematically related to desirable organizational outcomes. Our main objective is to understand how organizational and social processes interact to sustain the transfer of knowledge carried by advice relations. Using original fieldwork and data that we have collected on members of the top management team in a multiunit industrial group, we show that knowledge embedded in task advice relations is unlikely to crosscut intraorganizational boundaries, unless advice relations are reciprocated, and supported by the presence of hierarchical relations linking managers in different subunits. The results we report are based on a novel Bayesian Exponential Random Graph Models (BERGMs) framework that allows us to test and assess the empirical value of our hypotheses while at the same time accounting for structural characteristics of the intraorganizational network of advice relations. We rely on computational and simulation methods to establish the consistency of the network implied by the model we propose with the structure of the intraorganizational network that we actually observed

Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $P$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $P$ by an approximation $\hat{P}$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how 'close' the chain given by the transition kernel $\hat{P}$ is to the chain given by $P$. We apply these results to several examples from spatial statistics and network analysis.Comment: This version: results extended to non-uniformly ergodic Markov chain

Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.Comment: 26 pages, 2 figures, accepted in Journal of Computational and Graphical Statistics (http://www.amstat.org/publications/jcgs.cfm

Collaborations in environmental initiatives for an effective gover- nance of social-ecological systems: What the scientific literature suggests.

Moving from the scientific literature on evaluation of environmental projects and programs, this study identifies how and under which conditions collaborations are considered effective for adaptive gover- nance of SES. The method adopted is a systematic literature review based on the quantitative and qualitative analysis of 56 articles selected through specific queries on the SCOPUS database and published from 2004 to 2020. Results of the quantitative analysis underline conditions able to make collaborations effective for adaptive governance of SES: the importance of transdisciplinary research tackling both environmental and social sciences, the perceived urgency of stakeholders to tackle environmental challenges and consequently their inclusion in projects, the valorisation of different typologies of knowledge, and the adaptation to local culture and lifestyle. Results of the qualitative analysis provides specific recommendations for collaborations to be effective related to communication, equity, foresight, and respect, which need to be further strengthened. Multiplicity in visions and approaches should not be seen as a limit but as a resource able to stimulate creativity in social arrangements and environmental practices, making collaborations instrumental for the effectiveness of adaptive governance

Sustainable energy governance in South Tyrol (Italy): A probabilistic bipartite network model

At the national scale, almost all of the European countries have already achieved energy transition targets, while at the regional and local scales, there is still some potential to further push sustainable energy transitions. Regions and localities have the support of political, social, and economic actors who make decisions for meeting existing social, environmental and economic needs recognising local specificities. These actors compose the sustainable energy governance that is fundamental to effectively plan and manage energy resources. In collaborative relationships, these actors share, save, and protect several kinds of resources, thereby making energy transitions deeper and more effective. This research aimed to analyse a part of the sustainable energy governance composed of formal relationships between municipalities and public utilities and to investigate the opportunities to further spread sustainable energy development within a region. In the case study from South Tyrol, Italy, the network structures and dynamics of this part of the actual energy governance were investigated through a social network analysis and Bayesian exponential random graph models. The findings confirmed that almost all of the collaborations are based on spatial closeness relations and that the current network structures do not permit a further spread of the sustainable energy governance. The methodological approach can be replicated in other case studies and the findings are relevant to support energy planning choices at regional and local scales