Bayesian analysis of directed graphs data with applications to social networks

Summary.  A fully Bayesian analysis of directed graphs, with particular emphasis on applica- tions in social networks, is explored. The model is capable of incorporating the effects of covariates, within and between block ties and multiple responses. Inference is straightforward by using software that is based on Markov chain Monte Carlo methods. Examples are provided which highlight the variety of data sets that can be entertained and the ease with which they can be analysed.     

ELICITING A DIRECTED ACYCLIC GRAPH FOR A MULTIVARIATE TIME SERIES OF VEHICLE COUNTS IN A TRAFFIC NETWORK

The problem of modelling multivariate time series of vehicle counts in traffic networks is considered. It is proposed to use a model called the linear multiregression dynamic model (LMDM). The LMDM is a multivariate Bayesian dynamic model which uses any conditional independence and causal structure across the time series to break down the complex multivariate model into simpler univariate dynamic linear models. The conditional independence and causal structure in the time series can be represented by a directed acyclic graph (DAG). The DAG not only gives a useful pictorial representation of the multivariate structure, but it is also used to build the LMDM. Therefore, eliciting a DAG which gives a realistic representation of the series is a crucial part of the modelling process. A DAG is elicited for the multivariate time series of hourly vehicle counts at the junction of three major roads in the UK. A flow diagram is introduced to give a pictorial representation of the possible vehicle routes through the network. It is shown how this flow diagram, together with a map of the network, can suggest a DAG for the time series suitable for use with an LMDM.     

D-efficient window experimental designs

In the paper we present a new method of calculating sampling intervals, so-called windows, allowing an experimenter some flexibility in timing the sample collection, while a minimum required design efficiency for parameter estimation is assured. The method is based on the Equivalence Theorem for D-optimality what makes the length of each window related to the parameter sensitivities. An example of calculating the windows in a pharmacokinetic study is presented. Some other methods of calculating efficient sampling windows are briefly discussed.     

Adaptive Management: A Paradigm for Remediation of Public Facilities Following a Terrorist Attack

Terrorist actions are aimed at maximizing harm (health, psychological, economical, and political) through the combined physical impacts of the act and fear. Immediate and effective response to a terrorist act is critical to limit human and environmental harm, effectively restore facility function, and maintain public confidence. Though there have been terrorist attacks in public facilities that we have learned from, overall our experiences in restoration of public facilities following a terrorist attack are limited. Restoration of public facilities following a release of a hazardous material is inherently far more complex than in industrial settings and has many unique technical, economic, social, and political challenges. For example, there may be a great need to quickly restore the facility to full operation and allow public access even though it was not designed for easy or rapid restoration, and critical information is needed for quantitative risk assessment and effective restoration must be anticipated to be incomplete and uncertain. Whereas present planning documents have substantial linearity in their organization, the “adaptive management” paradigm provides a constructive parallel paradigm for restoration of public facilities that anticipates and plans for uncertainty, inefficiencies, and stakeholder participation. Adaptive management grew out of the need to manage and restore natural resources in highly complex and changing environments with limited knowledge about causal relationships and responses to restoration actions. Similarities between natural resource management and restoration of a public facility after a terrorist attack suggest that integration of adaptive management principles explicitly into restoration processes will result in substantially enhanced and flexible responses necessary to meet the uncertainties of potential terrorist attacks.     

Mission,money, and merit: Strategic decision making by nonprofit managers

Public and nonprofit organizations need to make strategic choices about where to invest their resources. They also need to expose hidden managerial assumptions and lack of adequate knowledge that prevent the attainment of consensus in strategic decision making. The approach we developed and tested in the field used a dynamic, three‐dimensional model that tracks individual programs in an organization's portfolio on their contribution to mission, money, and merit. The first dimension measures whether the organization is doing the right things; the second, whether it is doing things right financially; and the third, whether it doing things right in terms of quality. Senior managers provide their own evaluations of the organization's programs. Both the consensus view and the variation in individual assessments contribute to an improved managerial understanding of the organization's current situation and to richer discussions in strategic decision making. In field tests, this visual model proved to be a useful and powerful tool for illuminating underlying assumptions and variations in knowledge among managers facing the complex, multidimensional tradeoffs needed in strategic decision making.     

Loss functions for estimation of extrema with an application to disease mapping

It is often of interest to find the maximum or near maxima among a set of vector‐valued parameters in a statistical model; in the case of disease mapping, for example, these correspond to relative‐risk “hotspots” where public‐health intervention may be needed. The general problem is one of estimating nonlinear functions of the ensemble of relative risks, but biased estimates result if posterior means are simply substituted into these nonlinear functions. The authors obtain better estimates of extrema from a new, weighted ranks squared error loss function. The derivation of these Bayes estimators assumes a hidden‐Markov random‐field model for relative risks, and their behaviour is illustrated with real and simulated data.     

Bayesian inference for a discretely observed stochastic kinetic model

The ability to infer parameters of gene regulatory networks is emerging as a key problem in systems biology. The biochemical data are intrinsically stochastic and tend to be observed by means of discrete-time sampling systems, which are often limited in their completeness. In this paper we explore how to make Bayesian inference for the kinetic rate constants of regulatory networks, using the stochastic kinetic Lotka-Volterra system as a model. This simple model describes behaviour typical of many biochemical networks which exhibit auto-regulatory behaviour. Various MCMC algorithms are described and their performance evaluated in several data-poor scenarios. An algorithm based on an approximating process is shown to be particularly efficient.