Cox processes driven by transformed Gaussian processes on linear networks -- A review and new contributions

There is a lack of point process models on linear networks. For an arbitrary linear network, we consider new models for a Cox process with an isotropic pair correlation function obtained in various ways by transforming an isotropic Gaussian process which is used for driving the random intensity function of the Cox process. In particular we introduce three model classes given by log Gaussian, interrupted, and permanental Cox processes on linear networks, and consider for the first time statistical procedures and applications for parametric families of such models. Moreover, we construct new simulation algorithms for Gaussian processes on linear networks and discuss whether the geodesic metric or the resistance metric should be used for the kind of Cox processes studied in this paper

Modeling and estimation of multi-source clustering in crime and security data

While the presence of clustering in crime and security event data is well established, the mechanism(s) by which clustering arises is not fully understood. Both contagion models and history independent correlation models are applied, but not simultaneously. In an attempt to disentangle contagion from other types of correlation, we consider a Hawkes process with background rate driven by a log Gaussian Cox process. Our inference methodology is an efficient Metropolis adjusted Langevin algorithm for filtering of the intensity and estimation of the model parameters. We apply the methodology to property and violent crime data from Chicago, terrorist attack data from Northern Ireland and Israel, and civilian casualty data from Iraq. For each data set we quantify the uncertainty in the levels of contagion vs. history independent correlation.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS647 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Point process modeling for directed interaction networks

Network data often take the form of repeated interactions between senders and receivers tabulated over time. A primary question to ask of such data is which traits and behaviors are predictive of interaction. To answer this question, a model is introduced for treating directed interactions as a multivariate point process: a Cox multiplicative intensity model using covariates that depend on the history of the process. Consistency and asymptotic normality are proved for the resulting partial-likelihood-based estimators under suitable regularity conditions, and an efficient fitting procedure is described. Multicast interactions--those involving a single sender but multiple receivers--are treated explicitly. The resulting inferential framework is then employed to model message sending behavior in a corporate e-mail network. The analysis gives a precise quantification of which static shared traits and dynamic network effects are predictive of message recipient selection.Comment: 36 pages, 13 figures; includes supplementary materia

Reverse engineering of biochar

This study underpins quantitative relationships that account for the combined effects that starting biomass and peak pyrolysis temperature have on physico-chemical properties of biochar. Meta-data was assembled from published data of diverse biochar samples (n = 102) to (i) obtain networks of intercorrelated properties and (ii) derive models that predict biochar properties. Assembled correlation networks provide a qualitative overview of the combinations of biochar properties likely to occur in a sample. Generalized Linear Models are constructed to account for situations of varying complexity, including: dependence of biochar properties on single or multiple predictor variables, where dependence on multiple variables can have additive and/or interactive effects; non-linear relation between the response and predictors; and non-Gaussian data distributions. The web-tool Biochar Engineering implements the derived models to maximize their utility and distribution. Provided examples illustrate the practical use of the networks, models and web-tool to engineer biochars with prescribed properties desirable for hypothetical scenarios

Comment on Article by Ferreira and Gamerman

A utility-function approach to optimal spatial sampling design is a powerful way to quantify what "optimality" means. The emphasis then should be to capture all possible contributions to utility, including scientific impact and the cost of sampling. The resulting sampling plan should contain a component of designed randomness that would allow for a non-parametric design-based analysis if model-based assumptions were in doubt. [arXiv:1509.03410]Comment: Published at http://dx.doi.org/10.1214/15-BA944B in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/