In this paper, we offer a gentle introduction to Gaussian processes for time-series data analysis. The conceptual framework of Bayesian modelling for time-series data is discussed and the foundations of Bayesian non-parametric modelling presented for Gaussian processes. We discuss how domain knowledge influences design of the Gaussian process models and provide case examples to highlight the approaches.

Identifying overlapping communities in networks is a challenging task. In this work we present a probabilistic approach to community detection that utilizes a Bayesian non-negative matrix factorization model to extract overlapping modules from a network. The scheme has the advantage of soft-partitioning solutions, assignment of node participation scores to modules, and an intuitive foundation. We present the performance of the method against a variety of benchmark problems and compare and contrast it to several other algorithms for community detection.

Wavelet cross-correlation (WCC) is used to analyse the relationship between low-frequency oscillations in near-infrared spectroscopy (NIRS) measured cerebral oxyhaemoglobin (O2Hb) and mean arterial blood pressure (MAP) in patients suffering from autonomic failure and age-matched controls. Statistically significant differences are found in the wavelet scale of maximum cross-correlation upon posture change in patients, but not in controls. We propose that WCC analysis of the relationship between O2Hb and MAP provides a useful method of investigating the dynamics of cerebral autoregulation using the spontaneous low-frequency oscillations that are typically observed in both variables without having to make the assumption of stationarity of the time series. It is suggested that for a short-duration clinical test previous transfer-function-based approaches to analyse this relationship may suffer due to the inherent nonstationarity of low-frequency oscillations that are observed in the resting brain.

Provenance network analytics is a novel data analytics approach that helps infer properties of data, such as quality or importance, from their provenance. Instead of analysing application data, which are typically domain-dependent, it analyses the data's provenance as represented using the World Wide Web Consortium's domainagnostic PROV data model. Specifically, the approach proposes a number of network metrics for provenance data and applies established machine learning techniques over such metrics to build predictive models for some key properties of data. Applying this method to the provenance of real-world data from three different applications, we show that it can successfully identify the owners of provenance documents, assess the quality of crowdsourced data, and identify instructions from chat messages in an alternate-reality game with high levels of accuracy. By so doing, we demonstrate the different ways the proposed provenance network metrics can be used in analysing data, providing the foundation for provenance-based data analytics.

Crowdsourcing has become a popular means for quickly achieving various tasks in large quantities. CollabMap is an online mapping application in which we crowdsource the identification of evacuation routes in residential areas to be used for planning large-scale evacuations. So far, approximately 38,000 micro-tasks have been completed by over 100 contributors. In order to assist with data verification, we introduced provenance tracking into the application, and approximately 5,000 provenance graphs have been generated. They have provided us various insights into the typical characteristics of provenance graphs in the crowdsourcing context. In particular, we have estimated probability distribution functions over three selected characteristics of these provenance graphs: the node degree, the graph diameter, and the densification exponent. We describe methods to define these three characteristics across specific combinations of node types and edge types, and present our findings in this paper. Applications of our methods include rapid comparison of one provenance graph versus another, or of one style of provenance database versus another. Our results also indicate that provenance graphs represent a suitable area of exploitation for existing network analysis tools concerned with modelling, prediction, and the inference of missing nodes and edges.