Extending Functional kriging to a multivariate context

Environmental data usually have a spatio-temporal structure; pollutant concentrations, for example, are recorded along time and space. Generalized Additive Models (GAMs) represent a suitable tool to model spatial and/or temporal trends of this kind of data, that can be treated as functional, although they are collected as discrete observations. Frequently, the attention is focused on the prediction of a single pollutant at an unmonitored site and, at this aim, we extend kriging for functional data to a multivariate context by exploiting the correlation with the other pollutants. In particular, we propose two procedures: the first one (FKED) combines the regression of a variable (pollutant), of primary interest on the other variables, with functional kriging of the regression residuals; the second one (FCK) is based on linear unbiased prediction of spatially correlated multivariate random processes. The performance of the two proposed procedures is assessed by cross validation; data recorded during a year (2011) from the monitoring network of the state of California (USA) are considered

High-Dimensional Bayesian Geostatistics

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatiotemporal process models have become widely deployed statistical tools for researchers to better understand the complex nature of spatial and temporal variability. However, fitting hierarchical spatiotemporal models often involves expensive matrix computations with complexity increasing in cubic order for the number of spatial locations and temporal points. This renders such models unfeasible for large data sets. This article offers a focused review of two methods for constructing well-defined highly scalable spatiotemporal stochastic processes. Both these processes can be used as "priors" for spatiotemporal random fields. The first approach constructs a low-rank process operating on a lower-dimensional subspace. The second approach constructs a Nearest-Neighbor Gaussian Process (NNGP) that ensures sparse precision matrices for its finite realizations. Both processes can be exploited as a scalable prior embedded within a rich hierarchical modeling framework to deliver full Bayesian inference. These approaches can be described as model-based solutions for big spatiotemporal datasets. The models ensure that the algorithmic complexity has $\sim n$ floating point operations (flops), where $n$ the number of spatial locations (per iteration). We compare these methods and provide some insight into their methodological underpinnings

Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks constructed from real-world data sets (a location-based social media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis --- such as community structure and motif analysis --- of the reconstructed networks

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Peer reviewedPublisher PD

Cover Tree Bayesian Reinforcement Learning

This paper proposes an online tree-based Bayesian approach for reinforcement learning. For inference, we employ a generalised context tree model. This defines a distribution on multivariate Gaussian piecewise-linear models, which can be updated in closed form. The tree structure itself is constructed using the cover tree method, which remains efficient in high dimensional spaces. We combine the model with Thompson sampling and approximate dynamic programming to obtain effective exploration policies in unknown environments. The flexibility and computational simplicity of the model render it suitable for many reinforcement learning problems in continuous state spaces. We demonstrate this in an experimental comparison with least squares policy iteration

Testing the structure and process of personality using ambulatory assessment data : an overview of within-person and person-specific techniques

In the present article, we discuss the potential of ambulatory assessment for an idiographic study of the structure and process of personality. To this end, we first review important methodological issues related to the design and implementation of an ambulatory assessment study in the personality domain, including methods of ambulatory assessment, frequency of measurement and duration of the study, ambulatory assessment scales and questionnaires, participant selection, training and motivation, and ambulatory assessment hard- and software. Next, we provide a detailed outline of available analytical approaches that can be used to analyze the intensive longitudinal data generated by an ambulatory assessment study. By doing this, we hope to familiarize personality scholars with these methods and to provide guidance for their use in the field of personality psychology and beyond

Four not six: revealing culturally common facial expressions of emotion

As a highly social species, humans generate complex facial expressions to communicate a diverse range of emotions. Since Darwin’s work, identifying amongst these complex patterns which are common across cultures and which are culture-specific has remained a central question in psychology, anthropology, philosophy, and more recently machine vision and social robotics. Classic approaches to addressing this question typically tested the cross-cultural recognition of theoretically motivated facial expressions representing six emotions, and reported universality. Yet, variable recognition accuracy across cultures suggests a narrower cross-cultural communication, supported by sets of simpler expressive patterns embedded in more complex facial expressions. We explore this hypothesis by modelling the facial expressions of over 60 emotions across two cultures, and segregating out the latent expressive patterns. Using a multi-disciplinary approach, we first map the conceptual organization of a broad spectrum of emotion words by building semantic networks in two cultures. For each emotion word in each culture, we then model and validate its corresponding dynamic facial expression, producing over 60 culturally valid facial expression models. We then apply to the pooled models a multivariate data reduction technique, revealing four latent and culturally common facial expression patterns that each communicates specific combinations of valence, arousal and dominance. We then reveal the face movements that accentuate each latent expressive pattern to create complex facial expressions. Our data questions the widely held view that six facial expression patterns are universal, instead suggesting four latent expressive patterns with direct implications for emotion communication, social psychology, cognitive neuroscience, and social robotics