Multivariate Kalman Filtering for Spatio-Temporal Processes

An increasing interest in models for multivariate spatio-temporal processes has been noted in the last years. Some of these models are very flexible and can capture both marginal and cross spatial associations amongst the components of the multivariate process. In order to contribute to the statistical analysis of these models, this paper deals with the estimation and prediction of multivariate spatio-temporal processes by using multivariate state-space models. In this context, a multivariate spatio-temporal process is represented through the well-known Wold decomposition. Such an approach allows for an easy implementation of the Kalman filter to estimate linear temporal processes exhibiting both short and long range dependencies, together with a spatial correlation structure. We illustrate, through simulation experiments, that our method offers a good balance between statistical efficiency and computational complexity. Finally, we apply the method for the analysis of a bivariate dataset on average daily temperatures and maximum daily solar radiations from 21 meteorological stations located in a portion of south-central Chile.

Closing the Frontier, Opening Doors

In this article I examine a recent communal cocoa planting project in a Wide Bay Mengen community in East Pomio, Papua New Guinea in relation to histories of resource extraction. I discuss how the community members modeled the current planting of cocoa in accordance with earlier forms of agriculture, namely copra production and swidden horticulture. The cocoa planting project is linked to a longer history of labour and resource extraction in Pomio. I analyze the cycles of labour recruitment, logging, and oil palm expansion through the framework of the frontier, by which I mean a spatio-temporal process through which certain areas are portrayed as having abundant resources, which are made available for extraction. The cocoa planting project was a local response to these conditions and intended to be a source of income based on inalienated labour and local landholding and a spatial strategy of establishing points of access to other places, called 'doors' by the community members. My aim in this article is twofold. First, I argue that the frontier understood as a spatio-temporal process helps us to conceptualize cycles of resource extraction. Second, I show how people living in areas understood as frontiers form their own analyses and responses to the conditions under which their land, labour, and resources are made available to others. Keywords: cocoa, commodification, frontier, infrastructure, natural resources, oil palm, Papua New Guinea, place, territorialization

Spatial Hurst–Kolmogorov Clustering

The stochastic analysis in the scale domain (instead of the traditional lag or frequency domains) is introduced as a robust means to identify, model and simulate the Hurst–Kolmogorov (HK) dynamics, ranging from small (fractal) to large scales exhibiting the clustering behavior (else known as the Hurst phenomenon or long-range dependence). The HK clustering is an attribute of a multidimensional (1D, 2D, etc.) spatio-temporal stationary stochastic process with an arbitrary marginal distribution function, and a fractal behavior on small spatio-temporal scales of the dependence structure and a power-type on large scales, yielding a high probability of low- or high-magnitude events to group together in space and time. This behavior is preferably analyzed through the second-order statistics, and in the scale domain, by the stochastic metric of the climacogram, i.e., the variance of the averaged spatio-temporal process vs. spatio-temporal scale.

A Novel Measure of Real-Time Perseverative Thought

Perseverative thinking (PT), or repetitive negative thinking, has historically been measured using global self-report scales. New methods of assessment are needed to advance understanding of this inherently temporal process. We developed an intensive longitudinal method for assessing PT. A mixed sample of 77 individuals ranging widely in trait PT, including persons with PT-related disorders (generalized anxiety disorder, major depression) and persons without psychopathology, used a joystick to provide continuous ratings of thought valence and intensity following exposure to scenarios of differing valence. Joystick responses were robustly predicted by trait PT, clinical status, and stimulus valence. Higher trait perseverators exhibited more extreme joystick values overall, greater stability in values following threatening and ambiguous stimuli, weaker stability in values following positive stimuli, and greater inertia in values following ambiguous stimuli. The joystick method is a promising measure with the potential to shed new light on the dynamics and precipitants of perseverative thinking.

EU migrant retention and the temporalities of migrant staying: a new conceptual framework

Challenges of weak economic growth, population decline, and labour shortages led many countries across the world to introduce immigration policy changes in order to attract foreign migrants. This paper focuses on Japan (Tokyo) and the UK (Birmingham, Edinburgh and Glasgow) given common concerns over long term demographic trends and the burgeoning lack of labour supply in particular sectors of the economy through use of foreign labour. The paper shifts the focus from efforts focused on attracting and selecting foreign labour to the retention of such individuals. Drawing on research with EU migrants in Japan and the UK, the paper highlights how staying may occur after a period of mobility, rather than only being of relevance to those who never left their home region. The paper develops a new conceptual framework, which helps to identify different dimensions that shape migrant staying as a temporal process. It is highlighted how staying is shaped incrementally and facilitated or undermined over time in relation to the reciprocal importance of diverse assets, anchors and the changing biographies of migrants and the places in which they live – as well as the relational aspects of migrants’ ‘linked lives’.

The diffusing-velocity random walk: Capturing the interplay of diffusion and heterogeneous advection within a spatial-Markov framework

<p>The spatial distribution of a solute undergoing advection and diffusion is impacted by the velocity variability sampled by tracer particles. In spatially structured velocity fields, such as porous medium flows, Lagrangian velocities along streamlines are often characterized by a well-defined correlation length and can thus be described by spatial-Markov processes. Diffusion, on the other hand, is generally modeled as a temporal process, making it challenging to capture advective and diffusive dynamics in a single framework. In order to address this limitation, we have developed a description of transport based on a spatial-Markov velocity process along Lagrangian particle trajectories, incorporating the effect of diffusion as a local averaging process in velocity space. The impact of flow structure on this diffusive averaging is quantified through an effective shear rate. The latter is fully determined by the point statistics of velocity magnitudes together with characteristic longitudinal and transverse lengthscales associated with the flow field. For infinite longitudinal correlation length, our framework recovers Taylor dispersion, and in the absence of diffusion it reduces to a standard spatial-Markov velocity model. This novel framework allows us to derive dynamical equations governing the evolution of particle position and velocity, from which we obtain scaling laws for the dependence of longitudinal dispersion on Péclet number. Our results provide new insights into the role of shear and diffusion on dispersion processes in heterogeneous media.</p><p>In this presentation, I propose to discuss: (i) Spatial-Markov models and the modeling of diffusion as a spatial rather than temporal process; (ii) The concept of the effective shear rate and its role in the diffusive dynamics of tracer particle velocities; (iii) The role of transverse diffusion and its interplay with velocity heterogeneity on longitudinal solute dispersion.</p>

A method for spatio-temporal process assessment of eco-geological environmental security in mining areas using catastrophe theory and projection pursuit model

It is a universal problem that the eco-geological environment has been damaged by mineral resources exploitation. The accurate evaluation of eco-geological environmental security (EES) in mining areas is essential for restoring the environment of the mining area. However, a robust approach to obtaining an accurate evaluation of ESS has not yet been produced due to the complex spatio-temporal process of EES. Here, we developed a new method for enabling the quantitative evaluation of the EES spatio-temporal process. The EES evaluation index system of mining areas was established from both natural and anthropogenic aspects. The EES evaluation method was developed by combining the catastrophe theory and projection pursuit model (PPM). Then, with the support of remote sensing (RS) and a geographic information system (GIS), the method was applied to evaluate the spatio-temporal process of EES in Panxi mining area. The bifurcation curve and receiver operating characteristic curve were used to verify the developed method. The results showed that this method could accurately evaluate the spatio-temporal process of EES in a mining area and could successfully recognise the threshold value to distinguish the safe status and unsafe status. Strong spatio-temporal variations of EES in Panxi area were found, which may be the result of the combined effect of multiple factors (e.g. mineral resource exploitation, soil erosion, and ecological restoration). In summary, the combination of catastrophe theory and PPM with RS and GIS to quantitatively evaluate the spatio-temporal process of EES in mining areas is a robust method.