Detection of local and global outliers in mapping studies

Abstract

SUMMARYIn mapping studies, extreme risk areas may arise in proximity to one another in a smooth spatial surface. They may also arise as isolated 'hotspots' or 'lowspots', which are quite distinct from those of neighbouring sites. In this paper, we develop spatial methods which encompass both types of extreme risks. The former is modelled by a spatially smooth surface using a conditional autoregressive model; the latter is addressed with the addition of a discrete clustering component, which offers the flexibility of accommodating extreme isolated risks and is not limited by spatial smoothness. The autoregressive component incorporates the spatially correlated risk as a baseline surface, acknowledging that environmental activity, often spatially correlated, influences risk responses. The discrete component identifies hotspots/lowspots of activity beyond the spatially correlated baseline risk surface. Both types of extreme risk are important, but isolated extremes may provide insight into areas with potential of being a centre for future spatially correlated extreme risks. Hence these may be particularly important in terms of surveillance. A Bayesian approach to inference is employed and graphical techniques for isolating extremes are illustrated. Model assessment is conducted via cross-validation posterior predictive checks. Three examples demonstrate the utility of the methods and case studies show the procedures to be useful for pinpointing extreme risks. In addition, sensitivity to priors is investigated.

Associations between macrofauna and sediment hydrocarbons from treated ballast water effluent at a marine oil terminal in Port Valdez, Alaska

“…5 and 6). The spatio-temporal models for these polychaetes demonstrated a pattern expected in the presence of interactions (between PAH, fauna, and the environment) resulting in regions of sharp change or hotspots (Fortin and Dale 2005;Ainsworth and Dean 2008). G. oculata and Melinna spp.…”

Spatial and mixture models for recurrent event processes

“…Such spatial allocation to mixture components could be accomplished through a logistic transformation of an autoregressive Gaussian process or a latent autologistic process (Huffer and Wu, 1998) may be used to govern mixture allocations. Finally, note that Ainsworth and Dean (2006) discuss methods for simultaneously identifying extreme risks which are spatially correlated and those which are isolated extreme values. Such spatial methods could be employed in these models for longitudinal recurrent event data analyses to distinguish between these types of extremes.…”

Canadian contributions to environmetrics

“…This reflection of contributions focused on wildland fire science and management; however, there are many other fields where statisticians have had an impact. Of note, we mention the important field of forest ecology, with leadership in research provided by Marie‐Josée Fortin and important contributions by Ainsworth & Dean (2008) and Feng & Dean (2012) in zero‐heavy spatial modelling, and Dean, Nathoo & Nielsen (2007) in mixture models for pine weevil studies. With such a large field of research in forestry and much work to be done, there is a need for continued training and talent to engage in these areas.…”