Partial‐Likelihood Analysis of Spatio‐Temporal Point‐Process Data

Abstract

We investigate the use of a partial likelihood for estimation of the parameters of interest in spatio-temporal point-process models. We identify an important distinction between spatially discrete and spatially continuous models. We focus our attention on the spatially continuous case, which has not previously been considered. We use an inhomogeneous Poisson process and an infectious disease process, for which maximum-likelihood estimation is tractable, to assess the relative efficiency of partial versus full likelihood, and to illustrate the relative ease of implementation of the former. We apply the partial-likelihood method to a study of the nesting pattern of common terns in the Ebro Delta Natural Park, Spain.

stpp: AnRPackage for Plotting, Simulating and Analyzing Spatio-Temporal Point Patterns

“…Note that an infectious process in this sense may exhibit a combination of contagious and inhibitory properties. Diggle, Kaimi, and Abellana (2010) give an example of such a process to describe the pattern of colonization of a nesting ground, in which each new arrival tends to choose a nesting location close to established nests, but not so close as to invade their established territories.…”

Comparative interpretation of count, presence–absence and point methods for species distribution models

“…This may be an advantage if one wishes to avoid the effect of correlation on the parameter estimates and their standard errors, but if one is also interested in capturing the actual mechanism causing the clustering of organisms (Fieberg et al 2010), implementation of point methods may be more fruitful. The exponential IPP model does not address this latter form of clustering, but more complex point process models could be fit to address these issues (Baddeley & Turner 2000;Johnson et al 2008;Diggle, Kaimi & Abellana 2010a).…”

“…In particular, we focus on point and count data. Owing to work performed by others (Diggle 1990;Cressie 1993;Diggle & Rowlingson 1994;Baddeley & Turner 2000;Lele & Keim 2006;Lele 2009;Baddeley et al 2010;Diggle, Kaimi, & Abellana 2010a;Warton & Shepherd 2010), it is possible to show that the Poisson likelihood function used for count data, and likelihood functions used for point methods [e.g. Weighted Distribution Theory (WDT) and point Logistic regression] can be motivated by the same underlying inhomogeneous Poisson point process (IPP) model.…”

Review of statistical methods and data requirements to support post market environmental monitoring of agro ecosystems

“…Other developments in statistics that do affect the fitted models include challenging the independence of the responses by introducing the assumption of autocorrelated errors in time (and various forms of time series structures specified according to the autoregressive integrated moving average (ARIMA) framework) (see Chandler and Scott (2011) for many examples) and in space (with classical geostatistics and point process models now leading to more flexible space-time structures (Wackernegel, 2003;Diggle et al, 2010;Cressie and Wikle, 2011). These approaches and many further topics in detecting change in environmental and ecological data are covered in recent texts on model fitting for environmental applications, such as Chandler and Scott (2011) and the series of books from Highland Statistics: Zuur et al (2007), Zuur et al (2009), andZuur et al (2012).…”