Autologistic models for binary data on a lattice

Hughes, John R.; Haran, Murali; Caragea, Petruţa C.

doi:10.1002/env.1102

Cited by 65 publications

(73 citation statements)

References 29 publications

(49 reference statements)

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“…Our development of the AL model is consistent with that given in Hughes et al [25], which also gives an excellent review of the computational aspects of inference with the AL model. For more on MRFs and graphical models in general, see e.g., [27][28][29][30].…”

Section: Markov Random Fieldssupporting

confidence: 84%

“…They proposed the centered model to correct this problem, and recommended that it become the default for future use. This viewpoint was furthered by Hughes et al [25], who expanded on inferential and computational aspects of ALR, using the centered model exclusively.…”

Section: Introductionmentioning

confidence: 99%

“…3. The key references for the centered model [24,25] both refer to it as an autologistic model with a "centered parameterization, " and cite improved parameter interpretation as its main advantage.…”

Section: Introductionmentioning

confidence: 99%

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Better Autologistic Regression

Wolters

2017

Front. Appl. Math. Stat.

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Autologistic regression is an important probability model for dichotomous random variables observed along with covariate information. It has been used in various fields for analyzing binary data possessing spatial or network structure. The model can be viewed as an extension of the autologistic model (also known as the Ising model, quadratic exponential binary distribution, or Boltzmann machine) to include covariates. It can also be viewed as an extension of logistic regression to handle responses that are not independent. Not all authors use exactly the same form of the autologistic regression model. Variations of the model differ in two respects. First, the variable coding-the two numbers used to represent the two possible states of the variables-might differ. Common coding choices are (zero, one) and (minus one, plus one). Second, the model might appear in either of two algebraic forms: a standard form, or a recently proposed centered form. Little attention has been paid to the effect of these differences, and the literature shows ambiguity about their importance. It is shown here that changes to either coding or centering in fact produce distinct, non-nested probability models. Theoretical results, numerical studies, and analysis of an ecological data set all show that the differences among the models can be large and practically significant. Understanding the nature of the differences and making appropriate modeling choices can lead to significantly improved autologistic regression analyses. The results strongly suggest that the standard model with plus/minus coding, which we call the symmetric autologistic model, is the most natural choice among the autologistic variants.

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Section: Markov Random Fieldssupporting

confidence: 84%

Section: Introductionmentioning

confidence: 99%

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Better Autologistic Regression

Wolters

2017

Front. Appl. Math. Stat.

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“…In this paper, we consider both same-and different-species occurrence at neighbouring locations. Traditional autologistic models bias estimates of model parameters [58], but can be corrected by a centred parametrization of the autologistic model [59]. The presence/absence component of our model is an adaptation of the bivariate, centred autologistic model of Caragea & Berg [60].…”

Section: (E) Bayesian Modellingmentioning

confidence: 99%

The spatial distribution of African savannah herbivores: species associations and habitat occupancy in a landscape context

Anderson

White

Davis

et al. 2016

Phil. Trans. R. Soc. B

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Herbivores play an important role in determining the structure and function of tropical savannahs. Here, we (i) outline a framework for how interactions among large mammalian herbivores, carnivores and environmental variation influence herbivore habitat occupancy in tropical savannahs. We then (ii) use a Bayesian hierarchical model to analyse camera trap data to quantify spatial patterns of habitat occupancy for lions and eight common ungulates of varying body size across an approximately 1100 km 2 landscape in the Serengeti ecosystem. Our results reveal strong positive associations among herbivores at the scale of the entire landscape. Lions were positively associated with migratory ungulates but negatively associated with residents. Herbivore habitat occupancy differed with body size and migratory strategy: large-bodied migrants, at less risk of predation and able to tolerate lower quality food, were associated with high NDVI, while smaller residents, constrained to higher quality forage, avoided these areas. Small herbivores were strongly associated with fires, likely due to the subsequent high-quality regrowth, while larger herbivores avoided burned areas. Body mass was strongly related to herbivore habitat use, with larger species more strongly associated with riverine and woodlands than smaller species. Large-bodied migrants displayed diffuse habitat occupancy, whereas smaller species demonstrated fine-scale occupancy reflecting use of smaller patches of high-quality habitat. Our results demonstrate the emergence of strong positive spatial associations among a diverse group of savannah herbivores, while highlighting species-specific habitat selection strongly determined by herbivore body size. This article is part of the themed issue 'Tropical grassy biomes: linking ecology, human use and conservation'.

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“…After a profile inspection, the bottleneck step is computing the denominator of (5), which requires summing over all LOS connected paths. Several approximations have been proposed (e.g., Hoeting et al, 2000 andHughes et al, 2011), and it will be interesting to see whether these computational speed-ups require a substantial tradeoff in sampling accuracy.…”

Section: Discussionmentioning

confidence: 99%

A Regional Compound Poisson Process for Hurricane and Tropical Storm Damage

Mak

Bingham

2016

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary.In light of intense hurricane activity along the U.S. Atlantic coast, attention has turned to understanding both the economic impact and behaviour of these storms. The compound Poisson-lognormal process has been proposed as a model for aggregate storm damage, but does not shed light on regional analysis since storm path data are not used. In this paper, we propose a fully Bayesian regional prediction model which uses conditional autoregressive (CAR) models to account for both storm paths and spatial patterns for storm damage. When fitted to historical data, the analysis from our model both confirms previous findings and reveals new insights on regional storm tendencies. Posterior predictive samples can also be used for pricing regional insurance premiums, which we illustrate using three different risk measures.

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Autologistic models for binary data on a lattice

Cited by 65 publications

References 29 publications

Better Autologistic Regression

Better Autologistic Regression

The spatial distribution of African savannah herbivores: species associations and habitat occupancy in a landscape context

A Regional Compound Poisson Process for Hurricane and Tropical Storm Damage

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