## A latent discrete Markov random field approach to identifying and classifying historical forest communities based on spatial multivariate tree species counts.(English)Zbl 1435.62411

Summary: The Wisconsin Public Land Survey database describes historical forest composition at high spatial resolution and is of interest in ecological studies of forest composition in Wisconsin just prior to significant Euro-American settlement. For such studies it is useful to identify recurring subpopulations of tree species known as communities, but standard clustering approaches for subpopulation identification do not account for dependence between spatially nearby observations. Here, we develop and fit a latent discrete Markov random field model for the purpose of identifying and classifying historical forest communities based on spatially referenced multivariate tree species counts across Wisconsin. We show empirically for the actual dataset and through simulation that our latent Markov random field modeling approach improves prediction and parameter estimation performance. For model fitting we introduce a new stochastic approximation algorithm which enables computationally efficient estimation and classification of large amounts of spatial multivariate count data.

### MSC:

 62P12 Applications of statistics to environmental and related topics 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62H11 Directional data; spatial statistics 62M05 Markov processes: estimation; hidden Markov models
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### References:

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