64: A Zero-Inflated Weighted Distribution Mixture Model for Spatial Compositional Data in Ecology

Music City Center 

The Dirichlet distribution is often used to model compositional data. But there are limitations to using this distribution for some data. First, it does not account for spatial dependencies, meaning that for spatial data, values adjacent to each other would have no propensity to be more similar to each other than values far apart from each other. Secondly, the distribution does not allow for zero-values, creating obstacles when the observed compositional data includes zeros. Here, we propose a spatial, zero-inflated Dirichlet model that resolves these limitations. Our method involves setting the Dirichlet shape parameter α as a function of a GMM and calculates zero-values and the rest of data as separate terms in the likelihood function. We also propose a way to incorporate covariates of interest into the model. To estimate model parameters, we conduct Bayesian inference via MCMC, incorporating the Log Adaptive Proposal (Shaby/Wells, 2010) and a Dirichlet Process Prior on GMM weight parameters. We finally apply our model to a simulated dataset and an eBird (Fink et al., 2013) dataset of the spatial distributions of mallards across North America over several weeks.

spatial statistics

Bayesian statistics

ecology

Dirichlet Process prior

eBird 

Section on Statistics and the Environment