A Bayesian Nonparametric Approach to Ecological Risk Assessment

Abstract

We revisit a classical method for ecological risk assessment, the Species Sensitivity Distribution (SSD) approach, in a Bayesian nonparametric framework. SSD is a mandatory diagnostic required by environmental regulatory bodies from the European Union, the United States, Australia, China etc. Yet, it is subject to much scientific criticism, notably concerning a historically debated parametric assumption for modelling species variability. Tackling the problem using nonparametric mixture models, it is possible to shed this parametric assumption and build a statistically sounder basis for SSD. We use Normalized Random Measures with Independent Increments (NRMI) as the mixing measure because they offer a greater flexibility than the Dirichlet process. Indeed, NRMI can induce a prior on the number of components in the mixture model that is less informative than the Dirichlet process. This feature is consistent with the fact that SSD practitioners do not usually have a strong prior belief on the number of components. In this short paper, we illustrate the advantage of the nonparametric SSD over the classical normal SSD and a kernel density estimate SSD on several real datasets. We summarise the results of the complete study in Kon Kam King et al. (2016), where the method is generalised to censored data and a systematic comparison on simulated data is also presented, along with a study of the clustering induced by the mixture model to examine patterns in species sensitivity.

BNPdensity: Bayesian nonparametric mixture modelling in R

“…Barrios et al . (2013) and Kon Kam King, Arbel & Prünster (2017) show that NRMIs have better performance than Dirichlet process mixtures, kernel density estimates (the recent approach proposed by Wang et al . (2015)) or simple one‐component normal models.…”