The power and pitfalls of Dirichlet-multinomial mixture models for ecological count data

The Dirichlet-multinomial mixture model (DMM) and its extensions provide powerful new tools for interpreting the ecological dynamics underlying taxon abundance data. However, like many complex models, how effectively they capture the many features of empirical data is not well understood. In this work, we expand the DMM to an infinite mixture model (iDMM) and use posterior predictive distributions (PPDs) to explore the performance in three case studies, including two amplicon metagenomic time series. We avoid concentrating on fluctuations within individual taxa and instead focus on consortial-level dynamics, using straight-forward methods for visualizing this perspective. In each study, the iDMM appears to perform well in organizing the data as a framework for biological interpretation. Using the PPDs, we also observe several exceptions where the data appear to significantly depart from the model in ways that give useful ecological insight. We summarize the conclusions as a set of considerations for field researchers: problems with samples and taxa; relevant scales of ecological fluctuation; additional niches as outgroups; and possible violations of niche neutrality.

On Bayesian Mixture Credibility

We introduce a class of Bayesian infinite mixture models first introduced by Lo (1984) to determine the credibility premium for a non-homogeneous insurance portfolio. The Bayesian infinite mixture models provide us with much flexibility in the specification of the claim distribution. We employ the sampling scheme based on a weighted Chinese restaurant process introduced in Lo et al. (1996) to estimate a Bayesian infinite mixture model from the claim data. The Bayesian sampling scheme also provides a systematic way to cluster the claim data. This can provide some insights into the risk characteristics of the policyholders. The estimated credibility premium from the Bayesian infinite mixture model can be written as a linear combination of the prior estimate and the sample mean of the claim data. Estimation results for the Bayesian mixture credibility premiums will be presented.

On Bayesian Mixture Credibility

We introduce a class of Bayesian infinite mixture models first introduced by Lo (1984) to determine the credibility premium for a non-homogeneous insurance portfolio. The Bayesian infinite mixture models provide us with much flexibility in the specification of the claim distribution. We employ the sampling scheme based on a weighted Chinese restaurant process introduced in Lo et al. (1996) to estimate a Bayesian infinite mixture model from the claim data. The Bayesian sampling scheme also provides a systematic way to cluster the claim data. This can provide some insights into the risk characteristics of the policyholders. The estimated credibility premium from the Bayesian infinite mixture model can be written as a linear combination of the prior estimate and the sample mean of the claim data. Estimation results for the Bayesian mixture credibility premiums will be presented.