arXiv subjects

John Haslett

Publications and source records attributed to John Haslett.

5 recordsLinked to original sources

arXiv2021

Modelling excess zeros in count data: A new perspective on modelling approaches

We consider the analysis of count data in which the observed frequency of zero counts is unusually large, typically with respect to the Poisson distribution. We focus on two alternative modelling approaches: Over-Dispersion (OD) models, and Zero-Inflation (ZI) models, both of which can be seen as generalisations of the Poisson distribution; we refer to these as Implicit and Explicit ZI models, respectively. Although sometimes seen as competing approaches, they can be complementary; OD is a consequence of ZI modelling, and ZI is a by-product of OD modelling. The central objective in such analyses is often concerned with inference on the effect of covariates on the mean, in light of the apparent excess of zeros in the counts. Typically the modelling of the excess zeros per se is a secondary objective and there are choices to be made between, and within, the OD and ZI approaches. The contribution of this paper is primarily conceptual. We contrast, descriptively, the impact on zeros of the two approaches. We further offer a novel descriptive characterisation of alternative ZI models, including the classic hurdle and mixture models, by providing a unifying theoretical framework for their comparison. This in turn leads to a novel and technically simpler ZI model. We develop the underlying theory for univariate counts and touch on its implication for multivariate count data.

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arXiv2018

A general framework for modelling zero inflation

We propose a new framework for the modelling of count data exhibiting zero inflation (ZI). The main part of this framework includes a new and more general parameterisation for ZI models which naturally includes both over- and under-inflation. It further sheds new theoretical light on modelling and inference and permits a simpler alternative, which we term as multiplicative, in contrast to the dominant mixture and hurdle models. Our approach gives the statistician access to new types of ZI of which mixture and hurdle are special cases. We outline a simple parameterised modelling approach which can help to infer both ZI type and degree and provide an underlying treatment that shows that current ZI models are themselves typically within the exponential family, thus permitting much simpler theory, computation and classical inference. We outline some possibilities for a natural Bayesian framework for inference; and a rich basis for work on correlated ZI counts. The present paper is an incomplete report on the underlying theory. A later version will include computational issues and provide further examples.

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arXiv2014

Joint Inference of Misaligned Irregular Time Series with Application to Greenland Ice Core Data

Ice cores provide insight into the past climate over many millennia. Due to ice compaction, the raw data for any single core are irregular in time. Multiple cores have different irregularities; jointly these series are misaligned. After processing, such data are made available to researchers as regular time series: a data product. Typically, these cores are independently processed. In this paper, we consider a fast Bayesian method for the joint processing of multiple irregular series. This is shown to be more efficient. Further, our approach permits a realistic modelling of the impact of the multiple sources of uncertainty. The methodology is illustrated with the analysis of a pair of ice cores (GISP2 and GRIP). Our data products, in the form of marginal posterior distributions on an arbitrary temporal grid, are finite Gaussian mixtures. We can also produce sample paths from the joint posterior distribution to study non-linear functionals of interest. More generally, the concept of joint analysis via hierarchical Gaussian process model can be widely extended as the models used can be viewed within the larger context of continuous space-time processes.

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arXiv2014

Zero & $N$-inflated overdispersed binomial models for sum-constrained Poisson count processes

A frequent challenge encountered with compositional ecological data is how to interpret and model data with a high proportion of zeros and $N$'s. Such data frequently occur in ecological applications where counts of species are collected until a pre-specified total imposed (typically) by sampling cost is reached. In the bivariate count (two-species) setting we focus on in this article, zero-inflation of one species will result in $N$-inflation of the other. This can lead to species absence being attributed to an unsuitable habitat as opposed to missingness by chance. Similarly, an excess of $N$'s will lead to misleading inferences about habitat preference and abundance estimates. Our contribution is to identify that two independent zero-inflated Poisson processes subject to a sum constraint provide a novel biologically-motivated generating mechanism for the occurrence of binomial count data exhibiting zero and $N$-inflation. We identify an extension to the model to capture additional overdispersion within the data resulting in a novel zero and $N$-inflated beta-binomial model. We consider two motivating datasets, one involving a pesticide treatment for an invasive species, and a second involving the abundance of two plant species. We demonstrate that incorporation of covariates in each case enable learning about sources of zero and $N$-inflation as well as abundance. We show that the models result in improved understanding of underlying biological processes as well as improved predictive performance.

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arXiv2012

On Bayesian Modelling of the Uncertainties in Palaeoclimate Reconstruction

We outline a model and algorithm to perform inference on the palaeoclimate and palaeoclimate volatility from pollen proxy data. We use a novel multivariate non-linear non-Gaussian state space model consisting of an observation equation linking climate to proxy data and an evolution equation driving climate change over time. The link from climate to proxy data is defined by a pre-calibrated forward model, as developed in Salter-Townshend and Haslett (2012) and Sweeney (2012). Climatic change is represented by a temporally-uncertain Normal-Inverse Gaussian Levy process, being able to capture large jumps in multivariate climate whilst remaining temporally consistent. The pre-calibrated nature of the forward model allows us to cut feedback between the observation and evolution equations and thus integrate out the state variable entirely whilst making minimal simplifying assumptions. A key part of this approach is the creation of mixtures of marginal data posteriors representing the information obtained about climate from each individual time point. Our approach allows for an extremely efficient MCMC algorithm, which we demonstrate with a pollen core from Sluggan Bog, County Antrim, Northern Ireland.

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