arXiv subjects

Trevor Hefley

Publications and source records attributed to Trevor Hefley.

4 recordsLinked to original sources

arXiv2025

The evolving categories multinomial distribution: introduction with applications to movement ecology and vote transfer

We introduce the evolving categories multinomial (ECM) distribution for multivariate count data taken over time. This distribution models the counts of individuals following iid stochastic dynamics among categories, with the number and identity of the categories also evolving over time. We specify the one-time and two-times marginal distributions of the counts and the first and second order moments. When the total number of individuals is unknown, placing a Poisson prior on it yields a new distribution (ECM-Poisson), whose main properties we also describe. Since likelihoods are intractable or impractical, we propose two estimating functions for parameter estimation: a Gaussian pseudo-likelihood and a pairwise composite likelihood. We show two application scenarios: the inference of movement parameters of animals moving continuously in space-time with irregular survey regions, and the inference of vote transfer in two-rounds elections. We give three illustrations: a simulation study with Ornstein-Uhlenbeck moving individuals, paying special attention to the autocorrelation parameter; the inference of movement and behavior parameters of lesser prairie-chickens; and the estimation of vote transfer in the 2021 Chilean presidential election.

stat.AP↗

arXiv2024

Movement-based models for abundance data

We develop two statistical models for space-time abundance data based on a stochastic underlying continuous individual movement. In contrast to current models for abundance in statistical ecology, our models exploit the explicit connection between movement and counts, including the induced space-time auto-correlation. Our first model, called Snapshot, describes the counts of free moving individuals with a false-negative detection error. Our second model, called Capture, describes the capture and retention of moving individuals, and it follows an axiomatic approach based on three simple principles from which it is deduced that the density of the capture time is the solution of a Volterra integral equation of the second kind. Mild conditions are imposed to the underlying stochastic movement model, which is free to choose. We develop simulation methods for both models. The joint distribution of the space-time counts provides an example of a new multivariate distribution, here named the evolving categories multinomial distribution, for which we establish key properties. Since the general likelihood is intractable, we propose a pseudo-likelihood fitting method assuming multivariate Gaussianity respecting mean and covariance structures, justified by the central limit theorem. We conduct simulation studies to validate the method, and we fit our models to experimental data of a spreading population. We estimate movement parameters and compare our models to a basic ecological diffusion model. Movement parameters can be estimated using abundance data, but one must be aware of the necessary conditions to avoid underestimation of spread parameters.

stat.AP↗

arXiv2020

Model selection for ecological community data using tree shrinkage priors

Researchers and managers model ecological communities to infer the biotic and abiotic variables that shape species' ranges, habitat use, and co-occurrence which, in turn, are used to support management decisions and test ecological theories. Recently, species distribution models were developed for and applied to data from ecological communities. Model development and selection for ecological community data is difficult because a high level of complexity is desired and achieved by including numerous parameters, which can degrade predictive accuracy and be challenging to interpret and communicate. Like other statistical models, multi-species distribution models can be overparameterized. Regularization is a technique that optimizes predictive accuracy by shrinking or eliminating model parameters. For Bayesian models, the prior distribution automatically regularizes parameters. We propose a tree shrinkage prior for Bayesian multi-species distributions models that performs regularization and reduces the number of regression coefficients associated with predictor variables. Using this prior, the number of regression coefficients in multi-species distributions models is reduced by estimation of unique regression coefficients for a smaller number of guilds rather than a larger number of species. We demonstrated our tree shrinkage prior using examples of presence-absence data for six species of aquatic vegetation and relative abundance data for 15 species of fish. Our results show that the tree shrinkage prior can increase the predictive accuracy of multi-species distribution models and enable researchers to infer the number and species composition of guilds from ecological community data.

stat.AP↗

arXiv2013

Nondetection sampling bias in marked presence-only data

1. Species distribution models (SDM) are tools used to determine environmental features that influence the geographic distribution of species' abundance and have been used to analyze presence-only records. Analysis of presence-only records may require correction for nondetection sampling bias to yield reliable conclusions. In addition, individuals of some species of animals may be highly aggregated and standard SDMs ignore environmental features that may influence aggregation behavior. 2. We contend that nondetection sampling bias can be treated as missing data. Statistical theory and corrective methods are well developed for missing data, but have been ignored in the literature on SDMs. We developed a marked inhomogeneous Poisson point process model that accounted for nondetection and aggregation behavior in animals and tested our methods on simulated data. 3. Correcting for nondetection sampling bias requires estimates of the probability of detection which must be obtained from auxiliary data, as presence-only data do not contain information about the detection mechanism. Weighted likelihood methods can be used to correct for nondetection if estimates of the probability of detection are available. We used an inhomogeneous Poisson point process model to model group abundance, a zero-truncated generalized linear model to model group size, and combined these two models to describe the distribution of abundance. Our methods performed well on simulated data when nondetection was accounted for and poorly when detection was ignored. 4. We recommend researchers consider the effects of nondetection sampling bias when modeling species distributions using presence-only data. If information about the detection process is available, we recommend researchers explore the effects of nondetection and, when warranted, correct the bias using our methods.

q-bio.PE↗