Scholarly Work - Mathematical Sciences

Permanent URI for this collectionhttps://scholarworks.montana.edu/handle/1/8719

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The integrated nested Laplace approximation applied to spatial log-Gaussian Cox process models
(Informa UK Limited, 2023-04) Flagg, Kenneth; Hoegh, Andrew
Spatial point process models are theoretically useful for mapping discrete events, such as plant or animal presence, across space; however, the computational complexity of fitting these models is often a barrier to their practical use. The log-Gaussian Cox process (LGCP) is a point process driven by a latent Gaussian field, and recent advances have made it possible to fit Bayesian LGCP models using approximate methods that facilitate rapid computation. These advances include the integrated nested Laplace approximation (INLA) with a stochastic partial differential equations (SPDE) approach to sparsely approximate the Gaussian field and an extension using pseudodata with a Poisson response. To help link the theoretical results to statistical practice, we provide an overview of INLA for point process data and then illustrate their implementation using freely available data. The analyzed datasets include both a completely observed spatial field and an incomplete data situation. Our well-commented R code is shared in the online supplement. Our intent is to make these methods accessible to the practitioner of spatial statistics without requiring deep knowledge of point process theory.
Statistical assessment on determining local presence of rare bat species
(Wiley, 2022-06) Irvine, Kathryn M.; Banner, Katharine M.; Stratton, Christian; Ford, William M.; Reichert, Brian E.
Surveying cryptic, sparsely distributed taxa using autonomous recording units,although cost-effective, provides imperfect knowledge about species presence.Summertime bat acoustic surveys in North America exemplify the challenges with characterizing sources of uncertainty: observation error, inability to census populations, and natural stochastic variation. Statistical uncertainty, if not considered thoroughly, hampers determining rare species presence accurately and/or estimating range wide status and trends with suitable precision. Bat acoustic data are processed using an automated workflow in which proprietary or open-source algorithms assign a species label to each recorded high-frequency echolocation sequence. A false-negative occurs, if a species is actually present but not recorded and/or all recordings from the species are of such poor quality that a correct species identity cannot be assigned to any observation. False positives for a focal species are a direct result of the presence and incorrect identification of a recording from another species. We compare four analytical approaches in terms of parameter estimation and their resulting(in)correct decisions regarding species presence or absence using realistic data-generating scenarios for bat acoustic data within a simulation study. The cur-rent standard for deciding species presence or absence uses a multinomial likelihood-ratio test p value (maximum likelihood estimate [MLE]-metric) that accounts for known species misidentifications, but not imperfect detection and only returns a binary outcome (evidence of presence or not). We found that the MLE-metric had estimated median correct decisions less than 60% for presence and greater than 85% for absence. Alternatively, a multispecies count detection model was equivalent to or better than the MLE-metric for correct claims of rare species presence or absence using the posterior probability a species was present at a site and, importantly, provided unbiased estimates of relative activity and probability of occurrence, creating opportunities for reducing posterior uncertainty through the inclusion of meaningful covariates. Single-species occupancy models with and without false-positive detections removed were insufficient for determining local presence because of substantially biased occurrence and detection probabilities. We propose solutions to potential barriers for integrating local, short-term and range wide, long-term acoustic surveys within a cohesive statistical framework that facilitates determining local species presence with uncertainty concurrent with estimating species–environment relationships.