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R. J. Barker

Publications and source records attributed to R. J. Barker.

14 recordsLinked to original sources
USGS2009

Bayes factors and multimodel inference

Multimodel inference has two main themes: model selection, and model averaging. Model averaging is a means of making inference conditional on a model set, rather than on a selected model, allowing formal recognition of the uncertainty associated with model choice. The Bayesian paradigm provides a natural framework for model averaging, and provides a context for evaluation of the commonly used AIC weights. We review Bayesian multimodel inference, noting the importance of Bayes factors. Noting the sensitivity of Bayes factors to the choice of priors on parameters, we define and propose nonpreferential priors as offering a reasonable standard for objective multimodel inference.

Book chapter↗
USGS2008

Efficient estimation of abundance for patchily distributed populations via two-phase, adaptive sampling.

Many organisms are patchily distributed, with some patches occupied at high density, others at lower densities, and others not occupied. Estimation of overall abundance can be difficult and is inefficient via intensive approaches such as capture-mark-recapture (CMR) or distance sampling. We propose a two-phase sampling scheme and model in a Bayesian framework to estimate abundance for patchily distributed populations. In the first phase, occupancy is estimated by binomial detection samples taken on all selected sites, where selection may be of all sites available, or a random sample of sites. Detection can be by visual surveys, detection of sign, physical captures, or other approach. At the second phase, if a detection threshold is achieved, CMR or other intensive sampling is conducted via standard procedures (grids or webs) to estimate abundance. Detection and CMR data are then used in a joint likelihood to model probability of detection in the occupancy sample via an abundance-detection model. CMR modeling is used to estimate abundance for the abundance-detection relationship, which in turn is used to predict abundance at the remaining sites, where only detection data are collected. We present a full Bayesian modeling treatment of this problem, in which posterior inference on abundance and other parameters (detection, capture probability) is obtained under a variety of assumptions about spatial and individual sources of heterogeneity. We apply the approach to abundance estimation for two species of voles (Microtus spp.) in Montana, USA. We also use a simulation study to evaluate the frequentist properties of our procedure given known patterns in abundance and detection among sites as well as design criteria. For most population characteristics and designs considered, bias and mean-square error (MSE) were low, and coverage of true parameter values by Bayesian credibility intervals was near nominal. Our two-phase, adaptive approach allows efficient estimation of abundance of rare and patchily distributed species and is particularly appropriate when sampling in all patches is impossible, but a global estimate of abundance is required.

Ecology↗
USGS2008

Efficient implementation of the Metropolis-Hastings algorithm, with application to the Cormack?Jolly?Seber model

Judicious choice of candidate generating distributions improves efficiency of the Metropolis-Hastings algorithm. In Bayesian applications, it is sometimes possible to identify an approximation to the target posterior distribution; this approximate posterior distribution is a good choice for candidate generation. These observations are applied to analysis of the Cormack?Jolly?Seber model and its extensions.

Environmental and Ecological Statistics↗
USGS2007

Efficient implementation of the Metropolis-Hastings algorithm, with application to the Cormack-Jolly-Seber model

Judicious choice of candidate generating distributions improves efficiency of the Metropolis-Hastings algorithm. In Bayesian applications, it is sometimes possible to identify an approximation to the target posterior distribution; this approximate posterior distribution is a good choice for candidate generation. These observations are applied to analysis of the Cormack-Jolly-Seber model and its extensions. ?? Springer Science+Business Media, LLC 2007.

Conference Paper↗
USGS2006

Model weights and the foundations of multimodel inference

Statistical thinking in wildlife biology and ecology has been profoundly influenced by the introduction of AIC (Akaike?s information criterion) as a tool for model selection and as a basis for model averaging. In this paper, we advocate the Bayesian paradigm as a broader framework for multimodel inference, one in which model averaging and model selection are naturally linked, and in which the performance of AIC-based tools is naturally evaluated. Prior model weights implicitly associated with the use of AIC are seen to highly favor complex models: in some cases, all but the most highly parameterized models in the model set are virtually ignored a priori. We suggest the usefulness of the weighted BIC (Bayesian information criterion) as a computationally simple alternative to AIC, based on explicit selection of prior model probabilities rather than acceptance of default priors associated with AIC. We note, however, that both procedures are only approximate to the use of exact Bayes factors. We discuss and illustrate technical difficulties associated with Bayes factors, and suggest approaches to avoiding these difficulties in the context of model selection for a logistic regression. Our example highlights the predisposition of AIC weighting to favor complex models and suggests a need for caution in using the BIC for computing approximate posterior model weights.

Ecology↗
USGS2006

Multistate survival models and their extensions in Program MARK

Program MARK provides .100 models for the estimation of population parameters from mark?encounter data. The multistate model of Brownie et al. (1993) and Hestbeck et al. (1991) allows animals to move between states with a probability of transition. The simplest multistate model is an extension of the Cormack?Jolly?Seber (CJS) live recapture model. arameters estimated are state-specific survival rates and encounter probabilities and transition probabilities between states. The multistate model provides a valuable framework to evaluate important ecological questions. For example, estimation of state-specific survival and transition probabilities between the biological states of breeders and nonbreeders allows estimation of the cost of reproduction. Transitions between physical states, such as spatial areas, provide estimates needed for meta-population models. The basic multistate model uses only live recaptures, but 3 extensions are included in MARK. A multistate model with live and dead encounters is available, although the dead encounters are not state specific. Robust-design multistate models are also included in MARK, with both open and closed robust designs. These models assume that animals move between states only between primary sessions of the robust design. For the closed robust design, we can specify 12 different data types for the modeling of encounter probabilities during the primary session, including 6 versions of the closed model likelihood incorporating population size (N) directly in the likelihood, and 6 versions of the Huggins model in which N is estimated as a derived parameter outside the likelihood. One assumption that is generally necessary to estimate state-specific survival rates in the multistate model is that transitions take place immediately before encounter occasions. Otherwise, survival rates over the interval between encounter occasions are a mix of survival rates over multiple states. Advantages of using MARK to estimate the parameters of the various multistate models include flexibility of model specification to include group, time, and individual covariates, estimation of variance components, model averaging of parameter estimates, and Bayesian parameter estimation using Markov chain Monte Carlo procedures on the logit scale.

Journal of Wildlife Management↗
USGS2005

Quantifying production of salmon fry in an unscreened irrigation system: A case study on the Rangitata River, New Zealand

Diversion of out-migrant juvenile salmon into unscreened irrigation and hydroelectric canals is thought to have contributed significantly to declining populations of anadromous salmonids in the Pacific Northwest but is seldom studied in detail. Here we describe a program to study the fate of Chinook salmon Oncorhynchus tshawytscha fry diverted into the unscreened Rangitata Diversion Race (RDR) on the Rangitata River, New Zealand, by trapping fish in a random sample of on-farm canals in irrigation schemes (systems) served by the RDR. The catch rate at a site 9 km below the intake was strongly related to Rangitata River flow, but catches further downstream were unrelated to flow. Most fish entering the RDR were fry or early postfry (<70 mm fork length (FL)), but up to 92% of the fish trapped in on-farm canals were fingerlings (>70 mm FL), suggesting that many such fish became resident in the RDR for up to 3 months. Consequently, our estimate of the total number of fish leaving the RDR via on-farm canals (204,200 fish; 95% confidence limits = 127,100 and 326,700) is a conservative measure of the number lost from the Rangitata River because it does not allow for mortality within the RDR. We did not quantify the proportion of Rangitata River out-migrants that entered the RDR, but our results suggest that this figure was at least 5% and that it may have been as high as 25%, depending on mortality rates within the Rangitata River main stem and the RDR itself.

Rangitata River↗
USGS2004

Hierarchial mark-recapture models: a framework for inference about demographic processes

The development of sophisticated mark-recapture models over the last four decades has provided fundamental tools for the study of wildlife populations, allowing reliable inference about population sizes and demographic rates based on clearly formulated models for the sampling processes. Mark-recapture models are now routinely described by large numbers of parameters. These large models provide the next challenge to wildlife modelers: the extraction of signal from noise in large collections of parameters. Pattern among parameters can be described by strong, deterministic relations (as in ultrastructural models) but is more flexibly and credibly modeled using weaker, stochastic relations. Trend in survival rates is not likely to be manifest by a sequence of values falling precisely on a given parametric curve; rather, if we could somehow know the true values, we might anticipate a regression relation between parameters and explanatory variables, in which true value equals signal plus noise. Hierarchical models provide a useful framework for inference about collections of related parameters. Instead of regarding parameters as fixed but unknown quantities, we regard them as realizations of stochastic processes governed by hyperparameters. Inference about demographic processes is based on investigation of these hyperparameters. We advocate the Bayesian paradigm as a natural, mathematically and scientifically sound basis for inference about hierarchical models. We describe analysis of capture-recapture data from an open population based on hierarchical extensions of the Cormack-Jolly-Seber model. In addition to recaptures of marked animals, we model first captures of animals and losses on capture, and are thus able to estimate survival probabilities w (i.e., the complement of death or permanent emigration) and per capita growth rates f (i.e., the sum of recruitment and immigration rates). Covariation in these rates, a feature of demographic interest, is explicitly described in the model.

Animal Biodiversity and Conservation↗
USGS2004

Encounter history modeling of joint mark-recapture, tag-resighting and tag-recovery data under temporary emigration

We describe a joint analysis of mark-recapture, tag-resight and tag-recovery data that directly models the encounter history of an animal. The probability of the encounter history for each animal is partitioned into survival, recapture, resighting, and recovery components, and a component for the probability that the animal is never encountered again. Temporary migration enters into the likelihood through the recapture component, and movement of marked animals in and out of the area where they are subject to capture is modeled using a Markov chain. Random temporary emigration and permanent emigration are special cases. An important feature of directly modeling the encounter histories is that covariates that are specific to individuals can be included in the analysis. The model is applied to a brown trout tagging data set and provides strong evidence of Markovian temporary emigration. The new model is needed to provide correct estimates of trout survival probabilities which are shown to depend on the length of the fish at first capture.

Statistica Sinica↗
USGS1997

Sources of variation in waterfowl survival rates

Because of the need to manage hunted populations of waterfowl (Anatidae), biologists have studied many demographic traits of waterfowl by analyzing band recoveries. These analyses have produced the most extensive and best estimates of survival available for any group of birds. Using these data, we examined several factors that might explain variation among annual survival rates to explore large-scale patterns that might be useful in understanding waterfowl population dynamics. We found that geography, body mass, and tribe (i.e. phylogeny) were important in explaining variation in average waterfowl survival rates.

The Auk↗
USGS1995

Statistical aspects of point count sampling

The dominant feature of point counts is that they do not census birds, but instead provide incomplete counts of individuals present within a survey plot. Considering a simple model for point count sampling, we demon-strate that use of these incomplete counts can bias estimators and testing procedures, leading to inappropriate conclusions. A large portion of the variability in point counts is caused by the incomplete counting, and this within-count variation can be confounded with ecologically meaningful varia-tion. We recommend caution in the analysis of estimates obtained from point counts. Using; our model, we also consider optimal allocation of sampling effort. The critical step in the optimization process is in determining the goals of the study and methods that will be used to meet these goals. By explicitly defining the constraints on sampling and by estimating the relationship between precision and bias of estimators and time spent counting, we can predict the optimal time at a point for each of several monitoring goals. In general, time spent at a point will differ depending on the goals of the study.

Book chapter↗
USGS1994

Density estimation using the trapping web design: A geometric analysis

Population densities for small mammal and arthropod populations can be estimated using capture frequencies for a web of traps. A conceptually simple geometric analysis that avoid the need to estimate a point on a density function is proposed. This analysis incorporates data from the outermost rings of traps, explaining large capture frequencies in these rings rather than truncating them from the analysis.

Biometrics↗