Browsing by Subject "Probability distribution"

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    Open Access
    Revisiting the effect of capture heterogeneity on survival estimates in capture-mark-recapture studies: does it matter?
    (Public Library of Science, 2013) Abadi, Fitsum; Botha, Andre; Altwegg, Res
    Recently developed capture-mark-recapture methods allow us to account for capture heterogeneity among individuals in the form of discrete mixtures and continuous individual random effects. In this article, we used simulations and two case studies to evaluate the effectiveness of continuously distributed individual random effects at removing potential bias due to capture heterogeneity, and to evaluate in what situation the added complexity of these models is justified. Simulations and case studies showed that ignoring individual capture heterogeneity generally led to a small negative bias in survival estimates and that individual random effects effectively removed this bias. As expected, accounting for capture heterogeneity also led to slightly less precise survival estimates. Our case studies also showed that accounting for capture heterogeneity increased in importance towards the end of study. Though ignoring capture heterogeneity led to a small bias in survival estimates, such bias may greatly impact management decisions. We advocate reducing potential heterogeneity at the sampling design stage. Where this is insufficient, we recommend modelling individual capture heterogeneity in situations such as when a large proportion of the individuals has a low detection probability (e.g. in the presence of floaters) and situations where the most recent survival estimates are of great interest (e.g. in applied conservation).
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    Open Access
    A variational Bayes approach to the analysis of occupancy models
    (Public Library of Science, 2016) Clark, Allan E; Altwegg, Res; Ormerod, John T
    Detection-nondetection data are often used to investigate species range dynamics using Bayesian occupancy models which rely on the use of Markov chain Monte Carlo (MCMC) methods to sample from the posterior distribution of the parameters of the model. In this article we develop two Variational Bayes (VB) approximations to the posterior distribution of the parameters of a single-season site occupancy model which uses logistic link functions to model the probability of species occurrence at sites and of species detection probabilities. This task is accomplished through the development of iterative algorithms that do not use MCMC methods. Simulations and small practical examples demonstrate the effectiveness of the proposed technique. We specifically show that (under certain circumstances) the variational distributions can provide accurate approximations to the true posterior distributions of the parameters of the model when the number of visits per site ( K ) are as low as three and that the accuracy of the approximations improves as K increases. We also show that the methodology can be used to obtain the posterior distribution of the predictive distribution of the proportion of sites occupied (PAO).