Ross McVinish

University of Queensland, Brisbane, Queensland, Australia

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Publications (20)24.71 Total impact

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    R. McVinish, P. K. Pollett, Y. S. Chan
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    ABSTRACT: We study a variant of Hanski's incidence function model that accounts for the evolution over time of landscape characteristics which affect the persistence of local populations. In particular, we allow the probability of local extinction to evolve according to a Markov chain. This covers the widely studied case where patches are classified as being either suitable or unsuitable for occupancy. Threshold conditions for persistence of the population are obtained using an approximating deterministic model that is realized in the limit as the number of patches becomes large.
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    ABSTRACT: In this paper, we study the relationship between certain stochastic and deterministic versions of Hanski's incidence function model and the spatially realistic Levins model. We show that the stochastic version can be well approximated in a certain sense by the deterministic version when the number of habitat patches is large, provided that the presence or absence of individuals in a given patch is influenced by a large number of other patches. Explicit bounds on the deviation between the stochastic and deterministic models are given.
    Journal of Mathematical Biology 01/2014; DOI:10.1007/s00285-015-0865-4 · 2.39 Impact Factor
  • R. McVinish, P.K. Pollett
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    ABSTRACT: Hanski’s incidence function model is one of the most widely used metapopulation models in ecology. It models the presence/absence of a species at spatially distinct habitat patches as a discrete-time Markov chain whose transition probabilities are determined by the physical landscape. In this analysis, the limiting behaviour of the model is studied as the number of patches increases and the size of the patches decreases. Two different limiting cases are identified depending on whether or not the metapopulation is initially near extinction. Basic properties of the limiting models are derived.
    Journal of Applied Probability 01/2014; 51(2). DOI:10.1239/jap/1402578626 · 0.69 Impact Factor
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    ABSTRACT: We develop a stochastic metapopulation model that accounts for spatial structure as well as within patch dynamics. Using a deterministic approximation derived from a functional law of large numbers, we develop conditions for extinction and persistence of the metapopulation in terms of the birth, death and migration parameters. Interestingly, we observe the Allee effect in a metapopulation comprising two patches of greatly different sizes, despite there being decreasing patch specific per-capita birth rates. We show that the Allee effect is due to way the migration rates depend on the population density of the patches.
    Mathematical biosciences 11/2013; DOI:10.1016/j.mbs.2013.11.001 · 1.30 Impact Factor
  • R. McVinish, P.K. Pollett
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    ABSTRACT: We construct a stochastic patch occupancy metapopulation model that incorporates variation in habitat quality and an Allee-like effect. Using some basic results from stochastic ordering, we investigate the effect of habitat degradation on the persistence of the metapopulation. In particular, we show that for a metapopulation with Allee-like effect habitat degradation can cause a dramatic decrease in the level of persistence while in the absence of an Allee-like effect this decrease is more gradual.
    Ecological Modelling 01/2013; 249:84–89. DOI:10.1016/j.ecolmodel.2012.07.001 · 2.07 Impact Factor
  • R McVinish, P K Pollett
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    ABSTRACT: We consider a Markov chain model similar to the stochastic logistic model except that it allows for variation amongst individuals in the population. We prove that as the population size grows, the process can be approximated by a deterministic process. The equilibrium points of the limiting process and their stability are determined. Applications to modelling epidemics and metapopulations are discussed.
    Mathematical biosciences 10/2012; 241(1). DOI:10.1016/j.mbs.2012.10.001 · 1.30 Impact Factor
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    R McVinish, P K Pollett
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    ABSTRACT: Metapopulation models have been used to better understand the conditions necessary for the persistence of the metapopulation. In this paper, we study a stochastic patch occupancy model that incorporates variation in quality and connectivity of the habitat patches. Two important assumptions are imposed in our analysis. Firstly, the distance between patches has a special form. This amounts to assuming that migrating individuals follow certain pathways. Secondly, the area of the habitat patches is assumed to scale with the number of patches in the metapopulation. Under these assumptions, a deterministic limit is obtained as the number of patches goes to infinity. Using the deterministic limiting process, a condition for persistence of the metapopulation is derived.
    Journal of Mathematical Biology 07/2012; DOI:10.1007/s00285-012-0568-z · 2.39 Impact Factor
  • Ross S. McVinish, Philip K. Pollett
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    ABSTRACT: A discrete-time SIS model is presented that allows individuals in the population to vary in terms of their susceptibility to infection and their rate of recovery. This model is a generalisation of the metapopulation model presented in McVinish and Pollett (2010). The main result of the paper is a central limit theorem showing that fluctuations in the proportion of infected individuals around the limiting proportion converges to a Gaussian random variable when appropriately rescaled. In contrast to the case where there is no variation amongst individuals, the limiting Gaussian distribution has a nonzero mean.
    Journal of Applied Probability 06/2012; 49(2012). DOI:10.1239/jap/1339878802 · 0.69 Impact Factor
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    ABSTRACT: Since its introduction in the early 90’s, the idea of using importance sampling (IS) with Markov chain Monte Carlo (MCMC) has found many applications. This paper examines problems associated with its application to repeated evaluation of related posterior distributions with a particular focus on Bayesian model validation. We demonstrate that, in certain applications, the curse of dimensionality can be reduced by a simple modification of IS. In addition to providing new theoretical insight into the behaviour of the IS approximation in a wide class of models, our result facilitates the implementation of computationally intensive Bayesian model checks. We illustrate the simplicity, computational savings and potential inferential advantages of the proposed approach through two substantive case studies, notably computation of Bayesian p-values for linear regression models and simulation-based model checking. Supplementary materials including appendices and the R code for Section 3.1.2 are available online.
    Journal of Computational and Graphical Statistics 01/2012; DOI:10.1080/10618600.2012.681239 · 1.18 Impact Factor
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    ABSTRACT: In the Bayesian community, an ongoing imperative is to develop efficient algorithms. An appealing approach is to form a hybrid algorithm by combining ideas from competing existing techniques. This paper addresses issues in designing hybrid methods by considering selected case studies: the delayed rejection algorithm, the pinball sampler, the Metropolis adjusted Langevin algorithm, and the population Monte Carlo algorithm. We observe that even if each component of a hybrid algorithm has individual strengths, they may not contribute equally or even positively when they are combined. Moreover, even if the statistical efficiency is improved, from a practical perspective there are technical issues to be considered such as applicability and computational workload. In order to optimize performance of the algorithm in real time, these issues should be taken into account.
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    R McVinish, P K Pollett
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    ABSTRACT: Stochastic patch occupancy models (SPOMs) are a class of discrete time Markov chains used to model the presence/absence of a population in a collection of habitat patches. This class of model is popular with ecologists due to its ability to incorporate important factors of the habitat patch network such as connectivity and distance between patches as well as heterogeneity in patch characteristics. We present an asymptotic examination of a simple type of SPOM called the mainland-island model. In this model a single patch called the mainland is connected to a large number of smaller patches called islands and each island is only connected to the mainland. We discuss the limiting behaviour of the SPOM as the number of islands increases and the size of the islands decrease relative to the mainland. We demonstrate that a variety of limiting behaviours is possible depending on the scaling of the island size and on the heterogeneity of habitat quality.
    Journal of Mathematical Biology 05/2011; 64(5):775-801. DOI:10.1007/s00285-011-0429-1 · 2.39 Impact Factor
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    ABSTRACT: The population Monte Carlo algorithm is an iterative importance sampling scheme for solving static problems. We examine the population Monte Carlo algorithm in a simplified setting, a single step of the general algorithm, and study a fundamental problem that occurs in applying importance sampling to high-dimensional problem. The precision of the computed estimate from the simplified setting is measured by the asymptotic variance of estimate under conditions on the importance function. We demonstrate the exponential growth of the asymptotic variance with the dimension and show that the optimal covariance matrix for the importance function can be estimated in special cases. KeywordsAsymptotic variance of estimate–Central limit theorem–Importance sampling–Markov chain Monte Carlo–Population Monte Carlo
    Methodology And Computing In Applied Probability 01/2011; 13(2):369-389. DOI:10.1007/s11009-009-9154-2 · 0.78 Impact Factor
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    R. McVinish, P. K. Pollett
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    ABSTRACT: We propose a model for the presence/absence of a population in a collection of habitat patches. This model assumes that colonisation and extinction of the patches occur as distinct phases. Importantly, the local extinction probabilities are allowed to vary between patches. This permits an investigation of the effect of habitat degradation on the persistence of the population. The limiting behaviour of the model is examined as the number of habitat patches increases to ∞. This is done in the case where the number of patches and the initial number of occupied patches increase at the same rate, and for the case where the initial number of occupied patches remains fixed.
    Advances in Applied Probability 12/2010; DOI:10.1239/aap/1293113156 · 0.83 Impact Factor
  • R. McVinish
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    ABSTRACT: A new approximate Bayesian computation (ABC) algorithm is proposed specifically designed for models involving quantile distributions. The proposed algorithm compares favourably with two other ABC algorithms when applied to examples involving quantile distributions. KeywordsApproximate Bayesian computation-Likelihood-free inference-Markov chain Monte Carlo-Quantile distributions-Quantile regression
    Statistics and Computing 11/2010; 22(6):1-9. DOI:10.1007/s11222-010-9209-9 · 1.75 Impact Factor
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    ABSTRACT: Harmful algal blooms (HABs) are a worldwide problem that have been increasing in frequency and extent over the past several decades. HABs severely damage aquatic ecosystems by destroying benthic habitat, reducing invertebrate and fish populations, and affecting larger species such as dugong that rely on seagrasses for food. Few statistical models for predicting HAB occurrences have been developed, and in common with most predictive models in ecology, those that have been developed do not fully account for uncertainties in parameters and model structure. This makes management decisions based on these predictions more risky than might be supposed. We used a probit time series model and Bayesian model averaging (BMA) to predict occurrences of blooms of Lyngbya majuscula, a toxic cyanophyte, in Deception Bay, Queensland, Australia. We found a suite of useful predictors for HAB occurrence, with temperature figuring prominently in models with the majority of posterior support, and a model consisting of the single covariate, average monthly minimum temperature, showed by far the greatest posterior support. A comparison of alternative model averaging strategies was made with one strategy using the full posterior distribution and a simpler approach that utilized the majority of the posterior distribution for predictions but with vastly fewer models. Both BMA approaches showed excellent predictive performance with little difference in their predictive capacity. Applications of BMA are still rare in ecology, particularly in management settings. This study demonstrates the power of BMA as an important management tool that is capable of high predictive performance while fully accounting for both parameter and model uncertainty.
    Ecological Applications 10/2009; 19(7):1805-14. DOI:10.1890/08-1843.1 · 4.13 Impact Factor
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    ABSTRACT: We consider the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a non-parametric alternative. Sufficient conditions for consistency of the Bayes factor are determined and demonstrated with priors using certain mixtures of triangular densities.
    Scandinavian Journal of Statistics 06/2009; 36(2). DOI:10.1111/j.1467-9469.2008.00620.x · 1.06 Impact Factor
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    ABSTRACT: The sensitivity to the specification of the prior in a hidden Markov model describing homogeneous segments of DNA sequences is considered. An intron from the chimpanzee α-fetoprotein gene, which plays an important role in embryonic development in mammals, is analysed. Three main aims are considered: (i) to assess the sensitivity to prior specification in Bayesian hidden Markov models for DNA sequence segmentation; (ii) to examine the impact of replacing the standard Dirichlet prior with a mixture Dirichlet prior; and (iii) to propose and illustrate a more comprehensive approach to sensitivity analysis, using importance sampling. It is obtained that (i) the posterior estimates obtained under a Bayesian hidden Markov model are indeed sensitive to the specification of the prior distributions; (ii) compared with the standard Dirichlet prior, the mixture Dirichlet prior is more flexible, less sensitive to the choice of hyperparameters and less constraining in the analysis, thus improving posterior estimates; and (iii) importance sampling was computationally feasible, fast and effective in allowing a richer sensitivity analysis.
    Computational Statistics & Data Analysis 03/2009; DOI:10.1016/j.csda.2008.07.007 · 1.15 Impact Factor
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    Ross McVinish
    Electronic communications in probability 01/2008; DOI:10.1214/ECP.v13-1355 · 0.63 Impact Factor
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    R Mcvinish, P K Pollett
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    ABSTRACT: In this paper we consider the problem of estimating the parameters of a Markov queuing model from discrete time observations of the queue length. The proposed approach is an application of the martingale estimating function methodology which has been used extensively in mathematical finance. A small simulation study sug-gests that the estimator performs well, even for moderate sample size, and that it is an improvement over the Gaussian diffusion based, approximate maximum likelihood estimator.
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    ABSTRACT: Abstract: This paper takes a Bayesian-decision theoretic approach to transfer function estimation, nominal model estimation, and quantification of the resulting model error. Consistency of the nonparametric estimate of the transfer function is proved together with a rate of convergence. The required quantities can be computed routinely using reversible jump Markov chain Monte Carlo methods. The proposed methodology has connections with set membership identification which has been extensively studied for this problem.

Publication Stats

55 Citations
24.71 Total Impact Points

Institutions

  • 2009–2013
    • University of Queensland
      • School of Mathematics and Physics
      Brisbane, Queensland, Australia
    • Queensland University of Technology
      • School of Mathematical Sciences
      Brisbane, Queensland, Australia