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Autoregressive models for capture–recapture data: A Bayesian approach
, 2003
"... In this paper, we incorporate an autoregressive timeseries framework into models for animal survival using capturerecapture data. Researchers modelling animal survival probabilities as the realization of a random process have typically considered survival to be independent from one time period to ..."
Abstract

Cited by 4 (0 self)
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In this paper, we incorporate an autoregressive timeseries framework into models for animal survival using capturerecapture data. Researchers modelling animal survival probabilities as the realization of a random process have typically considered survival to be independent from one time period to the next. This may not be realistic for some populations. Using a Gibbs sampling approach we can estimate covariate coefficients and autoregressive parameters for survival models. The procedure is illustrated with a waterfowl band recovery dataset on Northern Pintails (Anas acuta). The analysis shows that the second lag autoregressive coefficient is significantly less than 0, suggesting that there is a triennial relationship between survival probabilities and emphasizing that modelling survival rates as independent random variables may be unrealistic in some cases. Software to implement the methodology is available at no charge on the internet.
Importance tempering
, 2007
"... Simulated tempering (ST) is an established Markov Chain Monte Carlo (MCMC) methodology for sampling from a multimodal density π(θ). The technique involves introducing an auxiliary variable k taking values in a finite subset of [0,1] and indexing a set of tempered distributions, say πk(θ) ∝ π(θ) k. ..."
Abstract

Cited by 2 (1 self)
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Simulated tempering (ST) is an established Markov Chain Monte Carlo (MCMC) methodology for sampling from a multimodal density π(θ). The technique involves introducing an auxiliary variable k taking values in a finite subset of [0,1] and indexing a set of tempered distributions, say πk(θ) ∝ π(θ) k. Small values of k encourage better mixing, but samples from π are only obtained when the joint chain for (θ,k) reaches k = 1. However, the entire chain can be used to estimate expectations under π of functions of interest, provided that importance sampling (IS) weights are calculated. Unfortunately this method, which we call importance tempering (IT), has tended not work well in practice. This is partly because the most immediately obvious implementation is naïve and can lead to high variance estimators. We derive a new optimal method for combining multiple IS estimators and prove that this optimal combination has a highly desirable property related to the notion of effective sample size. The methodology is applied in two modelling scenarios requiring reversiblejump MCMC, where the naïve approach to IT fails spectacularly: model averaging in treed models, and model selection for mark– recapture data. 1 Key words: simulated tempering, importance sampling, Markov chain Monte
Embedding Population Dynamics Models in Inference
, 708
"... Abstract. Increasing pressures on the environment are generating an everincreasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical models, so that the effects of management action can be ..."
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Abstract. Increasing pressures on the environment are generating an everincreasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical models, so that the effects of management action can be predicted, and the uncertainty in these predictions quantified. These models must be able to predict the response of populations to anthropogenic change, while handling the major sources of uncertainty. We describe a simple “building block” approach to formulating discretetime models. We show how to estimate the parameters of such models from time series of data, and how to quantify uncertainty in those estimates and in numbers of individuals of different types in populations, using computerintensive Bayesian methods. We also discuss advantages and pitfalls of the approach, and give an example using the British grey seal population. Key words and phrases: Hidden process models, filtering, Kalman filter, matrix population models, Markov chain Monte Carlo, particle