arXiv subjects

Ruth King

Publications and source records attributed to Ruth King.

21 records · Page 2Linked to original sources

arXiv2013

Maximum likelihood estimation of mark-recapture-recovery models in the presence of continuous covariates

We consider mark-recapture-recovery (MRR) data of animals where the model parameters are a function of individual time-varying continuous covariates. For such covariates, the covariate value is unobserved if the corresponding individual is unobserved, in which case the survival probability cannot be evaluated. For continuous-valued covariates, the corresponding likelihood can only be expressed in the form of an integral that is analytically intractable and, to date, no maximum likelihood approach that uses all the information in the data has been developed. Assuming a first-order Markov process for the covariate values, we accomplish this task by formulating the MRR setting in a state-space framework and considering an approximate likelihood approach which essentially discretizes the range of covariate values, reducing the integral to a summation. The likelihood can then be efficiently calculated and maximized using standard techniques for hidden Markov models. We initially assess the approach using simulated data before applying to real data relating to Soay sheep, specifying the survival probability as a function of body mass. Models that have previously been suggested for the corresponding covariate process are typically of the form of diffusive random walks. We consider an alternative nondiffusive AR(1)-type model which appears to provide a significantly better fit to the Soay sheep data.

stat.ME↗

arXiv2013

Modelling group dynamic animal movement

Group dynamic movement is a fundamental aspect of many species' movements. The need to adequately model individuals' interactions with other group members has been recognised, particularly in order to differentiate the role of social forces in individual movement from environmental factors. However, to date, practical statistical methods which can include group dynamics in animal movement models have been lacking. We consider a flexible modelling framework that distinguishes a group-level model, describing the movement of the group's centre, and an individual-level model, such that each individual makes its movement decisions relative to the group centroid. The basic idea is framed within the flexible class of hidden Markov models, extending previous work on modelling animal movement by means of multi-state random walks. While in simulation experiments parameter estimators exhibit some bias in non-ideal scenarios, we show that generally the estimation of models of this type is both feasible and ecologically informative. We illustrate the approach using real movement data from 11 reindeer (Rangifer tarandus). Results indicate a directional bias towards a group centroid for reindeer in an encamped state. Though the attraction to the group centroid is relatively weak, our model successfully captures group-influenced movement dynamics. Specifically, as compared to a regular mixture of correlated random walks, the group dynamic model more accurately predicts the non-diffusive behaviour of a cohesive mobile group.

q-bio.QM↗

arXiv2008

Importance Tempering

Simulated tempering (ST) is an established Markov chain Monte Carlo (MCMC) method for sampling from a multimodal density $π(θ)$. Typically, ST involves introducing an auxiliary variable $k$ taking values in a finite subset of $[0,1]$ and indexing a set of tempered distributions, say $π_k(θ) \propto π(θ)^k$. In this case, 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), can disappoint. 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 the resulting estimator has a highly desirable property related to the notion of effective sample size. We briefly report on the success of the optimal combination in two modelling scenarios requiring reversible-jump MCMC, where the naïve approach fails.

stat.CO↗