SMR samplers that update latent individual IDs instead of marginalizing them out.
We can only marginalize out individual IDs for Poisson count models. By conditioning on a possibly true data set and updating its elements, or equivalently, updating the individual IDs of each sample, we can do MCMC with any parametric count model. However, when using the Poisson observation model, the marginal approach in the Spatial-Mark-Resight-Marginal repository is more efficient, so you should use that approach. The data format here is the same as SMR Marginal. Currently, I'm adding negative binomial versions of some samplers in the marginal repository as a model for overdispersion. Luckily, it can still be fit when summing counts over occasions. Zero-truncated Poisson or negative binomial hurdle models are also good options, but require the full 3D capture history, so are slower to use.
https://github.com/benaug/Spatial-Mark-Resight-Marginal
Latent IDs of each sample are updated one at a time on each MCMC iteration in the same manner as they are in categorical SMR where each sample can have one or more categorical covariate, like sex or age class.
https://github.com/benaug/Spatial-Mark-Resight-IDCov
I have another approach working where we update all IDs at each trap at simultaneously, but it is slower than the one at a time approach, at least with fewer than 1000 samples spread over 81 traps.
Care is needed for the dispersion parameter, phi, prior. It can be weakly identified, particularly without abundant counts, and when not all marked individual samples are identified to individual (theta.marked[1] < 1). Identifiability is improved with telemetry and/or a marking process in generalized SMR. The model files are set up with moderately informative priors for moderate to strong overdispersion. This worked well in one simulation scenario and did not produce bias in another simulation scenario where I simulated Poisson (phi very large) data. So, it did not appear very influential, but it could be with very sparse data.
So far, this repository contains:
- Known number of marked individuals (Chandler and Royle 2013, Sollmann et al. 2013), Poisson and negative binomial.
https://www.jstor.org/stable/23566419 https://esajournals.onlinelibrary.wiley.com/doi/full/10.1890/12-1256.1
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Generalized SMR (gSMR) with known number of marked individuals. This includes a marking process to account for different spatial distributions of marked and unmarked individuals (Whittington et al. 2018).generalized SMR (gSMR) with known number of marked individuals. This includes a marking process to account for different spatial distributions of marked and unmarked individuals (Whittington et al. 2018). Poisson and negative binomial observation models.
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Mb version of 2. Negative binomial observation model only.
https://besjournals.onlinelibrary.wiley.com/doi/full/10.1111/1365-2664.12954
These models use N-prior data augmentation: https://github.com/benaug/SCR-N-Prior-Data-Augmentation