Connecting the Latent Multinomial

Extending the latent multinomial model with complex error processes and dynamic Markov bases

“…Link et al (2010) implied that Markov chains constructed with this algorithm would connect all elements in F n and hence be irreducible. Schofield and Bonner (2015) showed that this is true for model M tα provided that the right lattice basis is chosen and extended this result to a broader class of models in which errors constitute simple corruptions. However, they also provided examples of more complicated models for which the algorithm does not produce irreducible Markov chains.…”

“…However, the discussion implied that the algorithm could be implemented with any basis of ker(A) and could be applied whenever the observed counts can be written as a linear function of latent counts. Schofield and Bonner (2015) proved that the specific basis chosen for M tα when T = 2 does produce irreducible chains, but they showed that this is not true for all bases. They also provided examples of models with more complex error for which no set of linearly independent elements ker(A) can produce irreducible chains.…”

“…This MCMC algorithm used vectors from a basis for the kernel of the linear map between the true and observed counts to move between the possible configurations of the true data. Schofield and Bonner (2015) showed that a strict basis was sufficient for some models of the errors, including the model presented by Link et al (2010), but a larger set called a Markov basis may be required for more complex models. We address two further challenges with this approach: 1) that models with more complex error mechanisms do not fit easily within the LMM and 2) that the Markov basis can be difficult or impossible to compute for even moderate sized studies.…”

Using visual encounter data to improve capture-recapture abundance estimates

“…In this paper, we presented a motivation for including encounter data in capture-recapture studies based on abundance lower bounds from encounter and capture data. This relates to other approaches for handling imperfect individual identification in capture-recapture studies including misidentification (Link et al 2010, McClintock et al 2014a, Schofield and Bonner 2015) and partial identification (Augustine et al 2018). Given that encounter data are included via a modified likelihood and not a modified state model, this approach can be readily integrated with a variety of capture-recapture models, and may be useful for hard to capture species in data-limited settings.…”

Continuous-time Capture–Recapture in Closed Populations

“…Unfortunately many non‐invasive sampling approaches are likely to have some degree of misidentification. Approaches to account for misidentification include, Wright et al (); Link et al (); Barker et al (); Schofield and Bonner (); Bonner et al (), with Barker et al () focusing on data collected in continuous time.…”