The quantitative study of marked individuals in ecology, evolution ...

EURING 2003 Radolfzell
Computing & software (chairs: Jim Hines & Gary White)
Plenary Address - 01:15 PM - 01:55 PM
The "Mother of All Models"
Richard Barker
With an increasing proliferation of mark-recapture models and studies collecting
mark-recapture data, software and analysis methods are being continually revised.
We consider the construction of the likelihood for a general model that incorporates
all the features of the recently developed models: it is a multistate robust-design
mark-recapture model that includes dead recoveries and resightings of marked animals
and is parameterised in terms of state-specific recruitment, survival and capture
probabilities, state-specific abundances, and state-specific recovery and resighting
probabilities. The construction that we outline is based on a factorisation of the likelihood
function with each factor corresponding to a different component of the data.
Such a construction would allow the likelihood function for a mark-recapture analysis
to be customized according to the components that are actually present in the dataset.
Individual Papers
01:55 PM - 02:20 PM
Computing issues concerning hierarchical models
Ken Burnham
The subject of capture-recapture (CR) data analysis is incomplete without welldeveloped,
user capable software (such as MARK) that can fit models incorporating
random effects as well as fixed effects. The MCMC (i.e., Bayesian) model fitting approach
provides a sound theory for fitting all CR models. Why not just use it? Answer:
lack of software suitable for all potential users, and the relative slowness of MCMC
analysis (there are reasons why speed still matters). Pragmatically I maintain that likelihood
analysis, including profile likelihood intervals, as needed, is eminently adequate
for CR data analysis when models have all fixed effects: the inferential results
are virtually the same as those from MCMC with vague priors; but the analyses are
much faster. This talk considers what we might be able to do to obtain CR random
effects inferences, say incorporated into MARK, that are suitable approximations to
MCMC inferences at a fraction of the computing time.
The technical issue is simple. If all effects are considered fixed, numerical likelihood
inference only requires function evaluations over a K dimensional space. Exact inference
for a set of K random parameters requires integration of an even more complex
function (than the likelihood) over a K dimensional space. Such integration is computationally
more demanding than function maximization. MCMC analysis has complexity
at the same level as the integration approach. The random effects method in
MARK can be reformulated and extended. So doing has value, even though I accede
to the MCMC approach as the gold standard for rigor and generality.
The talk will note several possible approximate analyses approaches for some types
of random effects (along with fixed effects, so technically mixed models). Under any
inference computations we will augment the fixed effects likelihood with a model for
21