Occupancy with both false negatives and false positives in the detection
process (e.g. acoustic classifiers, citizen-science misidentification), using
the Miller et al. (2011) confirmed-detection design that makes the model
robustly identifiable. Each visit yields a detection state y in {0, 1, 2}:
0 = no detection, 1 = ambiguous detection (a true detection OR a false
positive), 2 = certain / confirmed detection (only possible when the site is
truly occupied). The latent occupancy z marginalises in closed form (two
states), so the fit maximises the exact marginal likelihood directly
(analytic-gradient BFGS, observed-information covariance) with a NUTS path over
the same marginal.
Details
Four site-level logit arms: occupancy psi (the tobs() formula), true
detection p11 (detection), false-positive rate p10, and the probability a
true detection is certain b. The p10 and b predictors default to
intercept-only and are set with the p10 = ~ ... and certainty = ~ ...
arguments to tobs() (certainty is the b arm). The response y is an
n_sites x J integer matrix in {0, 1, 2} (NA visits dropped).
References
Miller, D. A. W., Nichols, J. D., McClintock, B. T., Grant, E. H. C., Bailey, L. L., Weir, L. A. (2011). Improving occupancy estimation when two types of observational error occur. Ecology 92, 1422-1428. Royle, J. A., Link, W. A. (2006). Generalized site occupancy models allowing for false positive and false negative errors. Ecology 87, 835-841.