[Forum SIS] Seminario FARCOMENI

[Matteo Ruggiero]

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STATISTICS SEMINARS  -  COLLEGIO CARLO ALBERTO
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Venerdi' 10 Maggio 2013, alle ore 12:00, presso la sala rossa del 
Collegio Carlo Alberto, Moncalieri (TO), si terra' il seguente seminario:


ALESSIO FARCOMENI (Universita' di Roma - La Sapienza)

	
SEMIPARAMETRIC CAPTURE-RECAPTURE WITH HETEROGENEOUS CAPTURE PROBABILITIES


Abstract:
Capture-recapture experiments are commonly used to estimate the 
size of a closed population. Link (2003) has underlined identifiability 
problems when one wants to make inference with heterogeneous 
capture probabilities in a semiparametric framework. If subject-specific 
capture probabilities are random effects with no assumption on the 
mixing distribution, the conditional likelihood is not identifiable. 
Link (2003) invokes the equivalence of conditional and complete 
likelihood (Sanathanan, 1972) to conclude that semiparametric 
inference is not possible in recapture studies. We show (i) that a 
regularity condition of Sanathanan (1972) is not met, and hence such 
equivalence does not hold; (ii) that the complete likelihood is indeed 
identifiable. Surprisingly enough, we also show that the MLE is 
convergent but not consistent. We characterize the limiting value of 
the MLE as a "sharpest estimable lower bound" and prove that the MLE 
can never over estimate the true population size. In practice, the 
complete likelihood parameter space includes all possible mixing 
distributions with support on [0,1]. We use the theory of canonical 
moments and a logistic transform to obtain a finite dimensional and 
unconstrained parameter space. We then underline computational 
and philosophical problems related to maximum likelihood estimation. 
Consequently, we propose a Bayesian approach which is extended to 
the most general model in recapture studies, where heterogeneous 
detection probabilities are allowed also to depend on trapping occasion 
and behavioural reactions to first capture. We derive the Jeffrey's prior 
and illustrate the Bayesian and classical approaches with real 
examples and simulations.

Joint work with Luca Tardella.



Tutti gli interessati sono invitati a partecipare.

Il seminario e' organizzato dalla "de Castro" Statistics Initiative
(http://www.carloalberto.org/stats) in collaborazione con il 
Collegio Carlo Alberto.
Il programma dei seminari puo' essere consultato alla pagina
http://www.carloalberto.org/events/seminars/statistics/


---------
Matteo Ruggiero
University of Torino & Collegio Carlo Alberto
http://web.econ.unito.it/ruggiero

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