Index: Concept Notes - Counting the Unobserved

Concept Notes - Counting the Unobserved

Routing Summary

Synthesis notes (no raw source) filling topics where the primary paper was not legally obtainable or that cut across papers. Four notes.

• Lincoln-Petersen, Chapman, Otis models, dependence bias? → Concept - Closed-Population Capture-Recapture and Otis Models
• Summing out presence, abundance, class for NUTS? → Concept - Marginalising Latent Discrete Counts for HMC
• LCMCR and latent class MSE (concept; Manrique-Vallier 2016 not obtained)? → Concept - Latent Class and Dirichlet Process Models for Multiple Systems Estimation
• Unseen species (E30) and latent class raters (E69) bridges? → Concept - Unseen Species and Latent Class Links

Concept Map

Concept	Note	Type	Depends On	Key Result
Lincoln-Petersen / Chapman	Concept - Closed-Population Capture-Recapture and Otis Models	definition	-	$\hat{N}=n_1{n}_2/m$
Otis models, Chao bound	Concept - Closed-Population Capture-Recapture and Otis Models	definition	-	$M_h$ non-identifiable
Log-space marginalisation	Concept - Marginalising Latent Discrete Counts for HMC	definition	likelihoods	logsumexp over support
Truncation check	Concept - Marginalising Latent Discrete Counts for HMC	theorem	N-mixture	tail $P(\text{Pois}>N_{max})$
LCMCR	Concept - Latent Class and Dirichlet Process Models for Multiple Systems Estimation	definition	$M_{th}$	needs $2J\le K$
Chao1, Good-Turing	Concept - Unseen Species and Latent Class Links	definition	capture-recapture	$S\ge S_{obs}+f_1^2/(2f_2)$

Notes

• Concept - Closed-Population Capture-Recapture and Otis Models — CONTAINS: LP, Chapman, dependence bias, Otis table, Chao bound, Python.
• Concept - Marginalising Latent Discrete Counts for HMC — CONTAINS: marginalisation table, truncation check, recovery of latents, numpy and PyMC sketches.
• Concept - Latent Class and Dirichlet Process Models for Multiple Systems Estimation — CONTAINS: model, DP prior, identification bound, diagnostics, PyMC sketch.
• Concept - Unseen Species and Latent Class Links — CONTAINS: unseen-species estimators, raters vs MSE comparison, counting check.

Sources

• None (concept notes). Literature referenced: Otis et al. 1978; Seber 1982; Chapman 1951; Chao 1984, 1987; Link 2003; Fienberg 1972; Manrique-Vallier 2016; Dawid and Skene 1979; Hui and Walter 1980; Goodman 1974.

See Also

• MacKenzie 2002 - Site Occupancy with Imperfect Detection - Overview, Barker 2018 - Reliability of N-Mixture Models - Overview, Silverman 2020 - Multiple Systems Analysis for Modern Slavery - Overview.