Index: De Blasi 2015 - Gibbs-Type Priors

De Blasi 2015 - Gibbs-Type Priors

Routing Summary

Fully captures De Blasi, Favaro, Lijoi, Mena and Prunster (2015), Are Gibbs-type priors the most natural generalization of the Dirichlet process?, IEEE TPAMI 37(2) (arXiv 1503.00163; 44 pp.): EPPF, Pitman-Yor, Gibbs-type classification, priors on the number of clusters, unseen-species prediction and consistency. Seven notes.

• Need the paper on one page or the Source Map? → De Blasi 2015 - Gibbs-Type Priors - Overview
• Need EPPF definitions, DP/PY EPPF, predictive rules, PyMC sketch? → De Blasi 2015 - EPPF and Predictive Structure
• Need Proposition 1, Gibbs-type definition, sigma-diversity? → De Blasi 2015 - Gibbs-Type Priors Definition and Classification
• Need PY/NGG/Gnedin/finite-species weights? → De Blasi 2015 - Subclasses Pitman-Yor NGG and Finite-Species Priors
• Need the prior/posterior on number of clusters, Table 1? → De Blasi 2015 - Mixture Models and the Prior on the Number of Clusters
• Need unseen-species estimators, Good-Toulmin, Naegleria data? → De Blasi 2015 - Species Sampling and Unseen Species Prediction
• Need consistency results and dependent processes? → De Blasi 2015 - Consistency, Dependent Processes and Conclusions

Concept Map

Concept	Note	Type	Depends On	Key Result
Species sampling model	De Blasi 2015 - EPPF and Predictive Structure	definition	de Finetti	discrete $\tilde{p}$ with iid atoms
EPPF	De Blasi 2015 - EPPF and Predictive Structure	definition	species sampling	partition law; addition rule
DP and PY EPPF	De Blasi 2015 - EPPF and Predictive Structure	theorem	EPPF	${\theta }^k\prod (n_i-1)!/(\theta {)}_n$; PY product form
Proposition 1	De Blasi 2015 - Gibbs-Type Priors Definition and Classification	theorem	EPPF	DP iff new-prob depends on $n$ only
Gibbs-type prior	De Blasi 2015 - Gibbs-Type Priors Definition and Classification	definition	Prop. 1	$V_{n,k}\prod (1-\sigma {)}_{n_i-1}$
sigma-diversity	De Blasi 2015 - Gibbs-Type Priors Definition and Classification	theorem	Gibbs-type	$K_n/c_n(\sigma )\to S_{\sigma }$
PY, NGG, finite species	De Blasi 2015 - Subclasses Pitman-Yor NGG and Finite-Species Priors	definition	Gibbs-type	weights $V_{n,k}$
Prior on $K_n$	De Blasi 2015 - Mixture Models and the Prior on the Number of Clusters	theorem	EPPF	$V_{n,k}\mathcal{C}(n,k;\sigma )/{\sigma }^k$
New-species law	De Blasi 2015 - Species Sampling and Unseen Species Prediction	theorem	Gibbs-type	depends on $K_n$ only
PY estimators	De Blasi 2015 - Species Sampling and Unseen Species Prediction	theorem	new-species law	${\hat{K}}_m^{(n)}$, ${\hat{U}}_{n+m,0}$
Consistency	De Blasi 2015 - Consistency, Dependent Processes and Conclusions	theorem	Gibbs-type	limit $\alpha P^{\ast }+(1-\alpha )P_0$

Notes

• De Blasi 2015 - Gibbs-Type Priors - Overview — CONTAINS: question, contributions, key results, Source Map, E30 link, marketing relevance.
• De Blasi 2015 - EPPF and Predictive Structure — CONTAINS: species sampling definition, EPPF, DP/PY EPPFs and predictives, brute-force check, PyMC EPPF sketch.
• De Blasi 2015 - Gibbs-Type Priors Definition and Classification — CONTAINS: Prop. 1 with proof, Gibbs-type definition, predictive stages, sigma-diversity, product partition models.
• De Blasi 2015 - Subclasses Pitman-Yor NGG and Finite-Species Priors — CONTAINS: PY weights, finite species, Gnedin/Poisson/geometric, NGG, support.
• De Blasi 2015 - Mixture Models and the Prior on the Number of Clusters — CONTAINS: prior on $K_n$ theorem, five-prior comparison, Table 1, prior-K code.
• De Blasi 2015 - Species Sampling and Unseen Species Prediction — CONTAINS: new-species law, PY estimators, asymptotics, Table 2, Naegleria recomputation.
• De Blasi 2015 - Consistency, Dependent Processes and Conclusions — CONTAINS: general convergence, negative-sigma conditions, illustrations, dependent processes, conclusions.

Sources

• De Blasi et al 2015 - Are Gibbs-Type Priors the Most Natural Generalization of the Dirichlet Process — De Blasi P, Favaro S, Lijoi A, Mena RH, Prunster I (2015), IEEE TPAMI 37(2):212-229.

See Also

Teh 2010 - Dirichlet Process - Overview, Griffiths 2011 - The Indian Buffet Process - Overview, Nonparametric Models Overview