Equivalence classes of staged trees

被引：17

作者：

Gorgen, Christiane ^{[1
]}

Smith, Jim Q. ^{[1
]}

机构：

[1] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England

来源：

BERNOULLI | 2018年 / 24卷 / 4A期

基金：

英国工程与自然科学研究理事会;

关键词：

algebraic statistics; Chain Event Graphs; probability trees; staged trees; DIFFERENTIAL APPROACH; CHAIN; INFERENCE; SELECTION;

D O I：

10.3150/17-BEJ940

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we give a complete characterization of the statistical equivalence classes of CEGs and of staged trees. We are able to show that all graphical representations of the same model share a common polynomial description. Then, simple transformations on that polynomial enable us to traverse the corresponding class of graphs. We illustrate our results with a real analysis of the implicit dependence relationships within a previously studied dataset.

引用

页码：2676 / 2692

页数：17

共 25 条

[1]

Andersson SA, 1997, ANN STAT, V25, P505

[2]

[Anonymous], 2009, Lectures on algebraic statistics, volume 39 of Oberwolfach Seminars, DOI [DOI 10.1007/978-3-7643-8905-5, 10.1007/978-3-7643-8905-5]

[3]

[Anonymous], 1996, OXFORD STAT SCI SERI

[4] Refining a Bayesian Network using a Chain Event Graph [J].

Barclay, L. M. ;

Hutton, J. L. ;

Smith, J. Q. .

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2013, 54 (09) :1300-1309

[5]

Boutilier C, 1996, UNCERTAINTY IN ARTIFICIAL INTELLIGENCE, P115

[6]

Coudouel A., 2002, A sourcebook of poverty reduction strategies, P27

[7] Causal discovery through MAP selection of stratified chain event graphs [J].

Cowell, Robert G. ;

Smith, James Q. .

ELECTRONIC JOURNAL OF STATISTICS, 2014, 8 :965-997

[8] A differential approach to inference in Bayesian networks [J].

Darwiche, A .

JOURNAL OF THE ACM, 2003, 50 (03) :280-305

[9] SOCIAL AND FAMILY FACTORS IN CHILDHOOD HOSPITAL ADMISSION [J].

FERGUSSON, DM ;

HORWOOD, LJ ;

SHANNON, FT .

JOURNAL OF EPIDEMIOLOGY AND COMMUNITY HEALTH, 1986, 40 (01) :50-58

[10] Bayesian MAP model selection of chain event graphs [J].

Freeman, G. ;

Smith, J. Q. .

JOURNAL OF MULTIVARIATE ANALYSIS, 2011, 102 (07) :1152-1165

← 1 2 3 →