Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › fagfællebedømt

Standard

Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models. / DAWID, AP; Lauritzen, Steffen L.

I: Annals of Statistics, Bind 21, Nr. 3, 1993, s. 1272-1317.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › fagfællebedømt

Harvard

DAWID, AP & Lauritzen, SL 1993, 'Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models', Annals of Statistics, bind 21, nr. 3, s. 1272-1317. https://doi.org/10.1214/aos/1176349260, https://doi.org/10.1214/aos/1176324328

APA

DAWID, AP., & Lauritzen, S. L. (1993). Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models. Annals of Statistics, 21(3), 1272-1317. https://doi.org/10.1214/aos/1176349260, https://doi.org/10.1214/aos/1176324328

Vancouver

DAWID AP, Lauritzen SL. Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models. Annals of Statistics. 1993;21(3):1272-1317. https://doi.org/10.1214/aos/1176349260, https://doi.org/10.1214/aos/1176324328

Author

DAWID, AP ; Lauritzen, Steffen L. / Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models. I: Annals of Statistics. 1993 ; Bind 21, Nr. 3. s. 1272-1317.

Bibtex

@article{df3a74bdbcd3434faa26508ed1d1de72,
title = "Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models",
abstract = "This paper introduces and investigates the notion of a hyper Markov law, which is a probability distribution over the set of probability measures on a multivariate space that (i) is concentrated on the set of Markov probabilities over some decomposable graph, and (ii) satisfies certain conditional independence restrictions related to that graph. A stronger version of this hyper Markov property is also studied. Our analysis starts by reconsidering the properties of Markov probabilities, using an abstract approach which thereafter proves equally applicable to the hyper Markov case. Next, it is shown constructively that hyper Markov laws exist, that they appear as sampling distributions of maximum likelihood estimators in decomposable graphical models, and also that they form natural conjugate prior distributions for a Bayesian analysis of these models. As examples we construct a range of specific hyper Markov laws, including the hyper multinomial, hyper Dirichlet and the hyper Wishart and inverse Wishart laws. These laws occur naturally in connection with the analysis of decomposable log-linear and covariance selection models.",
author = "AP DAWID and Lauritzen, {Steffen L.}",
note = "Korrektion vedlagt, Annals of Statistics, 23:5, 1995",
year = "1993",
doi = "10.1214/aos/1176349260",
language = "English",
volume = "21",
pages = "1272--1317",
journal = "Annals of Statistics",
issn = "0090-5364",
publisher = "Institute of Mathematical Statistics",
number = "3",

}

RIS

TY - JOUR

T1 - Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models

AU - DAWID, AP

AU - Lauritzen, Steffen L.

N1 - Korrektion vedlagt, Annals of Statistics, 23:5, 1995

PY - 1993

Y1 - 1993

N2 - This paper introduces and investigates the notion of a hyper Markov law, which is a probability distribution over the set of probability measures on a multivariate space that (i) is concentrated on the set of Markov probabilities over some decomposable graph, and (ii) satisfies certain conditional independence restrictions related to that graph. A stronger version of this hyper Markov property is also studied. Our analysis starts by reconsidering the properties of Markov probabilities, using an abstract approach which thereafter proves equally applicable to the hyper Markov case. Next, it is shown constructively that hyper Markov laws exist, that they appear as sampling distributions of maximum likelihood estimators in decomposable graphical models, and also that they form natural conjugate prior distributions for a Bayesian analysis of these models. As examples we construct a range of specific hyper Markov laws, including the hyper multinomial, hyper Dirichlet and the hyper Wishart and inverse Wishart laws. These laws occur naturally in connection with the analysis of decomposable log-linear and covariance selection models.

AB - This paper introduces and investigates the notion of a hyper Markov law, which is a probability distribution over the set of probability measures on a multivariate space that (i) is concentrated on the set of Markov probabilities over some decomposable graph, and (ii) satisfies certain conditional independence restrictions related to that graph. A stronger version of this hyper Markov property is also studied. Our analysis starts by reconsidering the properties of Markov probabilities, using an abstract approach which thereafter proves equally applicable to the hyper Markov case. Next, it is shown constructively that hyper Markov laws exist, that they appear as sampling distributions of maximum likelihood estimators in decomposable graphical models, and also that they form natural conjugate prior distributions for a Bayesian analysis of these models. As examples we construct a range of specific hyper Markov laws, including the hyper multinomial, hyper Dirichlet and the hyper Wishart and inverse Wishart laws. These laws occur naturally in connection with the analysis of decomposable log-linear and covariance selection models.

U2 - 10.1214/aos/1176349260

DO - 10.1214/aos/1176349260

M3 - Journal article

VL - 21

SP - 1272

EP - 1317

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 3

ER -

ID: 127608073