Home > Research > Publications & Outputs > Efficient recursions for general factorisable m...

Research

Links

Text available via DOI:

Keywords

View graph of relations

Efficient recursions for general factorisable models.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

Standard

Efficient recursions for general factorisable models. / Pettitt, Anthony; Reeves, R.
In: Biometrika, Vol. 91, No. 3, 01.09.2004, p. 751-757.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Pettitt, A & Reeves, R 2004, 'Efficient recursions for general factorisable models.', Biometrika, vol. 91, no. 3, pp. 751-757. https://doi.org/10.1093/biomet/91.3.751

APA

Pettitt, A., & Reeves, R. (2004). Efficient recursions for general factorisable models. Biometrika, 91(3), 751-757. https://doi.org/10.1093/biomet/91.3.751

Vancouver

Pettitt A, Reeves R. Efficient recursions for general factorisable models. Biometrika. 2004 Sept 1;91(3):751-757. doi: 10.1093/biomet/91.3.751

Author

Pettitt, Anthony ; Reeves, R. / Efficient recursions for general factorisable models. In: Biometrika. 2004 ; Vol. 91, No. 3. pp. 751-757.

Bibtex

@article{645bea2040fe4e9c89da5cd342a33d96,
title = "Efficient recursions for general factorisable models.",
abstract = "Let n S-valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum computational efficiency as the subsets attain their minimum size. If each subset contains at most r+1 of the n components in the joint distribution, we term this a lag-r model, whose normalising constant can be computed using a forward recursion in O(Sr+1) computations, as opposed to O(Sn) for the direct computation. We show how a lag-r model represents a Markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood. We illustrate the method by showing how the normalising constant of the Ising or autologistic model can be computed.",
keywords = "Autologistic distribution, Gibbs distribution, Ising model, Normalising constant, Partition function, Markov chain Monte Carlo.",
author = "Anthony Pettitt and R. Reeves",
note = "RAE_import_type : Journal article RAE_uoa_type : Statistics and Operational Research",
year = "2004",
month = sep,
day = "1",
doi = "10.1093/biomet/91.3.751",
language = "English",
volume = "91",
pages = "751--757",
journal = "Biometrika",
issn = "1464-3510",
publisher = "Oxford University Press",
number = "3",

}

RIS

TY - JOUR

T1 - Efficient recursions for general factorisable models.

AU - Pettitt, Anthony

AU - Reeves, R.

N1 - RAE_import_type : Journal article RAE_uoa_type : Statistics and Operational Research

PY - 2004/9/1

Y1 - 2004/9/1

N2 - Let n S-valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum computational efficiency as the subsets attain their minimum size. If each subset contains at most r+1 of the n components in the joint distribution, we term this a lag-r model, whose normalising constant can be computed using a forward recursion in O(Sr+1) computations, as opposed to O(Sn) for the direct computation. We show how a lag-r model represents a Markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood. We illustrate the method by showing how the normalising constant of the Ising or autologistic model can be computed.

AB - Let n S-valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum computational efficiency as the subsets attain their minimum size. If each subset contains at most r+1 of the n components in the joint distribution, we term this a lag-r model, whose normalising constant can be computed using a forward recursion in O(Sr+1) computations, as opposed to O(Sn) for the direct computation. We show how a lag-r model represents a Markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood. We illustrate the method by showing how the normalising constant of the Ising or autologistic model can be computed.

KW - Autologistic distribution

KW - Gibbs distribution

KW - Ising model

KW - Normalising constant

KW - Partition function

KW - Markov chain Monte Carlo.

U2 - 10.1093/biomet/91.3.751

DO - 10.1093/biomet/91.3.751

M3 - Journal article

VL - 91

SP - 751

EP - 757

JO - Biometrika

JF - Biometrika

SN - 1464-3510

IS - 3

ER -