IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v65y2003i1p235-246.html
   My bibliography  Save this article

Efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice

Author

Listed:
  • A. N. Pettitt
  • N. Friel
  • R. Reeves

Abstract

Summary. Motivated by the autologistic model for the analysis of spatial binary data on the two‐dimensional lattice, we develop efficient computational methods for calculating the normalizing constant for models for discrete data defined on the cylinder and lattice. Because the normalizing constant is generally unknown analytically, statisticians have developed various ad hoc methods to overcome this difficulty. Our aim is to provide computationally and statistically efficient methods for calculating the normalizing constant so that efficient likelihood‐based statistical methods are then available for inference. We extend the so‐called transition method to find a feasible computational method of obtaining the normalizing constant for the cylinder boundary condition. To extend the result to the free‐boundary condition on the lattice we use an efficient path sampling Markov chain Monte Carlo scheme. The methods are generally applicable to association patterns other than spatial, such as clustered binary data, and to variables taking three or more values described by, for example, Potts models.

Suggested Citation

  • A. N. Pettitt & N. Friel & R. Reeves, 2003. "Efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 235-246, February.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:1:p:235-246
    DOI: 10.1111/1467-9868.00383
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9868.00383
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9868.00383?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Evans, Michael & Swartz, Timothy, 2000. "Approximating Integrals via Monte Carlo and Deterministic Methods," OUP Catalogue, Oxford University Press, number 9780198502784.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jin, Ick Hoon & Liang, Faming, 2014. "Use of SAMC for Bayesian analysis of statistical models with intractable normalizing constants," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 402-416.
    2. Magnussen, Steen & Reeves, Rob, 2008. "A method for bias-reduction of sample-based MLE of the autologistic model," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 103-111, September.
    3. Cécile Hardouin & Xavier Guyon, 2014. "Recursions on the marginals and exact computation of the normalizing constant for Gibbs processes," Computational Statistics, Springer, vol. 29(6), pages 1637-1650, December.
    4. Dormann, Carsten F., 2007. "Assessing the validity of autologistic regression," Ecological Modelling, Elsevier, vol. 207(2), pages 234-242.
    5. Daniel A Griffith, 2004. "A Spatial Filtering Specification for the Autologistic Model," Environment and Planning A, , vol. 36(10), pages 1791-1811, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:jss:jstsof:33:i11 is not listed on IDEAS
    2. Bo Wang & Jian Qing Shi, 2014. "Generalized Gaussian Process Regression Model for Non-Gaussian Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1123-1133, September.
    3. Episcopos, Athanasios, 2004. "The implied reserves of the Bank Insurance Fund," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1617-1635, July.
    4. Nott, David J. & Fielding, Mark & Leonte, Daniela, 2009. "On a generalization of the Laplace approximation," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1397-1403, June.
    5. Tian, Guo-Liang & Ng, Kai Wang & Li, Kai-Can & Tan, Ming, 2009. "Non-iterative sampling-based Bayesian methods for identifying changepoints in the sequence of cases of Haemolytic uraemic syndrome," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3314-3323, July.
    6. Berridge, S.J. & Schumacher, J.M., 2002. "An Irregular Grid Approach for Pricing High Dimensional American Options," Discussion Paper 2002-99, Tilburg University, Center for Economic Research.
    7. A. Kong & P. McCullagh & X.‐L. Meng & D. Nicolae & Z. Tan, 2003. "A theory of statistical models for Monte Carlo integration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 585-604, August.
    8. Fakhereddine, Rana & Haddad, Rami El & Lécot, Christian & Maalouf, Joseph El, 2017. "Stratified Monte Carlo simulation of Markov chains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 135(C), pages 51-62.
    9. Roberto Patuelli & Daniel A. Griffith & Michael Tiefelsdorf & Peter Nijkamp, 2011. "Spatial Filtering and Eigenvector Stability: Space-Time Models for German Unemployment Data," International Regional Science Review, , vol. 34(2), pages 253-280, April.
    10. Henry Lam & Jose Blanchet & Damian Burch & Martin Z. Bazant, 2011. "Corrections to the Central Limit Theorem for Heavy-tailed Probability Densities," Journal of Theoretical Probability, Springer, vol. 24(4), pages 895-927, December.
    11. Amarjit Budhiraja & Shu Lu & Yang Yu & Quoc Tran-Dinh, 2021. "Minimization of a class of rare event probabilities and buffered probabilities of exceedance," Annals of Operations Research, Springer, vol. 302(1), pages 49-83, July.
    12. Qian, Zhiguang & Shapiro, Alexander, 2006. "Simulation-based approach to estimation of latent variable models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1243-1259, November.
    13. Helton, J.C. & Johnson, J.D. & Oberkampf, W.L., 2006. "Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links," Reliability Engineering and System Safety, Elsevier, vol. 91(3), pages 320-348.
    14. Sugita, Katsuhiro, 2002. "Testing for Cointegration Rank Using Bayes Factors," Economic Research Papers 269467, University of Warwick - Department of Economics.
    15. Hankin, Robin K. S., 2010. "A Generalization of the Dirichlet Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i11).
    16. Khatun, Kaysara & Valdes, Paul J. & Knorr, Wolfgang & Chaturvedi, Rajiv Kumar, 2010. "Assessing the mitigation potential of forestry activities in a changing climate: A case study for Karnataka," Forest Policy and Economics, Elsevier, vol. 12(4), pages 277-286, April.
    17. Berridge, S.J. & Schumacher, J.M., 2004. "Pricing High-Dimensional American Options Using Local Consistency Conditions," Other publications TiSEM 8c8de631-5039-4eec-a965-3, Tilburg University, School of Economics and Management.
    18. Kuonen, Diego, 2003. "Numerical Integration in S-PLUS or R: A Survey," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 8(i13).
    19. Rebecca Lessem & Carl Sanders, 2020. "Immigrant Wage Growth In The United States: The Role Of Occupational Upgrading," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(2), pages 941-972, May.
    20. Helton, Jon C. & Pilch, Martin & Sallaberry, Cédric J., 2014. "Probability of loss of assured safety in systems with multiple time-dependent failure modes: Representations with aleatory and epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 171-200.
    21. L'Ecuyer, Pierre, 2004. "Random number generation," Papers 2004,21, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssb:v:65:y:2003:i:1:p:235-246. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.