IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v16y2014i2d10.1007_s11009-013-9367-2.html
   My bibliography  Save this article

On the Use of Particle Markov Chain Monte Carlo in Parameter Estimation of Space-Time Interacting Discs

Author

Listed:
  • Markéta Zikmundová

    (Charles University in Prague)

  • Kateřina Staňková Helisová

    (Czech Technical University in Prague)

  • Viktor Beneš

    (Charles University in Prague)

Abstract

A space-time random set is defined and methods of its parameters estimation are investigated. The evolution in discrete time is described by a state-space model. The observed output is a planar union of interacting discs given by a probability density with respect to a reference Poisson process of discs. The state vector is to be estimated together with auxiliary parameters of transitions caused by a random walk. Three methods of parameters estimation are involved, first of which is the maximum likelihood estimation (MLE) for individual outputs at fixed times. In the space-time model the state vector can be estimated by the particle filter (PF), where MLE serves to the estimation of auxiliary parameters. In the present paper the aim is to compare MLE and PF with particle Markov chain Monte Carlo (PMCMC). From the group of PMCMC methods we use specially the particle marginal Metropolis-Hastings (PMMH) algorithm which updates simultaneously the state vector and the auxiliary parameters. A simulation study is presented in which all estimators are compared by means of the integrated mean square error. New data are then simulated repeatedly from the model with parameters estimated by PMMH and the fit with the original model is quantified by means of the spherical contact distribution function.

Suggested Citation

  • Markéta Zikmundová & Kateřina Staňková Helisová & Viktor Beneš, 2014. "On the Use of Particle Markov Chain Monte Carlo in Parameter Estimation of Space-Time Interacting Discs," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 451-463, June.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:2:d:10.1007_s11009-013-9367-2
    DOI: 10.1007/s11009-013-9367-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-013-9367-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-013-9367-2?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mrkvicka, T. & Rataj, J., 2008. "On the estimation of intrinsic volume densities of stationary random closed sets," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 213-231, February.
    2. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    3. Markéta Zikmundová & Kateřina Staňková Helisová & Viktor Beneš, 2012. "Spatio-Temporal Model for a Random Set Given by a Union of Interacting Discs," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 883-894, September.
    4. Jesper Møller & Mohammad Ghorbani, 2012. "Aspects of second-order analysis of structured inhomogeneous spatio-temporal point processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(4), pages 472-491, November.
    5. Jesper Møller & Kateřina Helisová, 2010. "Likelihood Inference for Unions of Interacting Discs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 365-381, September.
    Full references (including those not matched with items on IDEAS)

    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. Kateřina Staňková Helisová & Jakub Staněk, 2014. "Dimension Reduction in Extended Quermass-Interaction Process," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 355-368, June.
    2. S. Bogan Aruoba & Pablo Cuba-Borda & Kenji Higa-Flores & Frank Schorfheide & Sergio Villalvazo, 2021. "Piecewise-Linear Approximations and Filtering for DSGE Models with Occasionally Binding Constraints," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 41, pages 96-120, July.
    3. Joshua Chan & Arnaud Doucet & Roberto León-González & Rodney W. Strachan, 2018. "Multivariate Stochastic Volatility with Co-Heteroscedasticity," Working Paper series 18-38, Rimini Centre for Economic Analysis.
    4. McKinley, Trevelyan J. & Ross, Joshua V. & Deardon, Rob & Cook, Alex R., 2014. "Simulation-based Bayesian inference for epidemic models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 434-447.
    5. Giesecke, K. & Schwenkler, G., 2019. "Simulated likelihood estimators for discretely observed jump–diffusions," Journal of Econometrics, Elsevier, vol. 213(2), pages 297-320.
    6. Aruoba, S. Borağan & Bocola, Luigi & Schorfheide, Frank, 2017. "Assessing DSGE model nonlinearities," Journal of Economic Dynamics and Control, Elsevier, vol. 83(C), pages 34-54.
    7. Piotr Szczepocki, 2020. "Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 173-187, June.
    8. Delis, Manthos D. & Tsionas, Mike G., 2018. "Measuring management practices," International Journal of Production Economics, Elsevier, vol. 199(C), pages 65-77.
    9. Johan Dahlin & Fredrik Lindsten & Thomas B. Schon, 2015. "Quasi-Newton particle Metropolis-Hastings," Papers 1502.03656, arXiv.org, revised Sep 2015.
    10. Matias Quiroz & Robert Kohn & Mattias Villani & Minh-Ngoc Tran, 2019. "Speeding Up MCMC by Efficient Data Subsampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 831-843, April.
    11. Tsionas, Mike G. & Michaelides, Panayotis G., 2017. "Bayesian analysis of chaos: The joint return-volatility dynamical system," MPRA Paper 80632, University Library of Munich, Germany.
    12. Nonejad, Nima, 2015. "Flexible model comparison of unobserved components models using particle Gibbs with ancestor sampling," Economics Letters, Elsevier, vol. 133(C), pages 35-39.
    13. James M. Nason & Gregor W. Smith, 2021. "Measuring the slowly evolving trend in US inflation with professional forecasts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(1), pages 1-17, January.
    14. Joshua Chan, 2023. "BVARs and Stochastic Volatility," Papers 2310.14438, arXiv.org.
    15. Jin, Guang & Matthews, David E. & Zhou, Zhongbao, 2013. "A Bayesian framework for on-line degradation assessment and residual life prediction of secondary batteries inspacecraft," Reliability Engineering and System Safety, Elsevier, vol. 113(C), pages 7-20.
    16. Delis, Manthos D. & Iosifidi, Maria & Kazakis, Pantelis & Ongena, Steven & Tsionas, Mike G., 2022. "Management practices and M&A success," Journal of Banking & Finance, Elsevier, vol. 134(C).
    17. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2018. "Measuring Uncertainty and Its Impact on the Economy," The Review of Economics and Statistics, MIT Press, vol. 100(5), pages 799-815, December.
    18. Th I Götz & G Lahmer & V Strnad & Ch Bert & B Hensel & A M Tomé & E W Lang, 2017. "A tool to automatically analyze electromagnetic tracking data from high dose rate brachytherapy of breast cancer patients," PLOS ONE, Public Library of Science, vol. 12(9), pages 1-31, September.
    19. Naoki Awaya & Yasuhiro Omori, 2021. "Particle Rolling MCMC with Double-Block Sampling ," CIRJE F-Series CIRJE-F-1175, CIRJE, Faculty of Economics, University of Tokyo.
    20. Tsionas, Mike G. & Michaelides, Panayotis G., 2017. "Neglected chaos in international stock markets: Bayesian analysis of the joint return–volatility dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 95-107.

    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:spr:metcap:v:16:y:2014:i:2:d:10.1007_s11009-013-9367-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.