IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v29y2014i5p1025-1043.html
   My bibliography  Save this article

Bayesian approach for mixture models with grouped data

Author

Listed:
  • Shiow-Lan Gau
  • Jean Dieu Tapsoba
  • Shen-Ming Lee

Abstract

Finite mixture modeling approach is widely used for the analysis of bimodal or multimodal data that are individually observed in many situations. However, in some applications, the analysis becomes substantially challenging as the available data are grouped into categories. In this work, we assume that the observed data are grouped into distinct non-overlapping intervals and follow a finite mixture of normal distributions. For the inference of the model parameters, we propose a parametric approach that accounts for the categorical features of the data. The main idea of our method is to impute the missing information of the original data through the Bayesian framework using the Gibbs sampling techniques. The proposed method was compared with the maximum likelihood approach, which uses the Expectation-Maximization algorithm for the estimation of the model parameters. It was also illustrated with an application to the Old Faithful geyser data. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Shiow-Lan Gau & Jean Dieu Tapsoba & Shen-Ming Lee, 2014. "Bayesian approach for mixture models with grouped data," Computational Statistics, Springer, vol. 29(5), pages 1025-1043, October.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:5:p:1025-1043
    DOI: 10.1007/s00180-013-0478-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-013-0478-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00180-013-0478-6?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. Albert, James H & Chib, Siddhartha, 1993. "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 1-15, January.
    2. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    3. Boldea, Otilia & Magnus, Jan R., 2009. "Maximum Likelihood Estimation of the Multivariate Normal Mixture Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1539-1549.
    4. Chen, Cathy W.S. & Chan, Jennifer S.K. & So, Mike K.P. & Lee, Kevin K.M., 2011. "Classification in segmented regression problems," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2276-2287, July.
    5. Pingping Qu & Yinsheng Qu, 2000. "A Bayesian Approach to Finite Mixture Models in Bioassay via Data Augmentation and Gibbs Sampling and Its Application to Insecticide Resistance," Biometrics, The International Biometric Society, vol. 56(4), pages 1249-1255, December.
    6. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
    7. Melnykov, Volodymyr & Melnykov, Igor, 2012. "Initializing the EM algorithm in Gaussian mixture models with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1381-1395.
    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. Kazuhiko Kakamu, 2022. "Bayesian analysis of mixtures of lognormal distribution with an unknown number of components from grouped data," Papers 2210.05115, arXiv.org, revised Sep 2023.
    2. Shen‐Ming Lee & Truong‐Nhat Le & Phuoc‐Loc Tran & Chin‐Shang Li, 2022. "Investigating the association of a sensitive attribute with a random variable using the Christofides generalised randomised response design and Bayesian methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1471-1502, November.

    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. Jiang, Yu, 2020. "Identification of business cycles and the Great Moderation in the post-war U.S. economy," Economics Letters, Elsevier, vol. 190(C).
    2. Chuku Chuku & Paul Middleditch, 2020. "Characterizing Monetary and Fiscal Policy Rules and Interactions when Commodity Prices Matter," Manchester School, University of Manchester, vol. 88(3), pages 373-404, June.
    3. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    4. Nima Nonejad, 2013. "Time-Consistency Problem and the Behavior of US Inflation from 1970 to 2008," CREATES Research Papers 2013-25, Department of Economics and Business Economics, Aarhus University.
    5. Sylvia Frühwirth‐Schnatter & Sylvia Kaufmann, 2006. "How do changes in monetary policy affect bank lending? An analysis of Austrian bank data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 275-305, April.
    6. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
    7. Sylvia Kaufmann, 2002. "Is there an asymmetric effect of monetary policy over time? A Bayesian analysis using Austrian data," Empirical Economics, Springer, vol. 27(2), pages 277-297.
    8. Patton, Andrew J. & Timmermann, Allan, 2007. "Properties of optimal forecasts under asymmetric loss and nonlinearity," Journal of Econometrics, Elsevier, vol. 140(2), pages 884-918, October.
    9. Montanari, Angela & Viroli, Cinzia, 2011. "Maximum likelihood estimation of mixtures of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2712-2723, September.
    10. Deschamps, Philippe J., 2012. "Bayesian estimation of generalized hyperbolic skewed student GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3035-3054.
    11. Philippe J. Deschamps, 2008. "Comparing smooth transition and Markov switching autoregressive models of US unemployment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 435-462.
    12. Philippe J. Deschamps, 2008. "Comparing smooth transition and Markov switching autoregressive models of US unemployment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 435-462.
    13. Brian Hartley, 2022. "Episodic incidence of Harrodian instability and the Kaleckian growth model: A Markov‐switching approach," Metroeconomica, Wiley Blackwell, vol. 73(1), pages 268-290, February.
    14. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    15. Maddalena Cavicchioli, 2021. "OLS Estimation of Markov switching VAR models: asymptotics and application to energy use," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 431-449, September.
    16. Chen, Cathy W.S. & Chan, Jennifer S.K. & So, Mike K.P. & Lee, Kevin K.M., 2011. "Classification in segmented regression problems," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2276-2287, July.
    17. Jiang, Yu & Fang, Xianming, 2015. "Bull, bear or any other states in US stock market?," Economic Modelling, Elsevier, vol. 44(C), pages 54-58.
    18. Neil Shephard & Siddhartha Chib, 1998. "Markov Chain Monte Carlo methods for Generalized Stochastic Volatility Models," Economics Series Working Papers 1998-W21, University of Oxford, Department of Economics.
    19. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(3), pages 409-431, August.
    20. Liu Xiaochun & Luger Richard, 2018. "Markov-switching quantile autoregression: a Gibbs sampling approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(2), pages 1, April.

    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:compst:v:29:y:2014:i:5:p:1025-1043. 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.