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Bayesian approach for mixture models with grouped data

Author

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  • 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
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    References listed on IDEAS

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    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. 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.
    5. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
    6. 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.
    7. 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.
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    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.

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