Bayesian framework for interval-valued data using Jeffreys’ prior and posterior predictive checking methods

References

• Beranger, B, H. Lin, and S. A. Sisson. 2020. New models for symbolic data analysis.
   Google Scholar
• Bertrand, P, and F. Goupil. 2000. Descriptive statistics for symbolic data. In Analysis of symbolic data. Studies in classification, data analysis, and knowledge organization, eds. H. H. Bock and E. Diday, 106–24. Berlin, Heidelberg: Springer.
   Google Scholar
• Billard, L, and E. Diday. 2000. Regression analysis for interval-valued data. In Data analysis, classification, and related methods, eds. H. A. L. Kiers, J.-P. Rasson, P. J. F. Groenen, and M. Schader, 369–74. Berlin, Heidelberg: Springer.
   Google Scholar
• Box, G. E, and G. C. Tiao. 1992. Bayesian inference in statistical analysis. Canada: Wiley Classics Library Edition.
   Google Scholar
• Chen, M. H., J. G. Ibrahim, and S. Kim. 2008. Properties and implementation of Jeffreys’s prior in binomial regression models. Journal of the American Statistical Association 103 (484):1659–64.
   PubMed Web of Science ®Google Scholar
• Diday, E. 1987. The symbolic approach in clustering and related methods of data analysis. In H. H. Bock, ed. Classification and Related Methods of Data Analysis, Aachen, dd5 1987. Proc. First Conference of the International Federation of Classification Societies (IFCS-87), dd8.
   Google Scholar
• Douzal-Chouakria, A., L. Billard, and E. Diday. 2011. Principal component analysis for interval-valued observations. Statistical Analysis and Data Mining: The ASA Data Science Journal 4 (2):229–46.
   Google Scholar
• Gelman, A., J. Carlin, H. Stern, D. Dunson, A. Vehtari, and D. Rubin. 2014. Bayesian data analysis, 3rd ed. Boca Raton, FL: Chapman and Hall/CRC.
   Google Scholar
• Gelman, A., X. L. Meng, and H. Stern. 1995. Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica 6:733–807.
   Web of Science ®Google Scholar
• Giordani, P. 2015. Lasso-constrained regression analysis for interval-valued data. Advances in Data Analysis and Classification 9 (1):5–19.
   Web of Science ®Google Scholar
• González-Rodríguez, G., Á. Blanco, N. Corral, and A. Colubi. 2007. Least squares estimation of linear regression models for convex compact random sets. Advances in Data Analysis and Classification 1 (1):67–81.
   Web of Science ®Google Scholar
• Han, A., Y. Hong, K. K. Lai, and S. Wang. 2008. Interval time series analysis with an application to the sterling-dollar exchange rate. Journal of Systems Science and Complexity 21 (4):558–73.
   Web of Science ®Google Scholar
• Khakifirooz, M., C. F. Chien, and Y. J. Chen. 2018. Bayesian inference for mining semiconductor manufacturing big data for yield enhancement and smart production to empower industry 4.0. Applied Soft Computing 68:990–9.
   Web of Science ®Google Scholar
• Le-Rademacher, J., and L. Billard. 2011. Likelihood functions and some maximum likelihood estimators for symbolic data. Journal of Statistical Planning and Inference 141 (4):1593–602.
   Web of Science ®Google Scholar
• Lima Neto, E. A., and F. A. de Carvalho. 2008. Centre and range method for fitting a linear regression model to symbolic interval data. Computational Statistics & Data Analysis 52 (3):1500–15.
   Web of Science ®Google Scholar
• Lima Neto, E. A., and F. A. de Carvalho. 2010. Constrained linear regression models for symbolic interval-valued variables. Computational Statistics & Data Analysis 54 (2):333–47.
   Web of Science ®Google Scholar
• Lin, W., and G. González-Rivera. 2016. Interval-valued time series models: Estimation based on order statistics exploring the agriculture marketing service data. Computational Statistics & Data Analysis 100:694–711.
   Web of Science ®Google Scholar
• Martin, G. M., and V. L. Martin. 2000. Bayesian inference in the triangular cointegration model using a jeffreys prior. Communications in Statistics - Theory and Methods 29 (8):1759–85.
   Web of Science ®Google Scholar
• Singh, S. S., F. Lindsten, and E. Moulines. 2017. Blocking strategies and stability of particle Gibbs samplers. Biometrika 104 (4):953–69.
   Web of Science ®Google Scholar
• Xiong, T., C. Li, Y. Bao, Z. Hu, and L. Zhang. 2015. A combination method for interval forecasting of agricultural commodity futures prices. Knowledge-Based Systems 77:92–102.
   Web of Science ®Google Scholar
• Zhang, X., B. Beranger, and S. A. Sisson. 2020. Constructing likelihood functions for interval-valued random variables. Scandinavian Journal of Statistics 47 (1):1–35.
   Web of Science ®Google Scholar