699
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Bayesian Analysis of Semiparametric Hidden Markov Models With Latent Variables

, , , &

References

  • Albert, J. H., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88, 669–679.
  • Altman, R. M. (2007). Mixed hidden Markov models. Journal of the American Statistical Association, 102, 201–210.
  • Bartolucci, F., and Farcomeni, A. (2009). A multivariate extension of the dynamic logit model for longitudinal data based on a latent Markov heterogeneity structure. Journal of the American Statistical Association, 104, 816–831.
  • Baum, L. E., Petrie, T., Soules, G., & Weiss, N. (1970). A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Annals of Mathematical Statistics, 41,164–171.
  • Behseta, S. (2005). Hierarchical models for assessing variability among functions. Biometrika, 92, 419–434.
  • Berry, S. M., Carroll, R. J., & Ruppert, D. (2002). Bayesian smoothing and regression splines for measurement error problems. Journal of the American Statistical Association, 97, 160–169.
  • Biller, C., & Fahrmeir, L. (2001). Bayesian varying-coefficient models using adaptive regression splines. Statistical Modelling, 1, 195–211.
  • Bollen, K. A. (1989). Structural equations with latent variables. New york, NY: Wiley.
  • Bulla, J., Lagona, F., Maruotti, A., & Picone, M. (2012). A multivariate hidden Markov model for the identification of sea regimes from incomplete skewed and circular time series. Journal of Agricultural Biological and Environmental Statistics, 17, 544–567.
  • Caldwell, B. M. & Bradley, R. H. (2003). Home observation for measurement of the environment: Administration manual. Tcmpc, Family & AZ: Human Dynamics Research Institute, Arizona State University.
  • Cappé, O., Moulines, E., & Rydén, T. (2005). Inference in hidden Markov models. New York, NY: Springer.
  • Celeux, G. & Durand, J.-B. (2008). Selecting hidden Markov model state number with cross-validated likelihood. Computational Statistics, 23, 541–564.
  • Celeux, G., Forbes, F., Robert, C. P., & Titterington, D. M. (2006). Deviance information criteria for missing data models. Bayesian Analysis, 1, 651–674.
  • Center for Human Resource Research (2004). The National Longitudinal Surveys NLSY user’s guide, 1979–2004. Columbus, OH: U.S. Department of Labor, Bureau of Labor Statistics.
  • Chow, S. M., Grimm, K. J., Guillaume, F., Dolan, C. V., & McArdle, J. J. (2013). Regime-switching bivariate dual change score model. Multivariate Behavioral Research, 48, 463–502.
  • De Boor, C. (2001). A practical guide to splines. New York: Springer-Verlag.
  • DiMatteo, I., Genovese, C. R., & Kass, R. E. (2001). Bayesian curve fitting with free-knot splines. Biometrika, 88, 1055–1071.
  • Dunn, L. M, and Markwardt, F. (1970). Peabody Individual Achievement Test manual. Circle Pines, MN: American Guidance Services.
  • Efron, B. (1983). Estimating the error rate of a prediction rule: Improvement on cross-validation. Journal of the American Statistical Association, 78, 316–331.
  • Eilers, P. H. C., and Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11, 89–121.
  • Fahrmeir, L., and Raach, A. (2007). A Bayesian semiparametric latent variable model for mixed responses. Psychometrika, 72, 327–346.
  • Fan, J., and Gijbels, I. (1996). Local Mynomial modelling and its applications. London, UK: Chapman and Hall.
  • Fox, E. B., Sudderth, E. B., Jordan, M. I., & Willsky, A. S. (2008). An HDP-HMM for systems with state persistence. In Cohen, W., McCallum, A., & Roweis, S. (Eds.), Proceedings of the 25th International Conference on Machine Learning (pp. 312–319). New York, NY: ACM Press.
  • Frühwirth-Schnatter, S. (2001). Markov chain Monte Carlo estimation of classical and dynamic switching and mixture models. Journal of the American Statistical Association, 96, 194–209.
  • Gelfand, A. E., & Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398–409.
  • Gelman, A. (1996). Inference and monitoring convergence. In W. R., Gilks, S., Richardson, & D. J., Spiegelhalter, eds, Markov chain Monte Carlo in practice, pp. 131–144. London UK: Chapman & Hall.
  • Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741.
  • Green, P. J. & Silverman, B. W. (1993). Nonparametric regression and generalized linear models: A roughness penalty approach. London UK: Chapman & Hall/CRCc.
  • Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97–109.
  • Hughes, J. P., & Guttorp, P. (1994). A class of stochastic models for relating synoptic atmospheric patterns to regional hydrologic phenomena. Water Resources Research, 30(5), 1535–1646.
  • Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90, 773–795.
  • Lagona, F., Jdanov, D., & Shkolnikova, M. (2014). Latent time-varying factors in longitudinal analysis: A linear mixed hidden Markov model for heart rates. Statistics in Medicine, 33, 4116–4134.
  • Lang, S. & Brezger, A. (2004). Bayesian P-splines. Journal of Computational and Graphical Statistics, 13, 183–212.
  • Maruotti, A. (2011). Mixed hidden Markov models for longitudinal data: An overview. International Statistical Review, 79, 427–454.
  • Maruotti, A. & Rydén, T. (2009). A semiparametric approach to hidden Markov models under longitudinal observations. Statistics and Computing, 19, 381–393.
  • Mastrantonio, G., Maruotti, A., & Giovanna, J. L. (2014). Bayesian hidden Markov modelling using circular-linear general projected normal distribution. Environmetrics, 26, 145–158.
  • Mastrantonio, G., Pollice, A., & Fedele, F. (2017). Distributions-oriented wind forecast verification by a hidden Markov model for multivariate circular-linear data. Stochastic Environmental Research and Risk Assessment. Advance online publication. doi:10.1007/s00477-017-1416-x
  • Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equations of state calculations by fast computing machine. The Journal of Chemical Physics, 21, 1087–1091.
  • Muthén, L. K. & Muthén, B. O. (2012). Mplus user’s guide. (7 th ed.). Los Angles, CA: Muthén & Muthén.
  • Panagiotelis, A., & Smith, M. (2008). Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models. Journal of Econometrics, 143, 291–316.
  • Plummer, M. (2008). Penalized loss functions for Bayesian model comparison. Biostatistics, 9, 523–539.
  • Polson, N. G., Scott, J. G., & Windle, J. (2013). Bayesian inference for logistic models using Pólya-Gamma latent variables. Journal of the American Statistical Association, 108, 1339–1349.
  • Robert, C. P., Ryden, T., & Titterington, D. M. (2000). Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62(1), 57–75.
  • Ruppert, D., Wand, M. P., & Carroll, R. J. (2003). Semiparametric regression. Cambridge, UK: Cambridge Unviersity Press.
  • Scott, S. L., James, G. M., & Sugar, C. A. (2005). Hidden Markov models for longitudinal comparisons. Journal of the American Statistical Association, 100, 359–369.
  • Shi, J. Q. & Lee, S. Y. (2000). Latent variable model with mixed continuous and polytomous data. Journal of the Royal Statistical Society, Series B, 62(1), 77–87.
  • Song, X. Y., & Lee, S. Y. (2012). Basic and advanced Bayesian structural equation modeling: With applications in the medical and behavioral sciences. Hoboken, NJ: John Wiley.
  • Song, X. Y., & Lu, Z. H. (2010). Semiparametric latent variable models with Bayesian P-splines. Journal of Computational and Graphical Statistics, 19, 590–608.
  • Song, X. Y., & Lu, Z. H. (2012). Semiparametric transformation models with Bayesian P-splines. Statistics and Computing, 22:1085–1098.
  • Song, X. Y., Lu, Z. H., Cai, J. H., & Ip, E. (2013). A Bayesian modeling approach for generalized semiparametric structural equation models. Psychometrika, 78, 624–647.
  • Song, X. Y., Xia, Y. M., & Zhu, H. T. (2017). Hidden Markov latent variable models with multivariate longitudinal data. Biometrics, 73, 313–323.
  • Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & van der Linde, A. (2002). Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society, Series B, 64, 583–639.
  • Tanner, M. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation (with discussion). Journal of the American Statistical Association, 82, 528–550.
  • Teh, Y. W., Jordan, M. I., Beal, M. J., & Blei, D. M. (2006). Hierarchical dirichlet processes. Journal of the American Statistical Association, 101, 1566–1581.
  • Windle, J., Carvalho, C. M., Scott, J. G., & Sun, L. (2013). Efficient data augmentation in dynamic models for binary and count data. Available at https://arxiv.org/abs/1308.0774
  • Yang, M. G., & Dunson, D. B. (2010). Bayesian semiparametric structural equation models with latent variables. Psychometrika, 75, 675–693.
  • Zeger, S. L., & Karim, M. R. (1991). Generalized linear models with random effects: A Gibbs sampling approach. Journal of the American Statistical Association, 86, 79–86.
  • Zill, N. (1985). Behavior problem scales developed from the 1981 Child Health Supplement to the National Health Interview Survey. Washington, DC: Child Trends.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.