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Bayesian Methods

Bayesian Heterogeneous Hidden Markov Models with an Unknown Number of States

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Pages 15-24 | Received 13 Jul 2022, Accepted 20 Jun 2023, Published online: 10 Aug 2023

References

  • Agresti, A. (2003), Categorical Data Analysis, Hoboken: Wiley.
  • Akaike, H. (1974), “New Look at Statistical-Model Identification,” IEEE Transactions on Automatic Control, 19, 716–723. DOI: 10.1109/TAC.1974.1100705.
  • Baum, L. E., Petrie, T., Soules, G., and Weiss, N. (1970), “A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains,” The Annals of Mathematical Statistics, 41, 164–171. DOI: 10.1214/aoms/1177697196.
  • Celeux, G., and Durand, J.-B. (2008), “Selecting Hidden Markov Model State Number with Cross-Validated Likelihood,” Computational Statistics, 23, 541–564. DOI: 10.1007/s00180-007-0097-1.
  • Chen, J., and Khalili, A. (2008), “Order Selection in Finite Mixture Models with a Nonsmooth Penalty,” Journal of the American Statistical Association, 103, 1674–1683. DOI: 10.1198/016214508000001075.
  • Dickerson, B., and Wolk, D. (2013), “Biomarker-based Prediction of Progression in MCI: Comparison of AD-Signature and Hippocampal Volume with Spinal Fluid Amyloid-β and Tau,” Front Aging Neurosci, 5, 55. DOI: 10.3389/fnagi.2013.00055.
  • Eunjee, L., Hongtu, Z., Dehan, K., Wang, Y., Giovanello, K. S., Ibrahim, J. G., et al. (2015), “BFLCRM: A Bayesian Functional Linear Cox Regression Model for Predicting Time to Conversion to Alzheimer’s Disease,” The Annals of Applied Statistics, 9, 2153–2178. DOI: 10.1214/15-AOAS879.
  • Green, P. J. (1995), “Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination,” Biometrika, 82, 711–732. DOI: 10.1093/biomet/82.4.711.
  • Guo, R., Zhu, H., Chow, S.-M., and Ibrahim, J. G. (2012), “Bayesian Lasso for Semiparametric Structural Equation Models,” Biometrics, 68, 567–577. DOI: 10.1111/j.1541-0420.2012.01751.x.
  • Harper, W., and Hooker, C. (1976), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Dordrecht: Springer.
  • Hung, Y., Wang, Y., Zarnitsyna, V., Zhu, C., and Wu, C.-F. (2013), “Hidden Markov Models with Applications in Cell Adhesion Experiments,” Journal of the American Statistical Association, 108, 1469–1479. DOI: 10.1080/01621459.2013.836973.
  • Ip, E., Zhang, Q., Rejeski, J., Harris, T., and Kritchevsky, S. (2013), “Partially Ordered Mixed Hidden Markov Model for the Disablement Process of Older Adults,” Journal of the American Statistical Association, 108, 370–384. DOI: 10.1080/01621459.2013.770307.
  • Kang, K., Song, X., Hu, X. J., and Zhu, H. (2019), “Bayesian Adaptive Group Lasso with Semiparametric Hidden Markov Models,” Statistics in Medicine, 38, 1634–1650. DOI: 10.1002/sim.8051.
  • Kantarci, K., Gunter, J., Tosakulwong, N., Weigand, S. D., Senjem, M. S., Petersen, R. C., et al. (2013), “Focal Hemosiderin Deposits and β-amyloid Load in the adni Cohort,” Alzheimer’s & Dementia: The Journal of the Alzheimer’s Association, 9, S116–S123.
  • Lin, Y., and Song, X. (2022), “Order Selection for Regression-based Hidden Markov Model,” Journal of Multivariate Analysis (to appear). DOI: 10.1016/j.jmva.2022.105061.
  • Liu, H., and Song, X. (2020), “Bayesian Analysis of Hidden Markov Structural Equation Models with an Unknown Number of Hidden States,” Econometrics and Statistics, 18, 29–43. DOI: 10.1016/j.ecosta.2020.03.003.
  • Mackay, R. (2002), “Estimating the Order of a Hidden Markov Model,” Canadian Journal of Statistics, 30, 573–589. DOI: 10.2307/3316097.
  • Manole, T., and Khalili, A. (2021), “Estimating the Number of Components in Finite Mixture Models via the Group-Sort-Fuse Procedure,” The Annals of Statistics, 49, 3043–3069. DOI: 10.1214/21-AOS2072.
  • Park, T., and Casella, G. (2008), “The Bayesian Lasso,” Journal of the American Statistical Association, 103, 681–686. DOI: 10.1198/016214508000000337.
  • Risacher, S. L., Kim, S., Nho, K., Foroud, T., Shen, L., Petersen, R. C., et al. (2015), “Apoe Effect on Alzheimer’s Disease Biomarkers in Older Adults with Significant Memory Concern,” Alzheimer’s & Dementia: The Journal of the Alzheimer’s Association, 11, 1417–1429. DOI: 10.1016/j.jalz.2015.03.003.
  • Schwarz, G. (1978), “Estimating the Dimension of a Model,” The Annals of Statistics, 6, 461–464. DOI: 10.1214/aos/1176344136.
  • Song, X., Xia, Y., and Zhu, H. (2017), “Hidden Markov Latent Variable Models with Multivariate Longitudinal Data,” Biometrics, 73, 313–323. DOI: 10.1111/biom.12536.
  • Via, J., and Lloret, A. (2010), “Why Women have more Alzheimer’s Disease than Men: Gender and Mitochondrial Toxicity of Amyloid-β Peptide,” Journal of Alzheimer’s Disease, 20, 527–533.
  • Ye, M., Lu, Z., Li, Y., and Song, X. (2019), “Finite Mixture of Varying Coefficient Model: Estimation and Component Selection,” Journal of Multivariate Analysis, 171, 452–474. DOI: 10.1016/j.jmva.2019.01.013.
  • Zhou, J., Song, X., and Sun, L. (2020), “Continuous Time Hidden Markov model for Longitudinal Data,” Journal of Multivariate Analysis, 179, 104646. DOI: 10.1016/j.jmva.2020.104646.

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