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Dynamics & sparsity in latent threshold factor models: a study in multivariate EEG signal processing. (English) Zbl 1385.62025

Summary: We discuss Bayesian analysis of multivariate time series with dynamic factor models that exploit time-adaptive sparsity in model parametrizations via the latent threshold approach. One central focus is on the transfer responses of multiple interrelated series to underlying, dynamic latent factor processes. Structured priors on model hyper-parameters are key to the efficacy of dynamic latent thresholding, and MCMC-based computation enables model fitting and analysis. A detailed case study of electroencephalographic (EEG) data from experimental psychiatry highlights the use of latent threshold extensions of time-varying vector autoregressive and factor models. This study explores a class of dynamic transfer response factor models, extending prior Bayesian modeling of multiple EEG series and highlighting the practical utility of the latent thresholding concept in multivariate, non-stationary time series analysis.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F15 Bayesian inference
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C55 Biomedical imaging and signal processing
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[1] Aguilar, O., Prado, R., Huerta, G. and West, M. (1999). Bayesian inference on latent structure in time series (with discussion). InBayesian Statistics, Vol. 6(J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 3-26. Oxford: Oxford University Press. · Zbl 0974.62066
[2] Aguilar, O. and West, M. (2000). Bayesian dynamic factor models and portfolio allocation.Journal of Business and Economic Statistics18, 338-357.
[3] Bernanke, B., Boivin, J. and Eliasz, P. (2005). Measuring the effects of monetary policy: A factor-augmented vector autoregressive (FAVAR) approach.The Quarterly Journal of Economics120, 387-422.
[4] Bhattacharya, A. and Dunson, D. B. (2011). Sparse Bayesian infinite factor models.Biometrika98, 291-306. · Zbl 1215.62025
[5] Carvalho, C. M., Chang, J., Lucas, J. E., Nevins, J. R., Wang, Q. and West, M. (2008). High-dimensional sparse factor modeling: Applications in gene expression genomics.Journal of the American Statistical Association103, 1438-1456. · Zbl 1286.62091
[6] Carvalho, C. M., Lopes, H. F. and Aguilar, O. (2011). Dynamic stock selection strategies: A structured factor model framework (with discussion). InBayesian Statistics, Vol. 9(J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West, eds.) 69-90. Oxford: Oxford University Press.
[7] Del Negro, M. and Otrok, C. M. (2008). Dynamic factor models with time-varying parameters: Measuring changes in international business cycles. Staff Report 326, Federal Reserve Bank of New York.DOI:10.2139/ssrn.1136163.
[8] Doornik, J. A. (2006).Ox: Object Oriented Matrix Programming. London: Timberlake Consultants Press.
[9] Dyro, F. M. (1989).The EEG Handbook. Boston: Little, Brown and Co.
[10] Huerta, G. and West, M. (1999). Priors and component structures in autoregressive time series models.Journal of the Royal Statistical Society, Series B61, 881-899. · Zbl 0940.62079
[11] Kimura, T. and Nakajima, J. (2016). Identifying conventional and unconventional monetary policy shocks: A latent threshold approach.The BE Journals in Macroeconomics16, 277-300.
[12] Kitagawa, G. and Gersch, W. (1996).Smoothness Priors Analysis of Time Series. Lecture Notes in Statistics116. New York: Springer. · Zbl 0853.62069
[13] Koop, G. and Korobilis, D. (2010). Bayesian multivariate time series methods for empirical macroeconomics.Foundations and Trends in Econometrics3, 267-358.DOI:10.1561/0800000013.
[14] Koop, G. M. and Potter, S. (2004). Forecasting in dynamic factor models using Bayesian model averaging.Econometrics Journal7, 550-565. · Zbl 1063.62032
[15] Lopes, H. F. and Carvalho, C. M. (2007). Factor stochastic volatility with time varying loadings and Markov switching regimes.Journal of Statistical Planning and Inference137, 3082-3091. · Zbl 1331.62064
[16] Lopes, H. F. and West, M. (2004). Bayesian model assessment in factor analysis.Statistica Sinica14, 41-67. · Zbl 1035.62060
[17] Lucas, J. E., Carvalho, C. M., Wang, Q., Bild, A. H., Nevins, J. R. and West, M. (2006). Sparse statistical modelling in gene expression genomics. InBayesian Inference for Gene Expression and Proteomics(K. A. Do, P. Mueller and M. Vannucci, eds.) 155-176. Cambridge: Cambridge University Press.
[18] Lucas, J. E., Carvalho, C. M. and West, M. (2009). A Bayesian analysis strategy for cross-study translation of gene expression biomarkers.Statistical Applications in Genetics and Molecular Biology8, Article no. 11. · Zbl 1276.92066
[19] Nakajima, J. and West, M. (2013a). Bayesian analysis of latent threshold dynamic models.Journal of Business & Economic Statistics31, 151-164.
[20] Nakajima, J. and West, M. (2013b). Bayesian dynamic factor models: Latent threshold approach.Journal of Financial Econometrics11, 116-153.DOI:10.1093/jjfinec/nbs013.
[21] Nakajima, J. and West, M. (2015). Dynamic network signal processing using latent threshold models.Digital Signal Processing47, 6-15.
[22] Pitt, M. and Shephard, N. (1999). Time varying covariances: A factor stochastic volatility approach (with discussion). InBayesian Statistics, Vol. 6(J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 547-570. Oxford: Oxford University Press. · Zbl 0956.62107
[23] Prado, R. (2010a). Characterization of latent structure in brain signals. InStatistical Methods for Modeling Human Dynamics(S. Chow, E. Ferrer and F. Hsieh, eds.) 123-153. New York: Routledge, Taylor and Francis.
[24] Prado, R. (2010b). Multi-state models for mental fatigue. InThe Handbook of Applied Bayesian Analysis(A. O’Hagan and M. West, eds.) 845-874. Oxford: Oxford University Press.
[25] Prado, R. and Huerta, G. (2002). Time-varying autoregressions with model order uncertainty.Journal of Time Series Analysis23, 599-618. · Zbl 1062.62201
[26] Prado, R. and West, M. (2010).Time Series Modeling, Computation, and Inference. New York: Chapman & Hall/CRC. · Zbl 1245.62105
[27] Prado, R., West, M. and Krystal, A. D. (2001). Multichannel electroencephalographic analyses via dynamic regression models with time-varying lag-lead structure.Journal of the Royal Statistical Society Series C Applied Statistics50, 95-109.
[28] Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit (with discussion).Journal of the Royal Statistical Society, Series B64, 583-639. · Zbl 1067.62010
[29] Weiner, R. D. and Krystal, A. D. (1994). The present use of electroconvulsive therapy.Annual Review of Medicine45, 273-281.
[30] West, M. (1997). Time series decomposition.Biometrika84, 489-494. · Zbl 0882.62088
[31] West, M. (2003). Bayesian factor regression models in the “large \(p\), small \(n\)” paradigm. InBayesian Statistics, Vol. 7(J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. David, D. Heckerman, A. F. M. Smith and M. West, eds.) 723-732. Oxford: Oxford University Press.
[32] West, M. (2013). Bayesian dynamic modelling. InBayesian Theory and Applications, Vol. 8(P. Damien, P. Dellaportes, N. G. Polson and D. A. Stephens, eds.) 145-166. Oxford: Oxford University Press.
[33] West, M. and Harrison, P. J. (1997).Bayesian Forecasting and Dynamic Models, 2nd ed. New York: Springer. · Zbl 0871.62026
[34] West, M., Prado, R. and Krystal, A. D. (1999). Evaluation and comparison of EEG traces: Latent structure in nonstationary time series.Journal of the American Statistical Association94, 375-387.
[35] Yoshida, R. and West, M. (2010). Bayesian learning in sparse graphical factor models via annealed entropy.Journal of Machine Learning Research11, 1771-1798. · Zbl 1242.68261
[36] Zhou, X., Nakajima, J. and West, M. (2014). Bayesian forecasting and portfolio decisions using dynamic dependent factor models.International Journal of Forecasting30, 963-980.
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