Brazilian Journal of Probability and Statistics

Dynamics & sparsity in latent threshold factor models: A study in multivariate EEG signal processing

Jouchi Nakajima and Mike West

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

Source
Braz. J. Probab. Stat., Volume 31, Number 4 (2017), 701-731.

Dates
Received: April 2016
Accepted: April 2017
First available in Project Euclid: 15 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1513328764

Digital Object Identifier
doi:10.1214/17-BJPS364

Mathematical Reviews number (MathSciNet)
MR3738175

Zentralblatt MATH identifier
1385.62025

Keywords
Dynamic factor models Dynamic sparsity EEG time series factor-augmented vector autoregression impulse response multivariate time series sparse time-varying loadings time-series decomposition transfer response factor models

Citation

Nakajima, Jouchi; West, Mike. Dynamics & sparsity in latent threshold factor models: A study in multivariate EEG signal processing. Braz. J. Probab. Stat. 31 (2017), no. 4, 701--731. doi:10.1214/17-BJPS364. https://projecteuclid.org/euclid.bjps/1513328764


Export citation

References

  • Aguilar, O., Prado, R., Huerta, G. and West, M. (1999). Bayesian inference on latent structure in time series (with discussion). In Bayesian Statistics, Vol. 6 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 3–26. Oxford: Oxford University Press.
  • Aguilar, O. and West, M. (2000). Bayesian dynamic factor models and portfolio allocation. Journal of Business and Economic Statistics 18, 338–357.
  • 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 Economics 120, 387–422.
  • Bhattacharya, A. and Dunson, D. B. (2011). Sparse Bayesian infinite factor models. Biometrika 98, 291–306.
  • 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 Association 103, 1438–1456.
  • Carvalho, C. M., Lopes, H. F. and Aguilar, O. (2011). Dynamic stock selection strategies: A structured factor model framework (with discussion). In Bayesian 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.
  • 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.
  • Doornik, J. A. (2006). Ox: Object Oriented Matrix Programming. London: Timberlake Consultants Press.
  • Dyro, F. M. (1989). The EEG Handbook. Boston: Little, Brown and Co.
  • Huerta, G. and West, M. (1999). Priors and component structures in autoregressive time series models. Journal of the Royal Statistical Society, Series B 61, 881–899.
  • Kimura, T. and Nakajima, J. (2016). Identifying conventional and unconventional monetary policy shocks: A latent threshold approach. The BE Journals in Macroeconomics 16, 277–300.
  • Kitagawa, G. and Gersch, W. (1996). Smoothness Priors Analysis of Time Series. Lecture Notes in Statistics 116. New York: Springer.
  • Koop, G. and Korobilis, D. (2010). Bayesian multivariate time series methods for empirical macroeconomics. Foundations and Trends in Econometrics 3, 267–358. DOI:10.1561/0800000013.
  • Koop, G. M. and Potter, S. (2004). Forecasting in dynamic factor models using Bayesian model averaging. Econometrics Journal 7, 550–565.
  • Lopes, H. F. and Carvalho, C. M. (2007). Factor stochastic volatility with time varying loadings and Markov switching regimes. Journal of Statistical Planning and Inference 137, 3082–3091.
  • Lopes, H. F. and West, M. (2004). Bayesian model assessment in factor analysis. Statistica Sinica 14, 41–67.
  • 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. In Bayesian Inference for Gene Expression and Proteomics (K. A. Do, P. Mueller and M. Vannucci, eds.) 155–176. Cambridge: Cambridge University Press.
  • 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 Biology 8, Article no. 11.
  • Nakajima, J. and West, M. (2013a). Bayesian analysis of latent threshold dynamic models. Journal of Business & Economic Statistics 31, 151–164.
  • Nakajima, J. and West, M. (2013b). Bayesian dynamic factor models: Latent threshold approach. Journal of Financial Econometrics 11, 116–153. DOI:10.1093/jjfinec/nbs013.
  • Nakajima, J. and West, M. (2015). Dynamic network signal processing using latent threshold models. Digital Signal Processing 47, 6–15.
  • Pitt, M. and Shephard, N. (1999). Time varying covariances: A factor stochastic volatility approach (with discussion). In Bayesian Statistics, Vol. 6 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 547–570. Oxford: Oxford University Press.
  • Prado, R. (2010a). Characterization of latent structure in brain signals. In Statistical Methods for Modeling Human Dynamics (S. Chow, E. Ferrer and F. Hsieh, eds.) 123–153. New York: Routledge, Taylor and Francis.
  • Prado, R. (2010b). Multi-state models for mental fatigue. In The Handbook of Applied Bayesian Analysis (A. O’Hagan and M. West, eds.) 845–874. Oxford: Oxford University Press.
  • Prado, R. and Huerta, G. (2002). Time-varying autoregressions with model order uncertainty. Journal of Time Series Analysis 23, 599–618.
  • Prado, R. and West, M. (2010). Time Series Modeling, Computation, and Inference. New York: Chapman & Hall/CRC.
  • 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 Statistics 50, 95–109.
  • 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 B 64, 583–639.
  • Weiner, R. D. and Krystal, A. D. (1994). The present use of electroconvulsive therapy. Annual Review of Medicine 45, 273–281.
  • West, M. (1997). Time series decomposition. Biometrika 84, 489–494.
  • West, M. (2003). Bayesian factor regression models in the “large $p$, small $n$” paradigm. In Bayesian 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.
  • West, M. (2013). Bayesian dynamic modelling. In Bayesian Theory and Applications, Vol. 8 (P. Damien, P. Dellaportes, N. G. Polson and D. A. Stephens, eds.) 145–166. Oxford: Oxford University Press.
  • West, M. and Harrison, P. J. (1997). Bayesian Forecasting and Dynamic Models, 2nd ed. New York: Springer.
  • 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 Association 94, 375–387.
  • Yoshida, R. and West, M. (2010). Bayesian learning in sparse graphical factor models via annealed entropy. Journal of Machine Learning Research 11, 1771–1798.
  • Zhou, X., Nakajima, J. and West, M. (2014). Bayesian forecasting and portfolio decisions using dynamic dependent factor models. International Journal of Forecasting 30, 963–980. DOI:10.1016/j.ijforecast.2014.03.017.