4,659
Views
9
CrossRef citations to date
0
Altmetric
Theory and Methods

Bayesian Model Search for Nonstationary Periodic Time Series

, , , &
Pages 1320-1335 | Received 23 Oct 2018, Accepted 12 May 2019, Published online: 09 Jul 2019

References

  • Akaike, H. (1974), “A New Look at the Statistical Model Identification,” IEEE Transactions on Automatic Control, 19, 716–723. DOI: 10.1109/TAC.1974.1100705.
  • Altevogt, B. M., and Colten, H. R. (2006), Sleep Disorders and Sleep Deprivation: An Unmet Public Health Problem, Washington, DC: National Academies Press.
  • Andrieu, C., and Doucet, A. (1999), “Joint Bayesian Model Selection and Estimation of Noisy Sinusoids via Reversible Jump MCMC,” IEEE Transactions on Signal Processing, 47, 2667–2676. DOI: 10.1109/78.790649.
  • Berlad, I., Shlitner, A., Ben-Haim, S., and Lavie, P. (1993), “Power Spectrum Analysis and Heart Rate Variability in Stage 4 and REM Sleep: Evidence for State-Specific Changes in Autonomic Dominance,” Journal of Sleep Research, 2, 88–90. DOI: 10.1111/j.1365-2869.1993.tb00067.x.
  • Bhaskaran, K., Gasparrini, A., Hajat, S., Smeeth, L., and Armstrong, B. (2013), “Time Series Regression Studies in Environmental Epidemiology,” International Journal of Epidemiology, 42, 1187–1195. DOI: 10.1093/ije/dyt092.
  • Bishop, C. M. (2006), Pattern Recognition and Machine Learning, Information Science and Statistics, New York: Springer-Verlag.
  • Bramness, J. G., Walby, F. A., Morken, G., and Røislien, J. (2015), “Analyzing Seasonal Variations in Suicide With Fourier Poisson Time-Series Regression: A Registry-Based Study From Norway, 1969–2007,” American Journal of Epidemiology, 182, 244–254. DOI: 10.1093/aje/kwv064.
  • Bretthorst, G. L. (1988), Bayesian Spectrum Analysis and Parameter Estimation (Vol. 48), New York: Springer-Verlag.
  • Bretthorst, G. L. (1990), “Bayesian Analysis. I. Parameter Estimation Using Quadrature NMR Models,” Journal of Magnetic Resonance, 88, 533–551. DOI: 10.1016/0022-2364(90)90287-J.
  • Bruce, S. A., Hall, M. H., Buysse, D. J., and Krafty, R. T. (2018), “Conditional Adaptive Bayesian Spectral Analysis of Nonstationary Biomedical Time Series,” Biometrics, 74, 260–269. DOI: 10.1111/biom.12719.
  • Carskadon, M. A., and Dement, W. C. (2005), “Normal Human Sleep: An Overview,” Principles and Practice of Sleep Medicine, 4, 13–23.
  • Dahlhaus, R. (1997), “Fitting Time Series Models to Nonstationary Processes,” The Annals of Statistics, 25, 1–37. DOI: 10.1214/aos/1034276620.
  • Davis, E. M., and O’Donnell, C. P. (2013), “Rodent Models of Sleep Apnea,” Respiratory Physiology & Neurobiology, 188, 355–361. DOI: 10.1016/j.resp.2013.05.022.
  • Davis, R. A., Lee, T. C. M., and Rodriguez-Yam, G. A. (2006), “Structural Break Estimation for Nonstationary Time Series Models,” Journal of the American Statistical Association, 101, 223–239. DOI: 10.1198/016214505000000745.
  • Djuric, P. M. (1996), “A Model Selection Rule for Sinusoids in White Gaussian Noise,” IEEE Transactions on Signal Processing, 44, 1744–1751. DOI: 10.1109/78.510621.
  • Dou, L., and Hodgson, R. (1995), “Bayesian Inference and Gibbs Sampling in Spectral Analysis and Parameter Estimation. I,” Inverse Problems, 11, 1069. DOI: 10.1088/0266-5611/11/5/011.
  • Dou, L., and Hodgson, R. (1996), “Bayesian Inference and Gibbs Sampling in Spectral Analysis and Parameter Estimation: II,” Inverse Problems, 12, 121. DOI: 10.1088/0266-5611/12/2/002.
  • Gilks, W. R., Richardson, S., and Spiegelhalter, D. (1995), Markov Chain Monte Carlo in Practice, Boca Raton, FL: CRC Press.
  • 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.
  • Han, F., Subramanian, S., Price, E. R., Nadeau, J., and Strohl, K. P. (2002), “Periodic Breathing in the Mouse,” Journal of Applied Physiology, 92, 1133–1140. DOI: 10.1152/japplphysiol.00785.2001.
  • Harsch, I. A., Schahin, S. P., Brückner, K., Radespiel-Tröger, M., Fuchs, F. S., Hahn, E. G., Konturek, P. C., Lohmann, T., and Ficker, J. H. (2004), “The Effect of Continuous Positive Airway Pressure Treatment on Insulin Sensitivity in Patients With Obstructive Sleep Apnoea Syndrome and Type 2 Diabetes,” Respiration, 71, 252–259. DOI: 10.1159/000077423.
  • Heinzer, R., Vat, S., Marques-Vidal, P., Marti-Soler, H., Andries, D., Tobback, N., Mooser, V., Preisig, M., Malhotra, A., Waeber, G., and Vollenweider, P. (2015), “Prevalence of Sleep-Disordered Breathing in the General Population: The Hypnolaus Study,” The Lancet Respiratory Medicine, 3, 310–318. DOI: 10.1016/S2213-2600(15)00043-0.
  • Huang, Q., Cohen, D., Komarzynski, S., Li, X.-M., Innominato, P., Lévi, F., and Finkenstädt, B. (2018), “Hidden Markov Models for Monitoring Circadian Rhythmicity in Telemetric Activity Data,” Journal of the Royal Society Interface, 15, 20170885. DOI: 10.1098/rsif.2017.0885.
  • Komarzynski, S., Huang, Q., Innominato, P. F., Maurice, M., Arbaud, A., Beau, J., Bouchahda, M., Ulusakarya, A., Beaumatin, N., Breda, G., and Finkenstädt, B. (2018), “Relevance of a Mobile Internet Platform for Capturing Inter- and Intrasubject Variabilities in Circadian Coordination During Daily Routine: Pilot Study,” Journal of Medical Internet Research, 20, e204. DOI: 10.2196/jmir.9779.
  • Kräuchi, K. (2002), “How Is the Circadian Rhythm of Core Body Temperature Regulated?,” Clinical Autonomic Research, 12, 147–149.
  • Krauchi, K., and Wirz-Justice, A. (1994), “Circadian Rhythm of Heat Production, Heart Rate, and Skin and Core Temperature Under Unmasking Conditions in Men,” American Journal of Physiology—Regulatory, Integrative and Comparative Physiology, 267, R819–R829. DOI: 10.1152/ajpregu.1994.267.3.R819.
  • Lal, C., Strange, C., and Bachman, D. (2012), “Neurocognitive Impairment in Obstructive Sleep Apnea,” Chest, 141, 1601–1610. DOI: 10.1378/chest.11-2214.
  • Lanfranchi, P. A., Braghiroli, A., Bosimini, E., Mazzuero, G., Colombo, R., Donner, C. F., and Giannuzzi, P. (1999), “Prognostic Value of Nocturnal Cheyne-Stokes Respiration in Chronic Heart Failure,” Circulation, 99, 1435–1440. DOI: 10.1161/01.CIR.99.11.1435.
  • Levi, F., and Schibler, U. (2007), “Circadian Rhythms: Mechanisms and Therapeutic Implications,” Annual Review of Pharmacology and Toxicology, 47, 593–628. DOI: 10.1146/annurev.pharmtox.47.120505.105208.
  • Li, Z., and Krafty, R. T. (2019), “Adaptive Bayesian Time–Frequency Analysis of Multivariate Time Series,” Journal of the American Statistical Association, 114, 453–465. DOI: 10.1080/01621459.2017.1415908.
  • Marin, J.-M., and Robert, C. (2007), Bayesian Core: A Practical Approach to Computational Bayesian Statistics, Berlin: Springer Science & Business Media.
  • McCullagh, P., and Nelder, J. (1989), Generalized Linear Models, Monographs on Statistics and Applied Probability Series (2nd ed.), London: Chapman & Hall.
  • Nakamura, A., Fukuda, Y., and Kuwaki, T. (2003), “Sleep Apnea and Effect of Chemostimulation on Breathing Instability in Mice,” Journal of Applied Physiology, 94, 525–532. DOI: 10.1152/japplphysiol.00226.2002.
  • Nieto, F. J., Peppard, P. E., Young, T., Finn, L., Hla, K. M., and Farré, R. (2012), “Sleep-Disordered Breathing and Cancer Mortality: Results From the Wisconsin Sleep Cohort Study,” American Journal of Respiratory and Critical Care Medicine, 186, 190–194. DOI: 10.1164/rccm.201201-0130OC.
  • Ombao, H. C., Raz, J. A., von Sachs, R., and Malow, B. A. (2001), “Automatic Statistical Analysis of Bivariate Nonstationary Time Series,” Journal of the American Statistical Association, 96, 543–560. DOI: 10.1198/016214501753168244.
  • Osorio, R. S., Ducca, E. L., Wohlleber, M. E., Tanzi, E. B., Gumb, T., Twumasi, A., Tweardy, S., Lewis, C., Fischer, E., Koushyk, V., and Cuartero-Toledo, M. (2016), “Orexin-A Is Associated With Increases in Cerebrospinal Fluid Phosphorylated-Tau in Cognitively Normal Elderly Subjects,” Sleep, 39, 1253–1260. DOI: 10.5665/sleep.5846.
  • Pace-Schott, E. F., and Hobson, J. A. (2002), “The Neurobiology of Sleep: Genetics, Cellular Physiology and Subcortical Networks,” Nature Reviews Neuroscience, 3, 591. DOI: 10.1038/nrn895.
  • Parish, J. M., Adam, T., and Facchiano, L. (2007), “Relationship of Metabolic Syndrome and Obstructive Sleep Apnea,” Journal of Clinical Sleep Medicine, 3, 467.
  • Priestley, M. B. (1981), Spectral Analysis and Time Series, London: Academic Press.
  • Quinn, B. G. (1989), “Estimating the Number of Terms in a Sinusoidal Regression,” Journal of Time Series Analysis, 10, 71–75. DOI: 10.1111/j.1467-9892.1989.tb00016.x.
  • Rife, D. C., and Boorstyn, R. R. (1976), “Multiple Tone Parameter Estimation From Discrete-Time Observations,” Bell System Technical Journal, 55, 1389–1410. DOI: 10.1002/j.1538-7305.1976.tb02941.x.
  • Rissanen, J. (1978), “Modeling by Shortest Data Description,” Automatica, 14, 465–471. DOI: 10.1016/0005-1098(78)90005-5.
  • Rosen, O., Stoffer, D. S., and Wood, S. (2009), “Local Spectral Analysis via a Bayesian Mixture of Smoothing Splines,” Journal of the American Statistical Association, 104, 249–262. DOI: 10.1198/jasa.2009.0118.
  • Rosen, O., Wood, S., and Stoffer, D. S. (2012), “AdaptSPEC: Adaptive Spectral Estimation for Nonstationary Time Series,” Journal of the American Statistical Association, 107, 1575–1589. DOI: 10.1080/01621459.2012.716340.
  • Shneerson, J. M. (2009), Sleep Medicine: A Guide to Sleep and Its Disorders, Hoboken, NJ: Wiley.
  • Shumway, R. H., and Stoffer, D. S. (2005), Time Series Analysis and Its Applications, Springer Texts in Statistics, New York: Springer-Verlag.
  • Stoica, P., Moses, R. L., Friedlander, B., and Soderstrom, T. (1989), “Maximum Likelihood Estimation of the Parameters of Multiple Sinusoids From Noisy Measurements,” IEEE Transactions on Acoustics, Speech, and Signal Processing, 37, 378–392. DOI: 10.1109/29.21705.
  • Sundaram, S. S., Halbower, A., Pan, Z., Robbins, K., Capocelli, K. E., Klawitter, J., Shearn, C. T., and Sokol, R. J. (2016), “Nocturnal Hypoxia-Induced Oxidative Stress Promotes Progression of Pediatric Non-alcoholic Fatty Liver Disease,” Journal of Hepatology, 65, 560–569. DOI: 10.1016/j.jhep.2016.04.010.
  • Tan, A., Cheung, Y. Y., Yin, J., Lim, W.-Y., Tan, L. W., and Lee, C.-H. (2016), “Prevalence of Sleep-Disordered Breathing in a Multiethnic Asian Population in Singapore: A Community-Based Study,” Respirology, 21, 943–950. DOI: 10.1111/resp.12747.
  • Van Someren, E. J. (2006), “Mechanisms and Functions of Coupling Between Sleep and Temperature Rhythms,” Progress in Brain Research, 153, 309–324.
  • White, G. C., and Bennetts, R. E. (1996), “Analysis of Frequency Count Data Using the Negative Binomial Distribution,” Ecology, 77, 2549–2557. DOI: 10.2307/2265753.
  • Whittle, P. (1957), “Curve and Periodogram Smoothing,” Journal of the Royal Statistical Society, Series B, 19, 38–63. DOI: 10.1111/j.2517-6161.1957.tb00242.x.
  • Yau, S.-F., and Bresler, Y. (1993), “Maximum Likelihood Parameter Estimation of Superimposed Signals by Dynamic Programming,” IEEE Transactions on Signal Processing, 41, 804–820. DOI: 10.1109/78.193219.
  • Zhang, Q., and Wong, K. M. (1993), “Information Theoretic Criteria for the Determination of the Number of Signals in Spatially Correlated Noise,” IEEE Transactions on Signal Processing, 41, 1652–1663. DOI: 10.1109/78.212737.