1. Modeling the Evolution of Neurophysiological Signals Mark Fiecas Hernando Ombao

2. Data Characteristics Small signal-to-noise ratios 2

3. Data Characteristics Nonstationary time series data 3

4. Data Characteristics Evolving over time within a replicate Nonidentical replicates across the experiment 4

5. Example 5

6. A Learning Association Experiment 6 Time

7. A Learning Association Experiment 7

8. Evolving Evolutionary Coherence 8

9. 9

10. Evolving Evolutionary Spectrum 10

11. Evolving Evolutionary Spectrum 11

12. The Time Series Models Weakly stationary time series (Brillinger, 1981): 12

13. The Time Series Models Locally stationary time series (Dahlhaus, 2000): 13

14. The Time Series Models Locally stationary time series with slowly evolving replicates: 14

15. The Time Series Models 1. Replicates are uncorrelated. For each replicate, use existing methods to address nonstationarity over time. 2. Smooth the estimates over time and replicate-time. 15

16. Performance 16

17. Hippocampus Log Periodogram 17

18. Nucleus Accumbens Log Periodogram 18

19. A Relevant Scientific Question Is the power in a frequency band of interest the same between “familiar” and “novel” trials? 19

20. Log Periodogram Models Weakly stationary data (Krafty et al, 2011): 20

21. Log Periodogram Models Weakly stationary data (Krafty et al, 2011): where 21

22. The Log Periodogram Models Locally stationary data (Krafty, 2007; Qin and Guo, 2009): 22

23. The Log Periodogram Models Locally stationary data (Krafty et al, 2007): where 23

24. The Proposed Log Periodogram Model 24

25. The Proposed Log Periodogram Model 25

26. The Proposed Log Periodogram Model 26

27. Calling All Statisticians “Understanding how the brain works is arguably one of the greatest scientific challenges of our time.” - Alivisatos et al, 2013 27

28. Calling All Statisticians The BRAIN Initiative (USA) The Human Brain Project (European Union) –86 Institutions in Europe involved –€1 billion in funding / year 28

29. Calling All Statisticians Very rich data sets –High temporal resolution (EEG, MEG, LFP) –High spatial resolution (PET, fMRI) –300k spatial locations in fMRI –Imaging genetics Many open problems 29

30. Calling All Statisticians Handbook of Modern Statistical Methods: Neuroimaging Data Analysis (eds: H. Ombao, M. Lindquist, W. Thompson, and J. Aston) 30

31. Acknowledgments Shaun Patel, Boston University Emad Eskandar, MGH 31