A Statistical Study of Wavelet Coherence for Stationary and Nonstationary Processes

The coherence function measures the correlation between a pair of random processes in the frequency domain. It is a well studied and understood concept, and the distributional properties of conventional coherence estimators for stationary processes have been derived and applied in a number of physical settings. In recent years the wavelet coherence measure has been used to analyse correlations between a pair of processes in the time-scale domain, typically in hypothesis testing scenarios, but it has proven resistant to analytic study with resort to simulations for statistical properties. As part of the null hypothesis being tested, such simulations invariably assume joint stationarity of the series. In this thesis two methods of calculating wavelet coherence have been developed and distributional properties of the wavelet coherence estimators have been fully derived. With the first method, in an analogous framework to multitapering, wavelet coherence is estimated using multiple orthogonal Morse wavelets. The second coherence estimator proposed uses time-domain smoothing and a single Morlet wavelet. Since both sets of wavelets are complex-valued, we consider the case of wavelet coherence calculated from discrete-time complex-valued and stationary time series. Under Gaussianity, the Goodman distribution is shown, for large samples, to be appropriate for wavelet coherence. The true wavelet coherence value is identified in terms of its frequency domain equivalent and degrees of freedom can be readily derived. The theoretical results are verified via simulations. The notion of a spectral function is considered for the nonstationary case. Particular focus is given to Priestley’s evolutionary process and a Wold-Cramér nonstationary representation where time-varying spectral functions can be clearly defined. Methods of estimating these spectra are discussed, including the continuous wavelet transform, which when performed with a Morlet wavelet and temporal smoothing is shown to bear close resemblance to Priestley’s own estimation procedure. The concept of coherence for bivariate evolutionary nonstationary processes is discussed in detail. In such situations it can be shown that the coherence function, as in the stationary case, is invariant of time. It is shown that for spectra that vary slowly in time the derived statistics of the temporally smoothed wavelet coherence estimator are appropriate. Further to this the similarities with Priestleys spectral estimator are exploited to derive distributional properties of the corresponding Priestley coherence estimator. A well known class of the evolutionary and Wold-Cramér nonstationary processes are the modulated stationary processes. Using these it is shown that bivariate processes can be constructed that exhibit coherence variation with time, frequency, and time-and-frequency. The temporally smoothed Morlet wavelet coherence estimator is applied to these processes. It is shown that accurate coherence estimates can be achieved for each type of coherence, and that the distributional properties derived under stationarity are applicable

University Scholar Series: Ed Cohen

Mental Health and Cultural Context in Vietnam On May 6, 2015, Dr. Ed Cohen spoke in the University Scholar Series hosted by Provost Andy Feinstein at the Dr. Martin Luther King, Jr. Library. In this presentation, Dr. Cohen explored current research about mental illness and approaches to treatment in Vietnam, in addition to this country’s world view about illness, wellness and emotional health. Cohen is an Associate Professor in the School of Social Work and a Co-Investigator of SJSU\u27s Social Work Education Enhancement Program in Vietnam.https://scholarworks.sjsu.edu/uss/1020/thumbnail.jp

\u3cem\u3eThe Practice of Research in Social Work.\u3c/em\u3e Rafael J. Engel and Russell K. Schutt.

Book note for Rafael J. Engel and Russell K. Schutt, The Practice of Research in Social Work. Thousand Oaks, Sage Publications, 2005. $74.95 papercover

Review of \u3cem\u3eCalifornia: America\u27s High Stakes Experiment.\u3c/em\u3e Peter Schrag. Reviewed by Bart Grossman.

Book review of John Gerring. Case Study Research: Principles and Practices. New York: Cambridge University Press, 2007. $70.00 hardcover,$24.99 papercover

Employee Participation in Pollution Reduction: Preliminary Analysis of the Toxics Release Inventory

Can the amount of toxic waste released into the environment by manufacturing facilities be reduced by formally involving employees in pollution prevention? Pursuant to the Pollution Prevention Act of 1990, the U.S. Environmental Protection Agency began requiring that manufacturers report human resource management strategies related to source reduction (reduction of waste at the source), as part of the Toxics Release Inventory (TRI). These strategies often involve employee participation in some form. Here we report the preliminary findings of an ongoing study of the effect of employee participation on source reduction, based on the 1991-1992 TRI database. We find, for example, that manufacturers using a certain combination of three formal employee participation practices had triple the reduction in emissions of manufacturers using none of these practices. We also discuss competing predictors of source reduction, and future research directions

The Medical Standard of Care in Mississippi

Commen

Rove

University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/156348/1/Thesis-Cohen.pd