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EMPIRICAL BAYES THRESHOLDING: ADAPTING TO SPARSITY WHEN IT ADVANTAGEOUS TO DO SO
Silverman Bernard W. The Korean Statistical Society 2007 Journal of the Korean Statistical Society Vol.36 No.1
Suppose one is trying to estimate a high dimensional vector of parameters from a series of one observation per parameter. Often, it is possible to take advantage of sparsity in the parameters by thresholding the data in an appropriate way. A marginal maximum likelihood approach, within a suitable Bayesian structure, has excellent properties. For very sparse signals, the procedure chooses a large threshold and takes advantage of the sparsity, while for signals where there are many non-zero values, the method does not perform excessive smoothing. The scope of the method is reviewed and demonstrated, and various theoretical, practical and computational issues are discussed, in particularly exploring the wide potential and applicability of the general approach, and the way it can be used within more complex thresholding problems such as curve estimation using wavelets.
A Class of Starlike Functions Defined by the Dziok-Srivastava Operator
Silverman, Herb,Murugusundaramoorhty, Gangadharan,Vijaya, Kaliappan Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.1
A comprehensive class of starlike univalent functions defined by Dziok-Srivastava operator is introduced. Necessary and sufficient coefficient bounds are given for functions in this class to be starlike. Further distortion bounds, extreme points and results on partial sums are investigated.
Michael J. Silverman 한국음악치료학회 2013 한국음악치료학회지 Vol.15 No.2
Psychoeducation is one of the six established evidence-based treatments for psychiatric consumers while quantitative knowledge of social supports constitutes a consequential area of psychoeducation for people diagnosed with mental disorders. The purpose of this study was to determine the effects of educational music therapy on quantitative knowledge of social supports in acute care psychiatric patients utilizing a cluster randomized three-group design. Acute psychiatric inpatients (N=65) were cluster randomized by group to one of three conditions: educational music therapy, education, or recreational music therapy. Participants completed brief pre- and posttests within each single treatment condition. Although there were no between-group differences, there were consistent increases and improvements from pre-to posttest concerning all dependent measures. Participants in the educational music therapy condition tended to have the highest scores, regardless of dependent measure.Within the time constraints of a single session, it seems that music therapy can be utilized in an educational context to teach acute care psychiatric patients about social supports. Due to the engaging and creative medium, educational music therapy may be a motivating psychoeducational treatment modality for acute care psychiatric patients. Limitations of the study, implications for clinical practice, and suggestions for future controlled inquiry are provided.