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Bayes' theorem is a simple algebraic consequence of conditional probability. Yet, its consequences are critical to philosophy, society, and technology. Starting from its simple derivation, we will show how its interpretation in terms of base rates (priors) and class-conditional likelihoods illuminates everyday problems in medicine and law, and provides signal processing, communications, machine learning, model selection, and other applications of statistics with powerful classification and estimation tools. Next, we will briefly examine some of the ways in which this theorem can be adopted to include multiple attributes, contexts, hypotheses, and levels of risk. Methods derived from or related to Bayes’ theorem include minimax, maximum-a posteriori (MAP), expectation maximization (EM), Markov random fields, hidden Markov models, the Kalman filter, the Viterbi algorithm, and Bayesian Belief Networks.
Mehmet Vurkaç is currently an Assistant Professor in the Department of Electrical Engineering & Renewable Energy at the Oregon Institute of Technology. He completed his Ph.D. in Electrical & Computer Engineering at Portland State University in 2011. Vurkaç has a B.A. in Math-Physics from Whitman College (1993), and an M.S. in ECE from Portland State University (1999). He has worked in the music industry (Roland Corp.) for four years as a hardware engineer, and served as an adjunct instructor at PSU’s ECE department (2004–09) and at Whitman College in the Music Department (Sound Synthesis, 1994). His dissertation research was in Neural Networks, Reconstructability Analysis, and Computational Ethnomusicology. His current research is in tempo-tracking and onset detection for Afro-Brazilian music in which Eurocentric priors for timing and accent structure do not always hold., Publications:
- On the Need for Clave-Direction Analysis: A New Arena for Educational and Creative Applications of Music Technology. Journal of Music, Technology and Education. Volume 4, Number 1, pp. 27–46, August, 2011.
- A Cross-Cultural Grammar for Temporal Harmony in Afro-Latin Musics: Clave, Partido-Alto and Other Timelines. Current Musicology. Number 94, Accepted, Fall 2012.
Bayesian statistical decision theory -- Applications, Machine learning, Statistical decision, Pattern recognition systems
Statistical Models | Statistical Theory
Vurkaç, Mehmet, "Bayesian and Related Methods: Techniques Based on Bayes' Theorem" (2012). Systems Science Friday Noon Seminar Series. 49.