Coherence: Signal Processing and Machine Learning

The reader will find new results for model fitting; for dimension reduction in models and ambient spaces; for detection, estimation, and space-time series analysis; for subspace averaging; and for uncertainty quantification. Throughout, the transformation invariances of statistics are clarified, geometries are illuminated, and null distributions are given where tractable. Shastic representations are emphasized, as these are central to Monte Carlo simulations. The appendices contain a comprehensive account of matrix theory, the SVD, the multivariate normal distribution, and many of the important distributions for coherence statistics.