Epilogue

David Ramírez, Ignacio Santamaría and Louis Scharf
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David Ramírez: Universidad Carlos III de Madrid
Ignacio Santamaría: Universidad de Cantabria
Louis Scharf: Colorado State University

Chapter 12 in Coherence, 2022, pp 345-346 from Springer

Abstract: Abstract Many of the results in this book have been derived from maximum likelihood reasoning in the multivariate normal model. This is not as constraining as it might appear, for likelihood in the MVN model actually leads to the optimization of functions that depend on sums and products of eigenvalues, which are themselves data dependent. Moreover, it is often the case that there is an illuminating Euclidean or Hilbert space geometry. Perhaps it is the geometry that is fundamental, and not the distribution theory that produced it. This suggests that geometric reasoning, detached from distribution theory, may provide a way to address vexing problems in signal processing and machine learning, especially when there is no theoretical basis for assigning a distribution to data. This suggestion is developed in more detail in the concluding epilogue to the book.

Keywords: Maximum likelihood; Geometric reasoning (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/978-3-031-13331-2_12

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