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Epilogue

In: Coherence

Author

Listed:
  • David Ramírez

    (Universidad Carlos III de Madrid)

  • Ignacio Santamaría

    (Universidad de Cantabria)

  • Louis Scharf

    (Colorado State University)

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.

Suggested Citation

  • David Ramírez & Ignacio Santamaría & Louis Scharf, 2022. "Epilogue," Springer Books, in: Coherence, chapter 12, pages 345-346, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-13331-2_12
    DOI: 10.1007/978-3-031-13331-2_12
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