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Connections to Statistical Inference and Epistemic Probabilities

In: Epistemic Processes

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  • Inge S. Helland

    (University of Oslo, Department of Mathematics)

Abstract

This chapter deals with theoretical issues that certainly can be more extensively discussed. The mathematics of the previous chapters is further developed, and some implied connections are indicated. My approach to quantum theory is first summarized and made precise in terms of positive operator valued measures and projection valued measures. Then it is shown that some of the concepts involved in this development also can be found again in the statistical theory of experimental design. A possible way to generalize statistical inference inspired by my version of quantum theory is sketched and indicated to be useful. The partial least squares regression history is told as an example where it is reasonable to develop reduced models from conceptual variables. Quantum probabilities can quite generally be seen as special cases of epistemic probabilities. Aspects of the opposite connection are also developed.

Suggested Citation

  • Inge S. Helland, 2021. "Connections to Statistical Inference and Epistemic Probabilities," Springer Books, in: Epistemic Processes, edition 2, chapter 0, pages 169-191, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-81923-1_6
    DOI: 10.1007/978-3-030-81923-1_6
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