A Theory of Relative Statistical Decision

Wenbin Zhou

Alexander Semenovich Holevo

Fuyuhiko Tanaka

Decades ago, Holevo established quantum statistical decision theory. However, this formulation arises from theoretical interests and still is unsatisfactory compared with the classical counterpart. From the viewpoint in modern statistics and aiming at more rich framework, we reformulate quantum statistical decision theory.

Emmanuel M. Pothos, Richard M. Shiffrin, Jerome R. Busemeyer

Masanari Asano, Andrei Yu. Khrennikov, Masanori Ohya +2 more

Richard David Gill, Mădălin Guţǎ, Michael Nussbaum

The classical metric theory of statistical models (experiments) has recently been extended towards an asymptotic equivalence paradigm, allowing to classify and relate problems which are essentially infinite dimensional and ill-posed. Modern statistical concepts like these are also being integrated into the emerging field of quantum statistics, which is developing on the background of technological breakthroughs in quantum engineering. The workshop brought together leading experts in these areas, with the goal of establishing a common language, and fostering collaborations between mathematical statisticians, theoretical physicists and experimentalists.