  Every experiment or observational study is made in a context. This context is
being explicitly considered in this book. To do so, a conceptual variable is
defined as any variable which can be defined by (a group of) researchers in a
given setting. Such variables are classified. Sufficiency and ancillarity are
defined conditionally on the context. The conditionality principle, the
sufficiency principle and the likelihood principle are generalized, and a
tentative rule for when one should not condition on an ancillary is motivated
by examples. The theory is illustrated by the case where a nuisance parameter
is a part of the context, and for this case, model reduction is motivated.
Model reduction is discussed in general from the point of view that there
exists a mathematical group acting upon the parameter space. It is shown that a
natural extension of this discussion also gives a conceptual basis from which
essential parts of the formalism of quantum mechanics can be derived. This
implies an epistemological basis for quantum theory, a kind of basis that has
also been advocated by part of the quantum foundation community in recent
years. Born's celebrated formula is shown to follow from a focused version of
the likelihood principle together with some reasonable assumptions on
rationality connected to experimental evidence. Some statistical consequences
of Born's formula are sketched. The questions around Bell's inequality are
approached by using the conditionality principle for each observer. The
objective aspects of the world are identified with the ideal inference results
upon which all observers agree (epistemological objectivity).
