  Taken traditionally as a no-go theorem against the theorization of inductive
processes, Duhem-Quine thesis may interfere with the essence of statistical
inference. This difficulty can be resolved by Micro-Macro duality \cite{Oj03,
Oj05} which clarifies the importance of specifying the pertinent aspects and
accuracy relevant to concrete contexts of scientific discussions and which
ensures the matching between what to be described and what to describe in the
form of the validity of duality relations. This consolidates the foundations of
the inverse problem, induction method, and statistical inference crucial for
the sound relations between theory and experiments. To achieve the purpose, we
propose here Large Deviation Strategy (LDS for short) on the basis of
Micro-Macro duality, quadrality scheme, and large deviation principle.
According to the quadrality scheme emphasizing the basic roles played by the
dynamics, algebra of observables together with its representations and
universal notion of classifying space, LDS consists of four levels and we
discuss its first and second levels in detail, aiming at establishing
statistical inference concerning observables and states. By efficient use of
the central measure, we will establish a quantum version of Sanov's theorem,
the Bayesian escort predictive state and the widely applicable information
criteria for quantum states in LDS second level. Finally, these results are
reexamined in the context of quantum estimation theory, and organized as
quantum model selection, i.e., a quantum version of model selection.
