Definitions, Summary, and Some Issues

Summary of Some Statistical Issues

In terms of statistical ideas, I would make a very broad distinction between two prominent sets of problems at this conference. First there are a number of problems in which the main feature is a very large amount of data, requiring new methods and considerable computing power. An example that has already been used with success in astronomy is the use of false discovery rates in problems involv...

Distinguishing between clinical practice and clinical research: A Review of definitions and ethical issues

While Clinical research and clinical practice are closely related, distinguishing and maintaining the boundaries between them has form determining debates in contemporary bioethics. The most important implication of the research-practice distinction is to identify which clinical activities need review and oversight by research ethics committees. Adopting distinct approaches to clinical research...

Some Algebraic Definitions and Constructions

Definition 1. A monoid is a set M with an element e and an associative multiplication M×M −→ M for which e is a two-sided identity element: em = m = me for all m ∈ M . A group is a monoid in which each element m has an inverse element m, so that mm = e = mm. A homomorphism f : M −→ N of monoids is a function f such that f(mn) = f(m)f(n) and f(eM ) = eN . A “homomorphism” of any kind of algebrai...

1 Some definitions 13

.1.2 Some Definitions

The feasible region of this LP is in general, a convex polyhedron. Visualize it as a polygon in 2 dimensions, for simplicity. Now, maximizing yT b is the same as maximizing the projection of the vector y in the direction represented by vector b. For whichever direction b we choose, the point y that maximizes yT b cannot lie strictly in the interior of the feasible region. The reason is that, fr...