User-friendly tail bounds for sums of random matrices

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales. In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.Comment: Current paper is the version of record. The material on Freedman's inequality has been moved to a separate note; other martingale bounds are described in Caltech ACM Report 2011-0

Systems to support health technology assessment (HTA) in member states of the European union with limited institutionalization of HTA

OBJECTIVES: The aim of this study was to support health technology assessment (HTA) capacity building in Member States of the European Union with limited experience or without institutionalized HTA. The main output is a Handbook on HTA Capacity Building. METHODS: The methods used were worldwide surveys of (i) HTA organizations, (ii) information management units, and (iii) HTA educational programs. The results of two surveys (i & ii) were combined with expert opinion to produce the Handbook on HTA Capacity Building. RESULTS: Survey of HTA organizations (n = 41, response rate 35 percent). Most of the organizations were established by the government (61 percent), and all were not-for-profit. Working on HTA (80.5 percent) and doing research (63.4 percent) were the main lines of activity. Survey on information management units (n = 23, response rate 23 percent). Most (74.2 percent) of the responding HTA agencies reported having personnel dedicated to HTA information services. Survey on HTA educational programs (n = 48, response rate 60 percent). In total, nine Master of Science (MSc) programs were identified (three MSc in HTA and six MSc in HTA-related areas). Handbook on HTA Capacity Building. A group of twenty experts from thirteen countries developed the handbook. It consists of nine chapters focusing on HTA institutional development (structural setup, work processes, and visibility). CONCLUSIONS: Setting up organizational structures and establishing effective HTA programs that guide key policy decisions is a challenging task. There are no standard models or pathways. 'One size fits all' is not a useful principle because of the wide systemic and cultural differences between countries. The Handbook on HTA Capacity Building includes approaches for overall institutional development, especially in formulating objectives, setting up structures, and defining work processe