Computing Bounds on the Expected Maximum of Correlated Normal Variables

Ross, Andrew M.

doi:10.1007/s11009-008-9097-z

Cited by 18 publications

(23 citation statements)

References 24 publications

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“…When suitably transformed, it can also be computed efficiently as a one-dimensional integral of a function of normal cumulative distribution functions. For details, see §4 of Ross (2003), which treats this computation under the name "the independent, different distributions case." Although sampling allocations n are generally discrete in nature, we may extend the function v continuously onto M + using the definition (4).…”

Section: Selection Decisionmentioning

confidence: 99%

Paradoxes in Learning and the Marginal Value of Information

Frazier

Powell

2010

Decision Analysis

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W e consider the Bayesian ranking and selection problem, in which one wishes to allocate an information collection budget as efficiently as possible to choose the best among several alternatives. In this problem, the marginal value of information is not concave, leading to algorithmic difficulties and apparent paradoxes. Among these paradoxes is that when there are many identical alternatives, it is often better to ignore some completely and focus on a smaller number than it is to spread the measurement budget equally across all the alternatives. We analyze the consequences of this nonconcavity in several classes of ranking and selection problems, showing that the value of information is "eventually concave," i.e., concave when the number of measurements of each alternative is large enough. We also present a new fully sequential measurement strategy that addresses the challenge that nonconcavity it presents.

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Section: Selection Decisionmentioning

confidence: 99%

Paradoxes in Learning and the Marginal Value of Information

Frazier

Powell

2010

Decision Analysis

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“…3(a)) and the correlation between the stage delays ( Fig. 3(b)) [7,8]. It can be observed that the increase in error in the standard deviation is more significant in both cases.…”

Section: Model Verificationmentioning

confidence: 85%

“…To estimate P D considering correlated SD i s, we approximate the overall pipeline delay (T P ) as a Gaussian random variable (with µ T and σ T estimated using (5)). Using this assumption P D is given by [7]:…”

Section: Estimation Of Yieldmentioning

confidence: 99%

“…The major source of error in the proposed modeling method is the assumption that the maximum of two Gaussian variables is also a Gaussian one (i.e. N n-1,n is Gaussian) [7,8]. This assumption is valid only for two uncorrelated variables [7,8].…”

Section: Model Verificationmentioning

confidence: 99%

“…N n-1,n is Gaussian) [7,8]. This assumption is valid only for two uncorrelated variables [7,8]. Hence, the errors in the estimation of the mean and the standard deviation are expected to increase with the increase in the number of pipeline stages ( Fig.…”

Section: Model Verificationmentioning

confidence: 99%

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Statistical Modeling of Pipeline Delay and Design of Pipeline under Process Variation to Enhance Yield in sub-100nm Technologies

Datta

Bhunia

Mukhopadhyay

et al.

Design, Automation and Test in Europe

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Approximate Dynamic Programming

Powell¹

2011

Wiley Series in Probability and Statistics

1,009

155

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This is my preface. I am going to explain why I wrote this book and who it is for. Chapter 1The challenges of dynamic programmingThe optimization of problems over time arises in many settings, ranging from the control of heating systems to managing entire economies. In between are examples including landing aircraft, purchasing new equipment, managing blood inventories, scheduling fleets of vehicles, selling assets, investing money in portfolios or just playing a game of tic-tac-toe or backgammon. These problems involve making decisions, then observing information, after which we make more decisions, and then more information, and so on. Known as sequential decision problems, they can be straightforward (if subtle) to formulate, but solving them is another matter.Dynamic programming has its roots in several fields. Engineering and economics tend to focus on problems with continuous states and decisions (these communities refer to decisions as controls), while the fields of operations research and artificial intelligence work primarily with discrete states and decisions (or actions). Problems that are modeled with continuous states and decisions (and typically in continuous time) are often addressed under the umbrella of "control theory" whereas problems with discrete states and decisions, modeled in discrete time, are studied at length under the umbrella of "Markov decision processes." Both of these subfields set up recursive equations that depend on the use of a state variable to capture history in a compact way. There are many high-dimensional problems such as those involving the allocation of resources that are generally studied using the tools of mathematical programming. Most of this work focuses on deterministic problems using tools such as linear, nonlinear or integer programming, but there is a subfield known as stochastic programming which incorporates uncertainty. Our presentation spans all of these fields.1 CHAPTER 1. THE CHALLENGES OF DYNAMIC PROGRAMMING

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Computing Bounds on the Expected Maximum of Correlated Normal Variables

Cited by 18 publications

References 24 publications

Paradoxes in Learning and the Marginal Value of Information

Paradoxes in Learning and the Marginal Value of Information

Statistical Modeling of Pipeline Delay and Design of Pipeline under Process Variation to Enhance Yield in sub-100nm Technologies

Approximate Dynamic Programming

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