*J. C. Gower and G. B. Dijksterhuis*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198510581
- eISBN:
- 9780191708961
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198510581.003.0009
- Subject:
- Mathematics, Probability / Statistics

This chapter is concerned with generalizations where the two sets of configurations X1 and X2 are replaced by K sets, X1 , X2 ...
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This chapter is concerned with generalizations where the two sets of configurations X1 and X2 are replaced by K sets, X1 , X2 ,..., XK , each with its own transformation matrix T1 ,..., Tk . All the variants of two-sets Procrustes problems generalize. Different choices of Tk , scaling, weighting, and the optimization criteria are discussed.Less

This chapter is concerned with generalizations where the two sets of configurations **X**_{1} and **X**_{2} are replaced by *K* sets, **X**_{1} , **X**_{2} ,..., **X**_{K} , each with its own transformation matrix **T**_{1} ,..., **T**_{k} . All the variants of two-sets Procrustes problems generalize. Different choices of **T**_{k} , scaling, weighting, and the optimization criteria are discussed.

*Robert B. Gramacy and Herbert K. H. Lee*

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199694587
- eISBN:
- 9780191731921
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199694587.003.0008
- Subject:
- Mathematics, Probability / Statistics

Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization ...
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Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the simulator must be invoked both to determine the typical real‐valued response and to determine if a constraint has been violated, either for physical or policy reasons. We develop a statistical approach based on Gaussian processes and Bayesian learning to both approximate the unknown function and estimate the probability of meeting the constraints. A new integrated improvement criterion is proposed to recognize that responses from inputs that violate the constraint may still be informative about the function, and thus could potentially be useful in the optimization. The new criterion is illustrated on synthetic data, and on a motivating optimization problem from health care policy.Less

Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, *i.e*., when the simulator must be invoked both to determine the typical real‐valued response *and* to determine if a constraint has been violated, either for physical or policy reasons. We develop a statistical approach based on Gaussian processes and Bayesian learning to *both* approximate the unknown function and estimate the probability of meeting the constraints. A new integrated improvement criterion is proposed to recognize that responses from inputs that violate the constraint may still be informative about the function, and thus could potentially be useful in the optimization. The new criterion is illustrated on synthetic data, and on a motivating optimization problem from health care policy.

*Thomas A. Weber*

- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015738
- eISBN:
- 9780262298483
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015738.003.0001
- Subject:
- Mathematics, Probability / Statistics

This chapter first sets out the book’s purpose, which is to introduce continuous-time systems and methods for solving dynamic optimization problems at three different levels: single-person decision ...
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This chapter first sets out the book’s purpose, which is to introduce continuous-time systems and methods for solving dynamic optimization problems at three different levels: single-person decision making, games, and mechanism design. It presents a brief history of optimal control. An overview of the subsequent chapters is also presented.Less

This chapter first sets out the book’s purpose, which is to introduce continuous-time systems and methods for solving dynamic optimization problems at three different levels: single-person decision making, games, and mechanism design. It presents a brief history of optimal control. An overview of the subsequent chapters is also presented.

*Peter Grindrod CBE*

- Published in print:
- 2014
- Published Online:
- March 2015
- ISBN:
- 9780198725091
- eISBN:
- 9780191792526
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198725091.003.0007
- Subject:
- Mathematics, Analysis, Probability / Statistics

This chapter considers the problem of conditioning models and making forecasts as more and more information arrives, moving away from a subjective prior estimate for a model. It presents applications ...
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This chapter considers the problem of conditioning models and making forecasts as more and more information arrives, moving away from a subjective prior estimate for a model. It presents applications to sales forecasts for new product launches energy demand forecasting using smart metre data from domestic consumers.Less

This chapter considers the problem of conditioning models and making forecasts as more and more information arrives, moving away from a subjective prior estimate for a model. It presents applications to sales forecasts for new product launches energy demand forecasting using smart metre data from domestic consumers.