Book chapter
Chapter 8 Efficient Computation of Confidence Intervals for Bayesian Model Predictions Based on Multidimensional Parameter Space
Methods in Enzymology, pp.213-231
Elsevier Science & Technology
2009
Handle:
https://hdl.handle.net/2376/106568
Abstract
A new algorithm is introduced to efficiently estimate confidence intervals for Bayesian model predictions based on multidimensional parameter space. The algorithm locates the boundary of the smallest confidence region in the multidimensional probability density function (pdf) for the model predictions by approximating a one-dimensional slice through the mode of the pdf with splines made of pieces of normal curve with continuous z values. This computationally efficient process (of order N) reduces estimation of the lower and upper bounds of the confidence interval to a multidimensional constrained nonlinear optimization problem, which can be solved with standard numerical procedures (of order N2 or less). Application of the new algorithm is illustrated with a five-dimensional example involving the computation of 95% confidence intervals for predictions made with a Bayesian forecasting model for cognitive performance deficits of sleep-deprived individuals.
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Details
- Title
- Chapter 8 Efficient Computation of Confidence Intervals for Bayesian Model Predictions Based on Multidimensional Parameter Space
- Creators
- Amber D Smith - Sleep and Performance Research Center, Washington State University, Spokane, WashingtonAlan Genz - Department of Mathematics, Washington State University, Pullman, WashingtonDavid M Freiberger - Sleep and Performance Research Center, Washington State University, Spokane, WashingtonGregory Belenky - Sleep and Performance Research Center, Washington State University, Spokane, WashingtonHans P.A Van Dongen - Sleep and Performance Research Center, Washington State University, Spokane, Washington
- Publication Details
- Methods in Enzymology, pp.213-231
- Academic Unit
- Mathematics and Statistics, Department of; Medical Education and Clinical Science, Department of
- Publisher
- Elsevier Science & Technology
- Identifiers
- 99900546869801842
- Language
- English
- Resource Type
- Book chapter