Smith Amber D, Genz Alan, Freiberger David M, Belenky Gregory, Van Dongen Hans P A
Sleep and Performance Research Center, Washington State University, Spokane, Washington, USA.
Methods Enzymol. 2009;454:213-31. doi: 10.1016/S0076-6879(08)03808-1.
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 N(2) 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.
引入了一种新算法，用于基于多维参数空间有效地估计贝叶斯模型预测的置信区间。该算法通过用具有连续z值的正态曲线片段组成的样条来近似通过概率密度函数（pdf）的众数的一维切片，从而在模型预测的多维概率密度函数中定位最小置信区域的边界。这个计算效率高的过程（阶数为N）将置信区间上下限的估计简化为一个多维约束非线性优化问题，该问题可以用标准数值程序（阶数为N(2)或更低）来解决。通过一个五维示例说明了新算法的应用，该示例涉及为睡眠不足个体的认知性能缺陷的贝叶斯预测模型所做的预测计算95%置信区间。
