FELLOW, IEEE, School of Electrical Engineering, Purdue University, West Lafayette, IN 47907.
IEEE Trans Pattern Anal Mach Intell. 1982 Feb;4(2):99-104. doi: 10.1109/tpami.1982.4767213.
This paper deals with the Bayesian method of choosing the best model for a given one-dimensional series among a finite number of candidates belonging to autoregressive (AR), moving average (MA), ARMA, and other families. The series could be either a sequence of observations in time as in speech applications, or a sequence of pixel intensities of a two-dimensional image. The observation set is not restricted to be Gaussian. We first derive an optimum decision rule for assigning the given observation set to one of the candidate models so as to minimize the average probability of error in the decision. We also derive an optimal decision rule so as to minimize the average value of the loss function. Then we simplify the decision rule when the candidate models are different Gaussian ARMA models of different orders. We discuss the consistency of the optimal decision rule and compare it with the other decision rules in the literature for comparing dynamical models.
本文讨论了在给定的有限数量的自回归（AR）、移动平均（MA）、ARMA 等候选模型中，为一维序列选择最佳模型的贝叶斯方法。该序列可以是时间序列中的观测序列，也可以是二维图像的像素强度序列。观测集不限于高斯分布。我们首先推导出一种最优决策规则，以便将给定的观测集分配给候选模型之一，从而最小化决策中的平均错误概率。我们还推导出一种最优决策规则，以便最小化损失函数的平均值。然后，当候选模型为不同阶数的不同高斯 ARMA 模型时，我们简化决策规则。我们讨论了最优决策规则的一致性，并将其与文献中的其他决策规则进行了比较，以比较动态模型。
