Classical model selection via simulated annealing
Classical model selection via simulated annealing
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DOI：
10.1111/1467-9868.00399
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发表时间：
2003-01-01
影响因子：
5.8
通讯作者：
King, R
中科院分区：
文献类型：
--
作者：
Brooks, SP;Friel, N;King, R
统计分析的经典方法通常是基于找到最大化似然函数的模型参数值。在这种情况下，模型选择通常也是基于似然函数，但增加了一个惩罚项的参数的数量。虽然模型可以通过使用例如似然比检验来成对地进行比较，但是当需要比较多个模型时，已经提出了各种标准（诸如赤池信息标准）作为替代。实际上，模型选择的经典方法通常涉及最大化与每个竞争模型相关的似然函数，然后计算相应的标准值。然而，当大量的模型是可能的，这很快就变得不可行，除非一个方法，同时最大化的参数和模型空间是可用的。我们提出了一个扩展到传统的模拟退火算法，允许移动，不仅改变参数值，但也在竞争模型之间移动。因此，这种跨维模拟退火算法可以用于定位模型和参数，这些模型和参数使赤池信息准则等准则最小化，但在单个算法内，消除了运行大量模拟的需要。我们讨论了实现的transdimensional模拟退火算法，并使用模拟研究，以检查其性能在现实复杂的建模情况。我们说明了我们的想法与教学的例子的基础上分析的自回归时间序列和两个更详细的例子：一个变量选择逻辑回归和其他模型选择的综合回收数据的分析。
The classical approach to statistical analysis is usually based upon finding values for model parameters that maximize the likelihood function. Model choice in this context is often also based on the likelihood function, but with the addition of a penalty term for the number of parameters. Though models may be compared pairwise by using likelihood ratio tests for example, various criteria such as the Akaike information criterion have been proposed as alternatives when multiple models need to be compared. In practical terms, the classical approach to model selection usually involves maximizing the likelihood function associated with each competing model and then calculating the corresponding criteria value(s). However, when large numbers of models are possible, this quickly becomes infeasible unless a method that simultaneously maximizes over both parameter and model space is available. We propose an extension to the traditional simulated annealing algorithm that allows for moves that not only change parameter values but also move between competing models. This transdimensional simulated annealing algorithm can therefore be used to locate models and parameters that minimize criteria such as the Akaike information criterion, but within a single algorithm, removing the need for large numbers of simulations to be run. We discuss the implementation of the transdimensional simulated annealing algorithm and use simulation studies to examine its performance in realistically complex modelling situations. We illustrate our ideas with a pedagogic example based on the analysis of an autoregressive time series and two more detailed examples: one on variable selection for logistic regression and the other on model selection for the analysis of integrated recapture-recovery data.