利用集成嵌套拉普拉斯近似进行高效模型探索

中文摘要 AI 辅助

模型和变量选择是贝叶斯推断中的重要课题。特别是，在分层模型中，由于固定效应、随机效应和超参数的复杂结构，选择不同的这些成分可能很困难。在本文中，我们介绍了近似贝叶斯推断在分层贝叶斯模型的模型和变量选择中的应用。该方法基于在模型空间上应用马尔可夫链蒙特卡洛方法。具体而言，使用Metropolis-Hastings算法从模型索引集合中采样。通过这种方式，利用边际似然来计算接受概率，从而无需直接估计参数模型。为此，我们使用集成嵌套拉普拉斯近似（INLA），因为它能提供边际似然的精确估计，并且还能提供模型参数的后验边际估计。该方法不仅适用于变量选择，还适用于广泛的模型不确定性问题。为了展示该方法的潜力，我们开发了变量选择、变点模型和对数高斯Cox过程的示例。

英文摘要

Model and variable selection are important topics in Bayesian inference. In particular, the selection of different fixed, random effects and hyperparameters in hierarchical models can be difficult because of their complex structure. In this paper, we introduce the use of approximate Bayesian inference for model and variable selection for hierarchical Bayesian models. The approach is based on the application of Markov chain Monte Carlo methods on the model space. In particular, the Metropolis-Hastings algorithm is used to sample from the set of model indices. In this way, the marginal likelihood is used to compute the acceptance probability so that it is not required to estimate the parameter models directly. For this, the integrated nested Laplace approximation (INLA) is used because it provides accurate estimates of the marginal likelihood and it can also provide estimates of the posterior marginal of the model parameters. This method can be applied not only to variable selection but to a wide range of problems subject to model uncertainty. To illustrate the potential of this approach, examples on variable selection, changepoint models and log-Gaussian Cox processes are developed.

发表机构

• Universidad de Castilla-La Mancha（卡斯蒂利亚-拉曼恰大学）

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