Reduced-Dimensional Monte Carlo Maximum Likelihood for Latent Gaussian Random Field Models
Reduced-Dimensional Monte Carlo Maximum Likelihood for Latent Gaussian Random Field Models
复制标题
潜在高斯随机场模型的降维蒙特卡罗最大似然
DOI：
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复制
发表时间：
2019
影响因子：
2.4
通讯作者：
M. Haran
中科院分区：
文献类型：
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作者：
Jaewoo Park;M. Haran
摘要蒙特卡罗极大似然(MCML)为寻找潜变量模型的极大似然估计量(MLEs)提供了一种很好的方法。然而，当潜在变量是高维和相关的时，MCML算法的计算代价很高，就像潜在的高斯随机场模型的情况一样。潜在高斯随机场模型被广泛应用于建立灵活的回归模型和空间相关数据的内插等许多研究领域，如疾病建模中的计数数据分析和冰盖的无人值守卫星图像。通过使用基于投影的方法来降低随机效应的维度，我们提出了一种计算高效的MCML算法。我们开发了一种迭代方法来寻找有效的重要性函数；这通常是一个具有挑战性的问题，也是MCML算法在计算上可行的关键。我们发现，我们的方法既适用于连续(潜高斯过程)模型，也适用于离散域(潜高斯马尔可夫随机场)模型。我们举例说明了我们的方法在挑战模拟和真实数据示例中的应用，否则最大似然估计将是非常具有挑战性的。此外，我们研究了潜在变量模型的MCML方法中一个经常被忽视的挑战：在计算结果估计的标准误差和评估由此产生的可信区间是否提供名义覆盖方面的实际问题。因此，我们的研究为实现高维潜变量模型的MCML算法的细节提供了有用的见解。这篇文章的补充材料可以在网上找到。
Abstract Monte Carlo maximum likelihood (MCML) provides an elegant approach to find maximum likelihood estimators (MLEs) for latent variable models. However, MCML algorithms are computationally expensive when the latent variables are high-dimensional and correlated, as is the case for latent Gaussian random field models. Latent Gaussian random field models are widely used, for example, in building flexible regression models and in the interpolation of spatially dependent data in many research areas such as analyzing count data in disease modeling and presence-absence satellite images of ice sheets. We propose a computationally efficient MCML algorithm by using a projection-based approach to reduce the dimensions of the random effects. We develop an iterative method for finding an effective importance function; this is generally a challenging problem and is crucial for the MCML algorithm to be computationally feasible. We find that our method is applicable to both continuous (latent Gaussian process) and discrete domain (latent Gaussian Markov random field) models. We illustrate the application of our methods to challenging simulated and real data examples for which maximum likelihood estimation would otherwise be very challenging. Furthermore, we study an often overlooked challenge in MCML approaches to latent variable models: practical issues in calculating standard errors of the resulting estimates, and assessing whether resulting confidence intervals provide nominal coverage. Our study therefore provides useful insights into the details of implementing MCML algorithms for high-dimensional latent variable models. Supplementary materials for this article are available online.