论文标题
最大稳定过程的变异推断
Variational inference for max-stable processes
论文作者
论文摘要
最大稳定过程为在一组空间位点观察到的空间极值建模提供了自然模型。然而，最大稳定数据的完全可能性推断会因可能性函数的形式而复杂，因为它包含在站点的所有分区上的总和。因此，随着站点数量和地点的数量和迅速计算的繁重，要越来越多的术语数量变得迅速增长。 我们提出了一种变异的推断方法，以解决有问题的总和。为了实现这一目标，我们首先提出一个分区分布的参数家族，可以从中取样分区。其次，我们与最大稳定模型一起优化了家族的参数，以找到数据最能支持的分区分布，并估算最大稳定模型参数。 在一项仿真研究中，我们表明我们的方法可以在更高的维度上完全推断出比以前的方法更高的推断，并且很容易适用于具有大量观察结果的数据集。此外，我们的方法很容易扩展到贝叶斯环境。代码可在https://github.com/lpandersson/maxstablevi.jl上找到。
Max-stable processes provide natural models for the modelling of spatial extreme values observed at a set of spatial sites. Full likelihood inference for max-stable data is, however, complicated by the form of the likelihood function as it contains a sum over all partitions of sites. As such, the number of terms to sum over grows rapidly with the number of sites and quickly becomes prohibitively burdensome to compute. We propose a variational inference approach to full likelihood inference that circumvents the problematic sum. To achieve this, we first posit a parametric family of partition distributions from which partitions can be sampled. Second, we optimise the parameters of the family in conjunction with the max-stable model to find the partition distribution best supported by the data, and to estimate the max-stable model parameters. In a simulation study we show that our method enables full likelihood inference in higher dimensions than previous methods, and is readily applicable to data sets with a large number of observations. Furthermore, our method can easily be extended to a Bayesian setting. Code is available at https://github.com/LPAndersson/MaxStableVI.jl.
