论文标题
在参数推断期间处理未知人口最小值的方法
Methods to Deal with Unknown Populational Minima during Parameter Inference
论文作者
论文摘要
有无数现象通过半无限分布家族进行更好的建模，其中许多现象在生存分析中进行了研究。当进行推断时，缺乏对人口最小值的知识成为一个问题，可以通过对其进行良好的猜测或手工制作初始参数的网格来解决这个问题，这些参数将对该特定问题有用。在分析一组样本时，这些解决方案是可以的，但是当有多个数据集时，这些解决方案变得不可行，并且逐案分析会太耗时。在本文中，我们提出了以算法，高效和/或简单方式处理人口最小值的方法。提出和分析了六种方法，其中两种具有完全的理论支持，但缺乏简单性。其他四个很简单，在非参数结果（例如迭代对数定律）中具有一些理论上的理由，并且在最大程度地提高可能性并能够回收数据集中初始参数的网格时，它们表现出非常好的结果。通过我们的结果，我们希望减轻从业者的推理过程，并希望这些方法最终将包含在软件包本身中。
There is a myriad of phenomena that are better modelled with semi-infinite distribution families, many of which are studied in survival analysis. When performing inference, lack of knowledge of the populational minimum becomes a problem, which can be dealt with by making a good guess thereof, or by handcrafting a grid of initial parameters that will be useful for that particular problem. These solutions are fine when analyzing a single set of samples, but it becomes unfeasible when there are multiple datasets and a case-by-case analysis would be too time consuming. In this paper we propose methods to deal with the populational minimum in algorithmic, efficient and/or simple ways. Six methods are presented and analyzed, two of which have full theoretical support, but lack simplicity. The other four are simple and have some theoretical grounds in non-parametric results such as the law of iterated logarithm, and they exhibited very good results when it comes to maximizing likelihood and being able to recycle the grid of initial parameters among the datasets. With our results, we hope to ease the inference process for practitioners, and expect that these methods will eventually be included in software packages themselves.
