If one is to judge by counts of citations of the fundamental paper (Dempster in JRSSB 39: 1–38, 1977), EM algorithms are a runaway success. But it is surprisingly easy to find published applications of EM that are unnecessary, in the sense that there are simpler methods available that will solve the relevant estimation problems. In particular, such problems can often be solved by the simple expedient of submitting the observed-data likelihood (or log-likelihood) to a general-purpose routine for unconstrained optimization. This can dispense with the need to derive and code (or modify) the E and M steps, a process which can sometimes be laborious or error-prone. Here, I discuss six such applications of EM in some detail, and in an appendix describe briefly some others that have already appeared in the literature. Whether these are atypical of applications of EM seems an open question, although one that may be difficult to answer; this question is of relevance to current practice, but may also be of historical interest. But it is clear that there are problems traditionally solved by EM (e.g. the fitting of finite mixtures of distributions) that can also be solved by other means. It is suggested that, before going to the effort of devising an EM algorithm to use on a new problem, the researcher should consider whether other methods (e.g. direct numerical maximization or an MM algorithm of some other kind) may be either simpler to implement or more efficient.

如果要通过对基础论文的引用次数来判断（Dempster in JRSSB 39：1-38，1977年），则EM算法是成功的捷径。但是，从某种意义上说，找到可用的更简单的方法来解决相关的估计问题，这是令人惊讶的容易找到不必要的已公开的EM应用程序。特别是，通常可以通过将观察数据的可能性（或对数似然性）提交给通用例程进行无约束优化的简单简便方法来解决此类问题。这可以免除导出和编码（或修改）E和M步骤的需要，该过程有时可能很费力或容易出错。在这里，我将详细讨论EM的六个此类应用程序，并在附录中简要描述文献中已经出现的其他一些应用程序。尽管这些可能难以回答，但这些是否是EM应用程序的非典型性似乎是一个悬而未决的问题。这个问题与当前的实践有关，但也可能具有历史意义。但是很明显，传统上有一些问题可以通过EM解决（例如，分布的有限混合的拟合），也可以通过其他方式解决。建议在尝试设计用于新问题的EM算法之前，研究人员应考虑其他方法（例如直接数值最大化或其他类型的MM算法）是否可能更易于实现或更高效。但是很明显，传统上有一些问题可以通过EM解决（例如，分布的有限混合的拟合），也可以通过其他方式解决。建议在尝试设计用于新问题的EM算法之前，研究人员应考虑其他方法（例如直接数值最大化或其他类型的MM算法）是否可能更易于实现或更高效。但是很明显，传统上有一些问题可以通过EM解决（例如，分布的有限混合的拟合），也可以通过其他方式解决。建议在尝试设计用于新问题的EM算法之前，研究人员应考虑其他方法（例如直接数值最大化或其他类型的MM算法）是否可能更易于实现或更高效。