Abstract Since the early 1970s, stellar population modelling has been one of the basic tools for understanding the physics of unresolved systems from observation of their integrated light. Models allow us to relate the integrated spectra (or colours) of a system with the evolutionary status of the stars of which it is composed and hence to infer how the system has evolved from its formation to its present stage. On average, observational data follow model predictions, but with some scatter, so that systems with the same physical parameters (age, metallicity, total mass) produce a variety of integrated spectra. The fewer the stars in a system, the larger is the scatter. Such scatter is sometimes much larger than the observational errors, reflecting its physical nature. This situation has led to the development in recent years (especially since 2010) of Monte Carlo models of stellar populations. Some authors have proposed that such models are more realistic than state-of-the-art standard synthesis codes that produce the mean of the distribution of Monte Carlo models. In this review, I show that these two modelling strategies are actually equivalent, and that they are not in opposition to each other. They are just different ways of describing the probability distributions intrinsic in the very modelling of stellar populations. I show the advantages and limitations of each strategy and how they complement each other. I also show the implications of the probabilistic description of stellar populations in the application of models to observational data obtained with high-resolution observational facilities. Finally, I outline some possible developments that could be realized in stellar population modelling in the near future.

中文翻译：

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恒星群体建模的随机性

摘要 自 1970 年代初以来，恒星群体建模一直是通过观察未解析系统的集成光来了解其物理特性的基本工具之一。模型使我们能够将一个系统的综合光谱（或颜色）与组成它的恒星的演化状态联系起来，从而推断该系统是如何从形成到目前阶段的演化过程。平均而言，观测数据遵循模型预测，但具有一定的分散性，因此具有相同物理参数（年龄、金属丰度、总质量）的系统会产生各种综合光谱。系统中的恒星越少，散射越大。这种散射有时比观测误差大得多，反映了它的物理性质。这种情况导致了近年来（尤其是 2010 年以来）恒星族群蒙特卡罗模型的发展。一些作者提出，这种模型比产生蒙特卡罗模型分布均值的最先进的标准合成代码更现实。在这篇评论中，我展示了这两种建模策略实际上是等效的，并且它们并不相互对立。它们只是描述恒星群体建模中固有的概率分布的不同方式。我展示了每种策略的优点和局限性以及它们如何相互补充。我还展示了恒星种群概率描述在模型应用于高分辨率观测设施获得的观测数据中的意义。最后，