The development of probabilistic inference in infants

尽管几十年来的研究强调了成年人在进行概率计算时面临的困难，但最近的大量研究表明，6个月大的婴儿就能进行基本的概率推理。也就是说，婴儿积极搜索和观察行为的证据表明，他们可以从样本到总体进行概括，推断出一个样本，比如4个白球和1个红球，更有可能是从一个以白球为主的盒子里随机抽取的，而不是从一个以红球为主的盒子里随机抽取的。诸如此类的概率推断代表了强大的学习能力：通过将特定实例（例如，样本中几个球的组成）扩展到更一般的情况（例如，整个群体）来进行推理，为快速学习提供了有效的引擎。尽管各种各样的实验表明婴儿会进行概率推理，但人们对他们如何进行这些推理知之甚少。这个研究项目的目标就是填补这一空白。首先，我将研究婴儿用来进行概率计算的输入类型，通过评估婴儿是使用数字表示还是连续量来进行概率推断。例如，在上面描述的实验中，婴儿可以用数字来表示群体中的比例，他们可能会认为它是“大约80个白球和20个红球”，或者相反，他们可能会认为它是连续的颜色区域“大约80%的白色和20%的红色”。之前的实验还没有检验婴儿使用哪一种表征来计算概率。其次，我将探讨婴儿是否可以使用概率进行预测。婴儿是观察一个群体并对该群体中的样本产生期望，还是他们只能通过观察一个群体和相应的样本来进行事后概率计算？解决这些关于婴儿如何计算概率的基本问题，将有助于深入了解这种能力有多复杂。

Despite decades of research highlighting the difficulties that adults face when making probability computations, a great deal of recent research has revealed that infants as young as 6 months can engage in rudimentary probabilistic reasoning. That is, evidence from infants' active search and looking behaviours suggests that they can make generalizations from samples to populations, inferring that a sample of, say, 4 white and 1 red balls is more likely to have been randomly drawn from a box of mostly white balls than a box of mostly red balls. Probabilistic inferences such as these represent a powerful learning ability: Reasoning by extending specific instances (e.g., the composition of a few balls in a sample) to more general cases (e.g., an entire population), provides an efficient engine for rapid learning. Although various experiments show that infants engage in probabilistic inference, very little is known about how they make these inferences. The goal of this research program is to fill this gap. First, I will investigate the kinds of input that infants use to make probability computations, by assessing whether infants use numerical representations or continuous quantities to make probabilistic inferences. For example, infants in the experiment described above could use numbers to represent the proportions in the population, they might perceive it as "approximately 80 white balls and 20 red balls" or, conversely, they might perceive it as continuous regions of colour "approximately 80% white stuff and 20% red stuff". Previous experiments have not yet examined which of these representations infants use to compute probabilities over. Second, I will explore whether infants can make predictions using probability. Do infants observe a population and develop expectations about what a sample from that population should look like, or are they are only capable of making after-the-fact probability computations, by observing both a population and a corresponding sample? Addressing these basic questions about how infants compute probability will provide insight into how sophisticated this ability is.