University of Waterloo, Department of Psychology, 200 University Ave. West, PAS 4020, Waterloo, Ontario, Canada N2L 3G1.
Cognition. 2013 Feb;126(2):285-300. doi: 10.1016/j.cognition.2012.10.010. Epub 2012 Nov 28.
We present a proposal-"The Sampling Hypothesis"-suggesting that the variability in young children's responses may be part of a rational strategy for inductive inference. In particular, we argue that young learners may be randomly sampling from the set of possible hypotheses that explain the observed data, producing different hypotheses with frequencies that reflect their subjective probability. We test the Sampling Hypothesis with four experiments on 4- and 5-year-olds. In these experiments, children saw a distribution of colored blocks and an event involving one of these blocks. In the first experiment, one block fell randomly and invisibly into a machine, and children made multiple guesses about the color of the block, either immediately or after a 1-week delay. The distribution of guesses was consistent with the distribution of block colors, and the dependence between guesses decreased as a function of the time between guesses. In Experiments 2 and 3 the probability of different colors was systematically varied by condition. Preschoolers' guesses tracked the probabilities of the colors, as should be the case if they are sampling from the set of possible explanatory hypotheses. Experiment 4 used a more complicated two-step process to randomly select a block and found that the distribution of children's guesses matched the probabilities resulting from this process rather than the overall frequency of different colors. This suggests that the children's probability matching reflects sophisticated probabilistic inferences and is not merely the result of a naïve tabulation of frequencies. Taken together the four experiments provide support for the Sampling Hypothesis, and the idea that there may be a rational explanation for the variability of children's responses in domains like causal inference.
我们提出了一个假设——“抽样假设”，该假设表明，幼儿反应的可变性可能是归纳推理的一种合理策略的一部分。具体来说，我们认为年轻的学习者可能会从解释观察到的数据的可能假设集中随机抽样，产生不同的假设，其频率反映了他们的主观概率。我们通过对 4 至 5 岁儿童进行的四项实验来检验抽样假设。在这些实验中，孩子们看到了一组彩色积木的分布和一个涉及其中一个积木的事件。在第一个实验中，一个积木随机且不可见地落入一台机器中，孩子们对积木的颜色进行了多次猜测，要么立即猜测，要么在一周后猜测。猜测的分布与积木颜色的分布一致，猜测之间的依赖关系随着猜测之间的时间间隔而减少。在实验 2 和 3 中，通过条件来系统地改变不同颜色的概率。如果幼儿是从可能的解释性假设集中进行抽样，那么他们的猜测应该与颜色的概率相吻合。实验 4 使用了一个更复杂的两步随机选择积木的过程，发现孩子们猜测的分布与该过程产生的概率相匹配，而不是与不同颜色的总体频率相匹配。这表明，儿童的概率匹配反映了复杂的概率推断，而不仅仅是对频率的简单计数结果。这四项实验共同为抽样假设提供了支持，同时也表明，在因果推理等领域，儿童反应的可变性可能存在合理的解释。
