Functional data analysis

在这个信息时代，我们经常收集连续时间数据：至少在概念上，我们的数据集由函数组成，而不仅仅是真实的数字和向量。 例如，在实验室用跑轮小鼠进行的实验中，我们可以连续监测每只小鼠随时间变化的活动水平。 因此，对于每只老鼠，我们观察到一个描述轮子运行的函数。 我们可能感兴趣的是车轮运行速度，或者它如何与，例如，体重 对这些数据进行统计分析的挑战是功能数据分析（FDA）的领域。进化生物学中的一些问题最好通过FDA方法来回答。 例如，假设上面提到的轮跑小鼠在8周龄时被饲养用于快速轮跑。我们预计他们的后代在8周龄时也会是快速的车轮跑步者。但在其他年龄呢？也许他们的后代在各个年龄段都能跑得很快。 或者也许年轻时的快与年老时的慢并存--也就是说，年轻时的快与年老时的慢是有权衡的。 人们必须研究整个轮跑的生活史，以了解选择的影响，并应考虑其他因素，如体重和食物消耗。

In this information age, we often collect continuous time data:  at least conceptually our data sets consist of functions, rather than just real numbers and vectors.   For instance, in lab experiments with wheel-running mice, we can continuously monitor the activity level of each mouse as a function of time.  So for each mouse we observe a function that describes wheel-running.  We may be interested in the wheel-running speed, or how it relates to, e.g., body mass.  The challenges of statistical analyses of such data are the realm of functional data analysis (FDA).Some questions in evolutionary biology are best answered via the FDA approach.  For instance, suppose the above-mentioned wheel-running mice were bred for fast wheel-running at age 8 weeks. We would expect that their progeny would also be fast wheel runners at age 8 weeks. But what about at other ages? Perhaps their progeny would be fast wheel runners at all ages.  Or perhaps being fast when young goes with being slow when old - that is, there is a trade-off for fastness in youth.   One must look at the entire life history of wheel running to understand the effects of  selection, and one should take into account other factors such as body mass and food consumption.