百度迁徙规模指数构造方法反演

An Inversion of the Constitution of the Baidu Migration Scale Index

百度提供了迁徙规模指数以反映迁入或迁出某一特定地域的人口规模,成为经济地理科学与流行病学的重要研究依据。然而该指数仅为一个无量纲数,其构造方法目前尚未公开。该文将此指数假定为实际迁徙人口的可微函数映射,利用迁徙数据中的一个内蕴等式,反演出实际迁徙人口与该指数满足简单正比关系y=kx。通过迁徙人口的离散特征和费马−欧拉定理推导得到迁徙人口的高概率互质特性,结合真实数据进行参数估计,得到线性关系的比例系数k为3.24×10^(−5)。在全部数据记录上考察了内蕴等式的可信程度:当考虑舍入误差时,93.81%的市际迁徙记录、82.65%的市−省迁徙记录和84.87%的省际迁徙记录完全支持内蕴等式;其余违例记录的误差峰值为357人,对应相对误差约0.5%,轻微的违例程度显示这种线性映射模型是自洽的。

Baidu migration scale index represents the human migration scale of a specific area in China,and it has been used widely in geo-economics,demography,and epidemiology.Nowadays,Baidu migration index is adopted as a key data source for studying epidemic models of COVID-19.But the index is just a dimensionless number,its constitution method is still ambiguous.In this paper,the index is assumed as an elementary function mapping result of the real human migrate populations.According to a hidden equation existing in the data set,the mapping function is deduced to be a linear function y=kx.Another key phenomenon in the data set is the minimum interval of the migration index.All the migration index values and their differentials are exactly divisible by this interval.Through Fermat-Euler Theorem,we prove the coprimeness of the human migrate populations,and then the relationship between the minimum interval and minimum counting unit of the migrate populations is built,which means k=3.24×10^(−5).In the experiments,the migration records between 01/01/2020−04/30/2020 are examined to verify the correctness of the hidden equation:while the rounding error is considered,there about 93.81%of the city-to-city migration records,82.65%city-to-province migration records and 84.87%province-to-province migration records can support the equation exactly;the maximum absolute error of the violation records is 357 peoples,which corresponds to about 0.5%relative error.The verifications support the self-consistency of the proposed linear mapping function.