客户购买行为的双变量多层贝叶斯预测模型研究

现有客户购买行为预测模型无法兼顾购买行为随机性、异质性及变量相关性的特征.单变量多层贝叶斯统计模型虽然解决了随机性、异质性问题,然而仍然忽略客户购买间隔与购买金额之间的相关性.双变量多层贝叶斯模型假设客户购买间隔和金额服从联合对数正态分布,借助"正态-Wishart"共轭先验分布族对后验近似标准分布进行推导,利用马尔科夫链蒙特卡洛模拟方法中的吉布斯抽样和梅托普利斯海斯丁算法估计参数.模型不仅满足变量相关性特点,提高了客户购买行为预测的准确性,正态性假设还能对客户购买行为的波动性进行预测.对一高分子企业进行实证研究,并进一步针对模拟次数和统计变量数量进行参数优化,结果证明其适用性与准确性都优于传统预测方法.

A bivariate hierarchical Bayesian approach to predicting customer purchase behavior

Existing approaches to predicting customer purchase behavior cannot effectively track randomici ty, heterogeneity, and correlations between variables. Although randomicity and heterogeneity are considered in the univariate hierarchical Bayesian approach, correlation between purchase intervals and purchase amounts are still ignored. But in the hivariate hierarchical Bayesian approach, it is assumed that purchase intervals and purchase amounts obey joint logarithmic normal distribution. In this way, posterior approximate standard distribution was deduced with the aid of conjugate prior distribution. Parameters were estimated with Gibbs sampling and the Metropolis-Hastings algorithm in a Markov chain Monte Carlo method. After considering the characteristic of customer behavior synthetically, the hivariate hierarchical Bayesian approach was seen to not only improve the accuracy of forecasts Of customer behavior, hut also to offer a method for forecasting fluctuations of customer behavior based on the assumption of normal distribution. The model was applied in a polymer enterprise to perform further parametric optimization in terns of simulation times and statistical variables. The results show that the proposed algorithm is superior to traditional models in applicability and accuracy.