Abstract

Cumulative probability models are standard tools for analyzing ordinal response data. The cumulative probability models can however be very restrictive in practice because of the inherent homogeneous assumption. In this work we propose a new Bayesian model to analyze ordinal data collected in statistically designed experiments. In the proposed model, we assume that the intercepts on the latent variable representation of cumulative probability models are realizations of different Gaussian processes that satisfy an order condition. By doing this, the homogeneous assumption is relaxed. Moreover, the order condition guaranties a positive probability when predicting the result under an arbitrary experimental setting. We use the Bayesian non-homogeneous cumulative probability model to analyze a foam experiment by which this work is motivated. From the analysis, we obtain a better fit than fitting conventional cumulative probability models to the data.

摘要

累积概率模型是分析有序响应数据的标准工具。然而，由于固有的同质假设，累积概率模型在实践中可能非常严格。在这项工作中，我们提出了一个新的贝叶斯模型来分析在统计设计的实验中收集的序数数据。在所提出的模型中，我们假设累积概率模型的潜在变量表示上的截距是满足顺序条件的不同高斯过程的实现。通过这样做，同质假设被放松了。此外，在任意实验设置下预测结果时，顺序条件保证了正概率。我们使用贝叶斯非齐次累积概率模型来分析激发这项工作的泡沫实验。