We present a probabilistic ranking model to identify the optimal treatment in multiple-response experiments. In contemporary practice, treatments are applied over individuals with the goal of achieving multiple ideal properties on them simultaneously. However, often there are competing properties, and the optimality of one cannot be achieved without compromising the optimality of another. Typically, we still want to know which treatment is the overall best. In our framework, we first formulate overall optimality in terms of treatment ranks. Then we infer the latent ranking that allow us to report treatments from optimal to least optimal, provided ideal desirable properties. We demonstrate through simulations and real data analysis how we can achieve reliability of inferred ranks in practice. We adopt a Bayesian approach and derive an associated Markov Chain Monte Carlo algorithm to fit our model to data. Finally, we discuss the prospects of adoption of our method as a standard tool for experiment evaluation in trials-based research.

翻译：我们提出了一种概率排序模型，用于识别多响应实验中的最优处理方案。在现代实践中，处理方案被应用于个体，旨在同时实现多个理想特性。然而，这些特性往往相互竞争，一个特性的最优性可能无法在不损害另一个特性的最优性的情况下实现。通常，我们仍希望了解哪种处理方案在整体上是最优的。在我们的框架中，我们首先根据处理方案的排序来定义整体最优性。然后，我们推断潜在排序，使我们能够根据理想的期望特性，从最优到最不优报告处理方案。通过模拟和实际数据分析，我们展示了如何在实践中实现推断排序的可靠性。我们采用贝叶斯方法，并推导出相关的马尔可夫链蒙特卡罗算法，以将模型拟合到数据。最后，我们讨论了将我们的方法作为基于试验的研究中实验评估标准工具的采用前景。