Ranking of Multi-Response Experiment Treatments

TL;DR

This paper introduces a Bayesian probabilistic model for ranking treatments in multi-response experiments, addressing the challenge of competing properties and providing a reliable, data-driven method for treatment selection.

Contribution

It develops a novel Bayesian ranking framework with MCMC inference for multi-response treatment evaluation, filling a gap in current experimental analysis methods.

Findings

Reliable treatment rankings achieved through simulations and real data.

Bayesian approach effectively captures treatment trade-offs.

Potential for standardization in experimental treatment assessment.

Abstract

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.