Funding agencies rely on peer review and expert panels to select the research deserving funding. Peer review has limitations, including bias against risky proposals or interdisciplinary research. The inter-rater reliability between reviewers and panels is low, particularly for proposals near the funding line. Funding agencies are also increasingly acknowledging the role of chance. The Swiss National Science Foundation (SNSF) introduced a lottery for proposals in the middle group of good but not excellent proposals. In this article, we introduce a Bayesian hierarchical model for the evaluation process. To rank the proposals, we estimate their expected ranks (ER), which incorporates both the magnitude and uncertainty of the estimated differences between proposals. A provisional funding line is defined based on ER and budget. The ER and its credible interval are used to identify proposals with similar quality and credible intervals that overlap with the funding line. These proposals are entered into a lottery. We illustrate the approach for two SNSF grant schemes in career and project funding. We argue that the method could reduce bias in the evaluation process. R code, data and other materials for this article are available online.

翻译：同侪审查有局限性,包括对风险提案或跨学科研究的偏见。审查者与小组之间的可靠性低,特别是在供资项目附近,审查者与小组之间的可靠性低。供资机构也日益认识到机会的作用。瑞士国家科学基金会(SNSF)对中层的好但非优秀提案采用彩票。在本条中,我们为评价进程采用巴耶斯等级模式。为了对建议进行排名,我们估计其预期等级(ER),其中既包括估计提案差异的规模,也包括不确定性。根据ER和预算确定了临时供资项目。ER及其可信的间隔用于确定质量相似、与供资项目周期相重叠的、质量相近和可信的建议。这些建议被输入到彩票中。我们要说明两个SNSF赠款计划在职业和项目筹资方面的做法。我们说,该方法可以减少评价过程中的偏差。可在线提供这一文章的R代码、数据和其他材料。