The `Jacobi prior' is an alternative Bayesian method for predictive models. It performs better than well-known methods such as Lasso, Ridge, Elastic Net, and MCMC-based Horse-Shoe Prior, particularly in terms of prediction accuracy and run-time. This method is implemented for Gaussian process classification, adeptly handling a nonlinear decision boundary. The Jacobi prior demonstrates its capability to manage partitioned data across global servers, making it highly useful in distributed computing environments. Additionally, we show that the Jacobi prior is more than a hundred times faster than these methods while maintaining similar predictive accuracy. As the method is both fast and accurate, it is advantageous for organisations looking to reduce their environmental impact and meet ESG standards. To demonstrate the effectiveness of the Jacobi prior, we conducted a detailed simulation study with four experiments focusing on statistical consistency, accuracy, and speed. We also present two empirical studies: the first evaluates credit risk by analysing default probability using data from the U.S. Small Business Administration (SBA), and the second uses the Jacobi prior for classifying stars, quasars, and galaxies in a three-class problem using multinomial logit regression on data from the Sloan Digital Sky Survey. Different filters were used as features in this study. All codes and datasets for this paper are available in the following GitHub repository : https://github.com/sourish-cmi/Jacobi-Prior/

翻译：雅可比先验是一种用于预测模型的替代性贝叶斯方法。其在预测精度和运行时间方面均优于Lasso、Ridge、Elastic Net以及基于MCMC的马蹄铁先验等知名方法。该方法已实现用于高斯过程分类，能够有效处理非线性决策边界。雅可比先验展现了其管理跨全局服务器分区数据的能力，使其在分布式计算环境中极具应用价值。此外，我们证明雅可比先验在保持相近预测精度的同时，运行速度比上述方法快百倍以上。由于该方法兼具快速与准确的特点，对于旨在减少环境影响并满足ESG标准的机构具有显著优势。为验证雅可比先验的有效性，我们开展了包含四个实验的详细模拟研究，重点关注统计一致性、精度与速度。我们还呈现了两项实证研究：第一项通过分析美国小企业管理局（SBA）数据评估违约概率以进行信用风险评价；第二项使用雅可比先验，基于斯隆数字巡天数据，通过多项逻辑回归对恒星、类星体与星系进行三分类研究，其中采用了不同滤波器作为特征。本文所有代码与数据集均可在以下GitHub仓库获取：https://github.com/sourish-cmi/Jacobi-Prior/