Bayesian inference often relies on Markov chain Monte Carlo (MCMC) methods, particularly required for non-Gaussian data families. When dealing with complex hierarchical models, the MCMC approach can be computationally demanding in workflows that require repeated model fitting or when working with models of large dimensions with limited hardware resources. The Integrated Nested Laplace Approximations (INLA) is a deterministic alternative for models with non-Gaussian data that belong to the class of latent Gaussian models (LGMs), yielding accurate approximations to posterior marginals in many applied settings. The INLA method was implemented in C as a standalone program, inla, that is widely used in R through the INLA package. This paper introduces PyINLA, a dedicated Python package that provides a Pythonic interface directly to the inla program. Therefore, PyINLA enables specifying LGMs, running INLA-based inference, and accessing posterior summaries directly from Python while leveraging the established INLA implementation. We describe the package design and illustrate its use on representative models, including generalized linear mixed models, time series forecasting, disease mapping, and geostatistical prediction, demonstrating how deterministic Bayesian inference can be performed in Python using INLA in a way that integrates naturally with common scientific computing workflows.

翻译：贝叶斯推理通常依赖于马尔可夫链蒙特卡洛（MCMC）方法，尤其是对于非高斯数据族。当处理复杂分层模型时，MCMC方法在需要重复模型拟合的工作流中，或在使用有限硬件资源处理大规模模型时，计算负担可能较重。积分嵌套拉普拉斯近似（INLA）是一种针对非高斯数据且属于潜在高斯模型（LGM）类的确定性替代方法，能在许多应用场景中对后验边缘分布提供精确近似。INLA方法以C语言实现为独立程序inla，并通过INLA包在R中广泛使用。本文介绍PyINLA，这是一个专用的Python包，提供了直接面向inla程序的Python风格接口。因此，PyINLA支持在Python中直接指定LGM、运行基于INLA的推理并获取后验汇总结果，同时利用已有的INLA实现。我们描述了该包的设计，并通过典型模型（包括广义线性混合模型、时间序列预测、疾病映射和地统计预测）展示了其应用，从而证明如何利用INLA在Python中执行确定性贝叶斯推理，并以与常见科学计算工作流自然整合的方式实现。