Approximate Bayesian inference based on Laplace approximation and quadrature methods have become increasingly popular for their efficiency at fitting latent Gaussian models (LGM), which encompass popular models such as Bayesian generalized linear models, survival models, and spatio-temporal models. However, many useful models fall under the LGM framework only if some conditioning parameters are fixed, as the design matrix would vary with these parameters otherwise. Such models are termed the conditional LGMs with examples in change-point detection, non-linear regression, etc. Existing methods for fitting conditional LGMs rely on grid search or Markov-chain Monte Carlo (MCMC); both require a large number of evaluations of the unnormalized posterior density of the conditioning parameters. As each evaluation of the density requires fitting a separate LGM, these methods become computationally prohibitive beyond simple scenarios. In this work, we introduce the Bayesian optimization sequential surrogate (BOSS) algorithm, which combines Bayesian optimization with approximate Bayesian inference methods to significantly reduce the computational resources required for fitting conditional LGMs. With orders of magnitude fewer evaluations compared to grid or MCMC methods, Bayesian optimization provides us with sequential design points that capture the majority of the posterior mass of the conditioning parameters, which subsequently yields an accurate surrogate posterior distribution that can be easily normalized. We illustrate the efficiency, accuracy, and practical utility of the proposed method through extensive simulation studies and real-world applications in epidemiology, environmental sciences, and astrophysics.

翻译：基于拉普拉斯近似和求积方法的近似贝叶斯推断因其拟合潜在高斯模型（LGM）的高效性而日益流行，这类模型涵盖贝叶斯广义线性模型、生存模型和时空模型等常见模型。然而，许多有用的模型仅在固定某些条件参数时才属于LGM框架，否则设计矩阵会随这些参数变化。这类模型被称为条件LGM，其示例包括变点检测和非线性回归等。现有拟合条件LGM的方法依赖网格搜索或马尔可夫链蒙特卡洛（MCMC）；两者均需对条件参数的未归一化后验密度进行大量评估。由于每次密度评估需要拟合独立的LGM，这些方法在简单场景之外会变得计算上不可行。本文提出贝叶斯优化序贯代理（BOSS）算法，该方法将贝叶斯优化与近似贝叶斯推断方法相结合，显著降低了拟合条件LGM所需的计算资源。与网格或MCMC方法相比，贝叶斯优化以数量级更少的评估次数为我们提供序贯设计点，这些设计点捕获了条件参数后验质量的主要部分，进而生成易于归一化的精确代理后验分布。通过大量模拟研究以及在流行病学、环境科学和天体物理学中的实际应用，我们展示了所提方法的效率、准确性和实用价值。