Rich data generating mechanisms are ubiquitous in this age of information and require complex statistical models to draw meaningful inference. While Bayesian analysis has seen enormous development in the last 30 years, benefitting from the impetus given by the successful application of Markov chain Monte Carlo (MCMC) sampling, the combination of big data and complex models conspire to produce significant challenges for the traditional MCMC algorithms. We review modern algorithmic developments addressing the latter and compare their performance using numerical experiments.

中文翻译：

---

贝叶斯计算的近似方法

在这个信息时代，丰富的数据生成机制无处不在，需要复杂的统计模型来得出有意义的推论。尽管受益于马尔可夫链蒙特卡罗（MCMC）采样的成功应用，贝叶斯分析在过去30年取得了巨大的发展，但大数据和复杂模型的结合给传统的MCMC算法带来了巨大的挑战。我们回顾了解决后者的现代算法发展，并使用数值实验比较了它们的性能。