This is an introduction to Bayesian inference with a focus on hierarchical models and hyper-parameters. We write primarily for an audience of Bayesian novices, but we hope to provide useful insights for seasoned veterans as well. Examples are drawn from gravitational-wave astronomy, though we endeavour for the presentation to be understandable to a broader audience. We begin with a review of the fundamentals: likelihoods, priors, and posteriors. Next, we discuss Bayesian evidence, Bayes factors, odds ratios, and model selection. From there, we describe how posteriors are estimated using samplers such as Markov Chain Monte Carlo algorithms and nested sampling. Finally, we generalise the formalism to discuss hyper-parameters and hierarchical models. We include extensive appendices discussing the creation of credible intervals, Gaussian noise, explicit marginalisation, posterior predictive distributions, and selection effects.

这是贝叶斯推理的简介，重点介绍层次模型和超参数。我们主要是为贝叶斯新手的读者撰写的，但我们也希望为经验丰富的退伍军人提供有用的见解。例子来自引力波天文学，尽管我们努力使演示文稿为广大读者所理解。我们首先回顾一下基本面：可能性，先验和后验。接下来，我们讨论贝叶斯证据，贝叶斯因子，优势比和模型选择。从那里，我们描述了如何使用采样器（例如Markov Chain Monte Carlo算法和嵌套采样）来估计后验。最后，我们推广形式主义以讨论超参数和层次模型。我们提供了广泛的附录，讨论了创建可信区间，高斯噪声，