This paper reviews Monte Carlo methods for Bayesian inference, focusing on their application in experimental physics. The key idea is to approximate integrals over posterior distributions using stochastic sampling. The paper discusses various Monte Carlo algorithms, including rejection sampling, importance sampling, and Markov chain Monte Carlo (MCMC) methods. It provides theoretical justification and practical advice for implementing these methods, emphasizing the importance of choosing an appropriate proposal distribution. The paper begins with an introduction to Bayesian inference and the need for numerical integration when analytical solutions are not available. It then presents a model inspired by the Pierre Auger experiment, where the goal is to infer parameters from a complex likelihood function. The paper explains how Monte Carlo methods can be used to approximate the posterior distribution, which is often intractable analytically. The paper then discusses the Monte Carlo principle, explaining how stochastic sampling can be used to approximate integrals. It reviews basic sampling methods, including the inverse cumulative distribution function method, transformation method, and rejection sampling. It also introduces importance sampling, which is more flexible than rejection sampling and can be used with unnormalized targets. The paper then presents MCMC methods, focusing on the Metropolis-Hastings algorithm. It explains how MCMC can be used to generate samples from a target distribution, even in high dimensions. The paper discusses the importance of choosing an appropriate proposal distribution and the challenges of convergence and autocorrelation in MCMC sampling. The paper also addresses advanced MCMC methods, including adaptive MCMC and transdimensional problems. It discusses the challenges of label switching in models with symmetric likelihoods and presents solutions such as relabeling algorithms. The paper concludes with a discussion of practical implementation tips and the importance of careful tuning of MCMC parameters.This paper reviews Monte Carlo methods for Bayesian inference, focusing on their application in experimental physics. The key idea is to approximate integrals over posterior distributions using stochastic sampling. The paper discusses various Monte Carlo algorithms, including rejection sampling, importance sampling, and Markov chain Monte Carlo (MCMC) methods. It provides theoretical justification and practical advice for implementing these methods, emphasizing the importance of choosing an appropriate proposal distribution. The paper begins with an introduction to Bayesian inference and the need for numerical integration when analytical solutions are not available. It then presents a model inspired by the Pierre Auger experiment, where the goal is to infer parameters from a complex likelihood function. The paper explains how Monte Carlo methods can be used to approximate the posterior distribution, which is often intractable analytically. The paper then discusses the Monte Carlo principle, explaining how stochastic sampling can be used to approximate integrals. It reviews basic sampling methods, including the inverse cumulative distribution function method, transformation method, and rejection sampling. It also introduces importance sampling, which is more flexible than rejection sampling and can be used with unnormalized targets. The paper then presents MCMC methods, focusing on the Metropolis-Hastings algorithm. It explains how MCMC can be used to generate samples from a target distribution, even in high dimensions. The paper discusses the importance of choosing an appropriate proposal distribution and the challenges of convergence and autocorrelation in MCMC sampling. The paper also addresses advanced MCMC methods, including adaptive MCMC and transdimensional problems. It discusses the challenges of label switching in models with symmetric likelihoods and presents solutions such as relabeling algorithms. The paper concludes with a discussion of practical implementation tips and the importance of careful tuning of MCMC parameters.