Variational inference is a technique for approximating intractable posterior distributions in Bayesian inference. The basic idea is to construct a simpler, tractable distribution (the variational distribution) that approximates the true posterior distribution, and then optimize the parameters of this variational distribution to minimize the difference between the two distributions.

Markov chain Monte Carlo (MCMC) methods provide powerful and widely applicable algorithms for simulating from probability distributions, including complex and high-dimensional distributions.