![[Pi_monte_carlo_all.gif|300]] # Sampling Techniques https://ermongroup.github.io/cs228-notes/inference/sampling/ > [!question] Why Do We Need Sampling Techniques? > Humans are really bad at picking things truly randomly, and most programming languages rely on *pseudo-random number generators (PRNGs)* that approximate the properties of random sequences. > > Basically, the simple methods we use to generate “random” numbers just don’t hold up in more complicated situations. Statistical inference is the method of making decisions about the parameters of a population, based on random sampling. There is a lot of overlap with the field of [[machine learning]]. The **law of large numbers (LLN)** … ## Properties of Sampling Techniques ### Sample Replacement - [ ] Sampling with replacement - [ ] Sampling without replacement ### Dependence vs Independence We generally can’t independently sample from ## Types of Sampling Techniques ### Forward Sampling ## Random Sampling ## Monte Carlo Simulations Rely on repeated random *sampling* Instead of needing Posterior: The joint probability distribution of some parameters of interest, $\theta$, conditioned upon some data, $D$, and a model/hypothesis, $M$. - “joint a-posteriori probability distribution”