# Bayesian Analysis ### Benefits I would argue that the most compelling benefit of Bayesian Analysis is that it is far more useful when you need to make **decisions**. Why is that that case? Well, out of the box the bayesian approach will provide: * Uncertainty quantification * Rich posterior distributions pertaining to the parameters of interest These **objects** can then be used in conjunction with *custom* decision rules; rules that are *tailored* to your specific problem! ### Key Ideas * What does Bayesian Analysis provide out of the box that a frequentist analysis does not? * A rich **posterior distribution**. * What does the posterior distribution that bayesian analysis provides allow us to do? * Quantify **uncertainty** in our estimates. * When conducting a Bayesian Analysis, what should you always start by doing? * Think about *how you data may have been generated*. * When trying to reduce a posterior distribution down to a single value, what aggregation/reduction technique is most appropriate? * The 95% least plausible value, because the mean does not take into account the *uncertainty* of the distribution. * When performing statistical inference, are we interested in payoffs or accuracy? * We are interested in payoffs, in other words, the results of the inference. * In Bayesian Inference, what do we think of our parameters as? * We think of them as **random variables** with prior and posterior distributions. * What is the Bayes Action? * The Bayes Action is the value that will minimize the **expected loss**: $\underset {\hat{\theta}} {\text{argmin}} \;\; E_{\theta} \big[ L(\theta, \hat{\theta}) \big]$ --- Date: 20220510 Links to: [Bayesian Inference](Bayesian%20Inference.md) Tags: References: Bayesian Methods for Hackers * []()