Bayesian Estimation

From a Bayesian perspective, we want to estimate a (posterior) distribution instead of simply generating a point estimate, i.e. we want $P(\theta |\mathcal{D})$. To do this, we rely on Bayes Rule, which necessitates the assertion of a prior distribution $P(\theta )$:

$$P(\theta |\mathcal{D})=\frac{P(\mathcal{D}|\theta )P(\theta )}{P(\mathcal{D})}.$$