Learning to be Bayesian without Supervision

Bayesian methods are widely used throughout engineering for estimating quantities from corrupted measurements. Those that minimize the mean squared error (known as Bayes least squares, or BLS) are particularly widespread. These estimators are usually derived assuming explicit knowledge of the observation process (expressed as the conditional density of the observation given the quantity to be estimated), and the prior density over that quantity. Despite its appeal, this approach is often criticized for the reliance on knowledge of the prior distribution, since the true prior is usually not known, and in many cases one does not have data drawn from this distribution with which to approximate it. In this case, it must be learned from the same observed measurements that are available in the estimation problem.