Weiss-Weinstein bounds for various priors
Florian Xaver, Christoph F. Mecklenbräuker, Peter Gerstoft, Gerald Matz · 2016
We address analytic solutions of the Weiss-Weinstein bound (WWB), which lower bounds the mean squared error of Bayesian inferrers. The bound supports discrete, absolutely continuous, and singular continuous probability distributions, the latter corresponding to joint estimation and detection. We present new analytical solutions for truncated Gaussian, Laplace, categorical, uniform, and Bernoulli distributions. We focus on sparse signals modeled by a Laplace prior as used in Bayesian LASSO methods, priors of truncated Gaussian densities, and uninformative priors. In general, finding the tightest WWB of a model is a non-convex optimization problem. Hence, we show numerical examples of known and new WWBs to gain additional insight.