Weiss-Weinstein Bounds for Various Priors

Publication Type:

Conference Paper

Source:

SAM (2016)

URL:

sites/default/files/SAMpaperRevised.pdf

Abstract:

Abstract — 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.