  Exponential varieties arise from exponential families in statistics. These
real algebraic varieties have strong positivity and convexity properties,
familiar from toric varieties and their moment maps. Among them are varieties
of inverses of symmetric matrices satisfying linear constraints. This class
includes Gaussian graphical models. We develop a general theory of exponential
varieties. These are derived from hyperbolic polynomials and their integral
representations. We compare the multidegrees and ML degrees of the gradient map
for hyperbolic polynomials.
