  We show that the predicted probability distributions for any $N$-parameter
statistical model taking the form of an exponential family can be explicitly
and analytically embedded isometrically in a $N{+}N$-dimensional Minkowski
space. That is, the model predictions can be visualized as control parameters
are varied, preserving the natural distance between probability distributions.
All pairwise distances between model instances are given by the symmetrized
Kullback-Leibler divergence. We give formulas for these intensive symmetrized
Kullback Leibler (isKL) coordinate embeddings, and illustrate the resulting
visualizations with the Bernoulli (coin toss) problem, the ideal gas, $n$ sided
die, the nonlinear least squares fit, and the Gaussian fit. We highlight how
isKL can be used to determine the minimum number of parameters needed to
describe probabilistic data, and conclude by visualizing the prediction space
of the two-dimensional Ising model, where we examine the manifold behavior near
its critical point.

Statistical Mechanics;Computational Physics;Data Analysis, Statistics and Probability