  In many domains, scientists build complex simulators of natural phenomena
that encode their hypotheses about the underlying processes. These simulators
can be deterministic or stochastic, fast or slow, constrained or unconstrained,
and so on. Optimizing the simulators with respect to a set of parameter values
is common practice, resulting in a single parameter setting that minimizes an
objective subject to constraints. We propose a post optimization posterior
analysis that computes and visualizes all the models that can generate equally
good or better simulation results, subject to constraints. These optimization
posteriors are desirable for a number of reasons among which easy
interpretability, automatic parameter sensitivity and correlation analysis and
posterior predictive analysis. We develop a new sampling framework based on
approximate Bayesian computation (ABC) with one-sided kernels. In collaboration
with two groups of scientists we applied POPE to two important biological
simulators: a fast and stochastic simulator of stem-cell cycling and a slow and
deterministic simulator of tumor growth patterns.
