POPE: post optimization posterior evaluation of likelihood free models

Background: 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.

Results: We propose algorithms for post optimization posterior evaluation (POPE) of simulators. The algorithms
compute and visualize all simulations that can generate results of the same or better quality than the optimum,
subject to constraints. These optimization posteriors are desirable for a number of reasons among which are easy
interpretability, automatic parameter sensitivity and correlation analysis, and posterior predictive analysis. Our
algorithms are simple extensions to an existing simulation-based inference framework called approximate Bayesian
computation. POPE is applied two biological simulators: a fast and stochastic simulator of stem-cell cycling and a slow
and deterministic simulator of tumor growth patterns.

Conclusions: POPE allows the scientist to explore and understand the role that constraints, both on the input and
the output, have on the optimization posterior. As a Bayesian inference procedure, POPE provides a rigorous
framework for the analysis of the uncertainty of an optimal simulation parameter setting.