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.
Informatics Institute, University of Amsterdam, Amsterdam, The Netherlands. E.W.F.Meeds@uva.nl.
Edward
E
Meeds
School of Biological Sciences, University of California, Irvine, USA. mcah5a@gmail.com.
Michael
M
Chiang
Department of Mathematics, University of California, Irvine, USA. mary.lee@uci.edu.
Mary
M
Lee
School of Biological Sciences, University of California, Irvine, USA. olivier.cinquin@uci.edu.
Olivier
O
Cinquin
Department of Mathematics, University of California, Irvine, USA. lowengrb@math.uci.edu.
John
J
Lowengrub
Informatics Institute, University of Amsterdam, Amsterdam, The Netherlands. welling.max@gmail.com.|Donald Bren School of Informatics, University of California, Irvine, USA. welling.max@gmail.com.
Max
M
Welling
D000465:Algorithms; D001499:Bayes Theorem; D003110:Colonic Neoplasms / Q000378:metabolism / Q000473:pathology*; D003198:Computer Simulation; D006801:Humans; D008962:Models, Theoretical; D014411:Neoplastic Stem Cells / Q000378:metabolism / Q000473:pathology*; D011336:Probability; D015398:Signal Transduction; D055153:Stem Cell Niche; D013269:Stochastic Processes