POPE: Post Optimization Posterior Evaluation of Likelihood Free Models

TL;DR

POPE introduces a novel posterior analysis method for likelihood-free models, enabling comprehensive visualization and interpretation of all parameter configurations that produce optimal or near-optimal simulation results.

Contribution

It develops a new ABC-based sampling framework with one-sided kernels for post-optimization posterior analysis of complex simulators.

Findings

Applied to biological simulators of stem-cell cycling and tumor growth.

Enabled automatic sensitivity and correlation analysis.

Provided interpretable visualization of model parameter spaces.

Abstract

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.