Evaluating the Role of Simulation-Based Inference in Addressing Analytical Intractability in Modern Statistics

Posted: Oct 06, 2018

• Riley Perez
• Sophia Smith
• Owen Flores

Abstract

Modern statistical analysis increasingly confronts models characterized by analytically intractable likelihood functions, presenting fundamental challenges to traditional inference methodologies. This paper comprehensively evaluates simulation-based inference (SBI) as a transformative framework for addressing these limitations across diverse statistical contexts. We develop a novel classification schema for analytical intractability, identifying four distinct categories: computational complexity barriers, implicit model specifications, high-dimensional integration challenges, and non-standard data structures. Our methodological contribution centers on a unified SBI framework that integrates approximate Bayesian computation, neural density estimation, and likelihood-free variational inference within a coherent theoretical structure. Through extensive empirical investigations across synthetic and real-world datasets, we demonstrate that SBI methods achieve statistical efficiency comparable to exact inference in tractable scenarios while successfully extending inference capabilities to previously inaccessible model classes. Particularly noteworthy are our findings regarding the robustness of neural ratio estimation in high-dimensional parameter spaces and the surprising effectiveness of sequential Monte Carlo approaches for models with complex dependency structures. The research establishes practical guidelines for SBI implementation, identifies domain-specific performance characteristics, and delineates the boundaries of applicability for various SBI techniques. Our results substantiate SBI as not merely a computational convenience but as an essential methodological advancement that fundamentally expands the scope of statistical inquiry, enabling rigorous inference in problem domains previously considered statistically impenetrable.