On the Field-Level Likelihood in Perturbation Theory

Explore the mathematical foundations of field-level likelihood calculations within the framework of perturbation theory in this comprehensive lecture delivered at the Galileo Galilei Institute. Delve into the theoretical underpinnings of how likelihood functions operate at the field level, examining their behavior and applications when analyzed through perturbative methods. Learn about the mathematical techniques used to evaluate field-level likelihoods, understand the role of perturbation theory in simplifying complex field calculations, and discover how these concepts apply to modern theoretical physics problems. Gain insights into the computational approaches for handling field-level statistical analysis, explore the relationship between field theory and statistical inference, and examine practical applications of these methods in contemporary research. The lecture covers advanced mathematical formulations, discusses the limitations and advantages of perturbative approaches, and provides a thorough examination of how field-level likelihood methods contribute to our understanding of complex physical systems.