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Explore the comparative effectiveness of field-level inference versus joint power spectrum and bispectrum analysis in cosmological parameter estimation through this 19-minute conference lecture. Examine how both methods perform similarly within the perturbative regime when constraining cosmological parameters, while discovering the critical importance of using correct likelihood functions in field-level inference. Learn why Gaussian field-level likelihood applied to mock data with non-Gaussian noise produces significant biases in cosmological parameter inference, whereas joint power spectrum and bispectrum analysis reliably recovers input parameters under Gaussian likelihood due to the central limit theorem. Understand the fundamental challenges that correct likelihood specification presents for extending field-level inference methods to smaller scales, even within perturbative regimes, and gain insights into the theoretical foundations that determine when field-level approaches truly provide advantages over traditional statistical methods in cosmological analysis.
