Nhat-Minh Nguyen and Beatrice Tucci tell us about their recent work comparing the performance of field inference (FLI) and simulation based inference (SBI). In an apples to apples comparison, they find that FLI comfortably outperforms SBI, even in what is essentially the “best case scenario” for SBI.
Field level inference gives up on using “summary statistics” to construct a cosmological likelihood (e.g. the power spectrum, the bispectrum, the location of the BAO peak, voids, etc) and instead constructs the cosmological likelihood at the level of the field itself. In other words the likelihood step of a statistical analysis is done comparing the measured density field at each point in Fourier space to a model’s actual density field. This means the set of model “parameters” necessarily also includes the entire set of Fourier modes of the initial conditions. Then, for example, when one would then talk about the “maximum likelihood” parameters in a FLI inference, one is talking also about the maximum likelihood set of initial conditions.
One then does the rest of the statistical analysis more or less the same as if one is analysing a measured power spectrum, e.g. one has priors on the inferred parameters, one has the likelihood function, and one produces posterior probability distributions for all of the model parameters.
In this analysis they fixed all cosmological parameters except the overall amplitude of the initial density fluctuations, via σ8. This means they also restricted the set of initial density fluctuations to those with a certain spectral index, but varied over all sets of initial density fluctuations that do produce this spectral index. They then evolve the initial conditions forward in time using the LEFTfield framework and do the FLI analysis on the evolved field.
SBI however still uses summary statistics, in this case the power spectrum and bispectrum, but uses simulations to construct the likelihood, rather than making model based assumptions for what these statistics should look like.
In this analysis they are only comparing the performance of FLI and SBI at reconstructing the parameters of simulations, because the observed data in e.g. BOSS or DESI is only well-calibrated at the level of the power spectrum (and maybe the bispectrum?), but not the full non-linear density field that FLI can probe – and where its true improvements lie.
However, they find FLI outperforms SBI with error bars substantially smaller (by factors of 2-5 depending on the scales and simulations considered). This shows that if we could perform field level inference on current or future data sets, the level of constraints we could obtain would also be substantially improved (e.g, maybe even a 1σ deviation would become a 5σ detection!?)
Minh: https://minhmpa.github.io/
Cosmology Talks 