Simulation-based inference has its own Dodelson–Schneider effect (but it knows that it does)

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Table 1

Describing the experiments we ran.

	$\hat{Σ} = Σ$ $\[\hat{\Sigma}=\Sigma\]$	$\hat{Σ} = S$ $\[\hat{\Sigma}=S\]$	$\hat{Σ} = S_{diag.}$ $\[\hat{\Sigma}=S_{\text {diag.}}\]$	NN
NPE	C, M	C, M	C, M	C, M
	(n_s)	(2n_s)	(2n_s)	(2n_s)
NLE	C, M	C, M	C, M	C, M
	(n_s)	(2n_s)	(2n_s)	(2n_s)

Notes. For each method of density-estimation SBI (NPE or NLE), a density estimator model (either a CNF, denoted ‘C’, or MAF, denoted ‘M’) was fitted to simulations compressed with $\hat{Σ}$ $\[\hat{\Sigma}\]$ or a neural network (NN). We also show multiples of the number of simulations, n_s, input into each experiment, depending on the compression methods. We ran 200 experiments with independent data vectors and covariance matrices (when estimated) for each combination in this table.

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