Burn-in of the posterior matter power spectra from the inferred initial conditions from a BORG analysis. The colour scale shows the evolution of the matter power spectrum with the number of samples: the Markov chain is initialized with a Gaussian initial density field scaled by a factor 10⁻³ and the amplitudes of the power spectrum systematically drift towards the fiducial values. Monitoring this drift allows us to identify when the Markov chain approaches a stationary distribution and provides unbiased estimates of the target distribution. The dashed lines indicate the underlying power spectrum and the 1- and 2-σ cosmic variance limits. At the end of the warm-up phase, the algorithm recovers the true matter power spectrum in all range of Fourier modes.