Amplitudes of the posterior primordial matter power-spectrum at different Fourier modes traced during the warm-up phase of the MCMC sampler for the LPT (upper panel) and PPT with annealing (lower panel). As can be seen, initially, modes perform a coherent drift towards the high probability region in posterior distribution and start oscillating around their fiducial values once the Markov chain has reached a stationary state. The fiducial values are reached faster with the PPT annealing, reducing the computational cost of the warm-up phase.