High redshift ΛCDM cosmology: To bin or not to bin?

We construct observational Hubble H(z) and angular diameter distance DA(z) mock data collected in redshift bins with baseline Planck ΛCDM input values, before fitting the ΛCDM model to study evolution of probability density functions (PDFs) of best fit cosmological parameters (H0,Ωm,Ωk) across the bins. We find that PDF peaks only agree with the input parameters in low redshift (z≲1) bins for H(z) and DA(z) constraints, and in all redshift bins when H(z) and DA(z) constraints are combined. When input parameters are not recovered, we observe that PDFs exhibit non-Gaussian tails towards larger Ωm values and shifts to (less pronounced) peaks at smaller Ωm values. This flattening of the PDF is expected as H(z) and DA(z) observations only constrain combinations of cosmological parameters at higher redshifts, so uniform PDFs are expected. Our analysis leaves us with a choice to bin high redshift data in the knowledge that it may be unlikely to recover Planck values, or conduct full sample analysis that biases ΛCDM inferences to the lower redshift Universe.