We construct observational Hubble $H(z)$ and angular diameter distance
$D_{A}(z)$ mock data with baseline Planck $\Lambda$CDM input values, before
fitting the $\Lambda$CDM model to study evolution of probability density
functions (PDFs) of best fit cosmological parameters $(H_0, \Omega_m,
\Omega_k)$ across redshift bins. We find that PDF peaks only agree with the
input parameters in low redshift ($z \lesssim 1$) bins for $H(z)$ and
$D_{A}(z)$ constraints, and in all redshift bins when $H(z)$ and $D_{A}(z)$
constraints are combined. When input parameters are not recovered, we observe
that PDFs exhibit non-Gaussian tails towards larger $\Omega_m$ values and
shifts to (less pronounced) peaks at smaller $\Omega_m$ values. This flattening
of the PDF is expected as $H(z)$ and $D_{A}(z)$ 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 we may be unlikely to recover Planck values, or conduct full
sample analysis that biases $\Lambda$CDM inferences to the lower redshift
Universe.
