  Markov Chain Monte Carlo approach is frequently used within Bayesian
framework to sample the target posterior distribution. Its efficiency strongly
depends on the proposal used to build the chain. The best jump proposal is the
one that closely resembles the unknown target distribution, therefore we
suggest an adaptive proposal based on Kernel Density Estimation (KDE). We group
parameters of the model according to their correlation and build KDE based on
the already accepted points for each group. We adapt the KDE-based proposal
until it stabilizes. We argue that such a proposal could be helpful in
applications where the data volume is increasing and in the hyper-model
sampling. We tested it on several astrophysical datasets (IPTA and LISA) and
have shown that in some cases KDE-based proposal also helps to reduce the
autocorrelation length of the chains. The efficiency of this proposal is
reduces in case of the strong correlations between a large group of parameters.
