  Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their
versatility in sampling from complicated probability distributions. However, as
the dimension of the distribution gets larger, the computational costs for a
satisfactory exploration of the sampling space become challenging. Adaptive
MCMC methods employing a choice of proposal distribution can address this issue
speeding up the convergence. In this paper we show an alternative way of
performing adaptive MCMC, by using the outcome of Bayesian Neural Networks as
the initial proposal for the Markov Chain. This combined approach increases the
acceptance rate in the Metropolis-Hasting algorithm and accelerate the
convergence of the MCMC while reaching the same final accuracy. Finally, we
demonstrate the main advantages of this approach by constraining the
cosmological parameters directly from Cosmic Microwave Background maps.
