  Our aim is to present a fast and general Bayesian inference framework based
on the synergy between machine learning techniques and standard sampling
methods and apply it to infer the physical properties of clumpy dusty torus
using infrared photometric high spatial resolution observations of active
galactic nuclei. We make use of the Metropolis-Hastings Markov Chain Monte
Carlo algorithm for sampling the posterior distribution function. Such
distribution results from combining all a-priori knowledge about the parameters
of the model and the information introduced by the observations. The main
difficulty resides in the fact that the model used to explain the observations
is computationally demanding and the sampling is very time consuming. For this
reason, we apply a set of artificial neural networks that are used to
approximate and interpolate a database of models. As a consequence, models not
present in the original database can be computed ensuring continuity. We focus
on the application of this solution scheme to the recently developed public
database of clumpy dusty torus models. The machine learning scheme used in this
paper allows us to generate any model from the database using only a factor
10^-4 of the original size of the database and a factor 10^-3 in computing
time. The posterior distribution obtained for each model parameter allows us to
investigate how the observations constrain the parameters and which ones remain
partially or completely undetermined, providing statistically relevant
confidence intervals. As an example, the application to the nuclear region of
Centaurus A shows that the optical depth of the clouds, the total number of
clouds and the radial extent of the cloud distribution zone are well
constrained using only 6 filters.
