  Recent success in explaining several properties of the dusty torus around the
central engine of active galactic nuclei has been gathered with the assumption
of clumpiness. The properties of such clumpy dusty tori can be inferred by
analyzing spectral energy distributions (SEDs), sometimes with scarce sampling
given that large aperture telescopes and long integration times are needed to
get good spatial resolution and signal. We aim at using the information already
present in the data and the assumption of clumpy dusty torus, in particular,
the CLUMPY models of Nenkova et al., to evaluate the optimum next observation
such that we maximize the constraining power of the new observed photometric
point. To this end, we use the existing and barely applied idea of Bayesian
adaptive exploration, a mixture of Bayesian inference, prediction and decision
theories. The result is that the new photometric filter to use is the one that
maximizes the expected utility, which we approximate with the entropy of the
predictive distribution. In other words, we have to sample where there is
larger variability in the SEDs compatible with the data with what we know of
the model parameters. We show that Bayesian adaptive exploration can be used to
suggest new observations, and ultimately optimal filter sets, to better
constrain the parameters of the clumpy dusty torus models. In general, we find
that the region between 10 and 200 um produces the largest increase in the
expected utility, although sub-mm data from ALMA also prove to be useful. It is
important to note that here we are not considering the angular resolution of
the data, which is key when constraining torus parameters. Therefore, the
expected utilities derived from this methodology must be weighted with the
spatial resolution of the data.
