  Model fitting is possibly the most extended problem in science. Classical
approaches include the use of least-squares fitting procedures and maximum
likelihood methods to estimate the value of the parameters in the model.
However, in recent years, Bayesian inference tools have gained traction.
Usually, Markov chain Monte Carlo methods are applied to inference problems,
but they present some disadvantages, particularly when comparing different
models fitted to the same dataset. Other Bayesian methods can deal with this
issue in a natural and effective way. We have implemented an importance
sampling algorithm adapted to Bayesian inference problems in which the power of
the noise in the observations is not known a priori. The main advantage of
importance sampling is that the model evidence can be derived directly from the
so-called importance weights -- while MCMC methods demand considerable
postprocessing. The use of our adaptive target, adaptive importance sampling
(ATAIS) method is shown by inferring, on the one hand, the parameters of a
simulated flaring event which includes a damped oscillation {and, on the other
hand, real data from the Kepler mission. ATAIS includes a novel automatic
adaptation of the target distribution. It automatically estimates the variance
of the noise in the model. ATAIS admits parallelisation, which decreases the
computational run-times notably. We compare our method against a nested
sampling method within a model selection problem.
