A Bayesian inference and model selection algorithm with an optimisation scheme to infer the model noise power

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.

A likely magnetic activity cycle for the exoplanet host M dwarf GJ 3512

Current radial velocity data from specialized instruments contain a large amount of information that may pass unnoticed if their analysis is not accurate. The joint use of Bayesian inference tools and frequency analysis has been shown effective to reveal exoplanets but they have been used less frequently to investigate stellar activity. We intend to use radial velocity data of the exoplanet host star GJ 3512 to investigate its magnetic activity. Our study includes the analysis of the photometric data available. The main objectives of our work are to constrain the orbital parameters of the exoplanets in the system, to determine the current level of activity of the star and to derive an activity cycle length for it. An adaptive importance sampling method was used to determine the parameters of the exoplanets orbit. Generalized Lomb-Scargle periodograms were constructed with both radial velocity curve and photometric data. A careful analysis of the harmonic frequencies was conducted in each periodogram. Our fit to multiple Keplerian orbits constrained the orbital parameters of two giant gas planets orbiting the star GJ 3512. The host star showed an increase of its magnetic activity during the last observing campaign. The accurate fit of the radial velocity curve data to the multi-Keplerian orbit permitted to reveal the star rotation in the residuals of the best fit and estimate an activity cycle length of ~ 14 years.