RT Journal Article
T1 A Bayesian inference and model selection algorithm with an optimization scheme to infer the model noise power
A1 López Santiago, Javier
A1 Martino, Luca
A1 Vázquez López, Manuel Alberto
A1 Míguez Arenas, Joaquín
AB 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 (MCMC) methods are applied to inference problems, but they present some disadvantages, particularly when comparing different models fitted to the same data set. Other Bayesian methods can deal with this issue in a natural and effective way. We have implemented an importance sampling (IS) 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 IS 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 that 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 parallelization, which decreases the computational run-times notably. We compare our method against a nested sampling method within a model selection problem.
PB Oxford Academic
SN 0035-8711
YR 2021
FD 2021-11
LK https://hdl.handle.net/10016/39064
UL https://hdl.handle.net/10016/39064
LA eng
NO This work was supported by the Office of Naval Research (N00014-19-1-2226), Spanish Ministry of Science and Innovation (CLARA; RTI2018-099655-B-I00), and Regional Ministry of Education and Research for the Community of Madrid (PRACTICO; Y2018/TCS4705). This paper includes data collected by the Kepler mission and obtained from the MAST data archive at the Space Telescope Science Institute (STScI). Funding for the Kepler mission is provided by the NASA Science Mission Directorate. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. The authors acknowledges fruitful discussion with the referee to improve this paper.
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RD 1 jul. 2024