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

Abstract

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.

arXiv commentThis article has been accepted for publication in MNRAS, published by Oxford University Press on behalf of the Royal Astronomical Society

References in corpus (28)

• dynesty: A Dynamic Nested Sampling Package for Estimating Bayesian Posteriors and Evidences
• Importance Nested Sampling and the MultiNest Algorithm
• Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems
• Inferring the eccentricity distribution
• Radial-Velocity Fitting Challenge. II. First results of the analysis of the data set
• Nested Sampling Methods
• Layered Adaptive Importance Sampling
• A Review of Multiple Try MCMC algorithms for Signal Processing
• Improving Population Monte Carlo: Alternative Weighting and Resampling Schemes
• On the use of marginal posteriors in marginal likelihood estimation via importance-sampling
• Bayesian Re-analysis of the Gliese 581 Exoplanet System
• Estimation of cosmological parameters using adaptive importance sampling
• An Empirically Derived Three-Dimensional Laplace Resonance in the Gliese 876 Planetary System
• Is there NaI in the atmosphere of HD 209458b? Effect of the centre-to-limb variation and Rossiter-McLaughlin effect in transmission spectroscopy studies
• Quantifying the Bayesian Evidence for a Planet in Radial Velocity Data
• The periodic variations of a white-light flare observed with ULTRACAM
• A population Monte Carlo scheme with transformed weights and its application to stochastic kinetic models
• Solar Bayesian Analysis Toolkit -- a new Markov chain Monte Carlo IDL code for Bayesian parameter inference
• Plasma sloshing in pulse-heated solar and stellar coronal loops
• Bayesian Model Selection and Extrasolar Planet Detection
• Discovery of WASP-113b and WASP-114b, two inflated hot-Jupiters with contrasting densities
• Progenitor properties of type II supernovae: fitting to hydrodynamical models using Markov chain Monte Carlo methods
• HADES RV program with HARPS-N at TNG. IX. A super-Earth around the M dwarf Gl686
• Two Jovian planets around the giant star HD202696. A growing population of packed massive planetary pairs around massive stars?
• Star-disk interaction in classical T Tauri stars revealed using wavelet analysis
• Detection of Photospheric Features in the Near-Infrared Spectrum of a Class 0 Protostar
• MCMC determination of the cosmic UV background at $z\simeq 0$ from H$\alpha$ fluorescence
• Dynamical modelling of disc vertical structure in superthin galaxy `UGC 7321' in braneworld gravity: An MCMC study

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