Bayesian data analysis techniques in noisy environments

Abstract

The Bayesian method, Ensemble Learning was newly applied to the problem of galaxy shape measurements and biased shear estimates. Based on Bayes' theorem, Ensemble Learning provides an alternative technique to derive approximate posterior distributions of individual galaxy shape measurements and shear estimates. Gravitational lensing describes the event when an astronomical body appears distorted as observed from a telescope due to foreground matter acting as a lens. Measuring the variations in the shape provides a direct measure of the shear that, if inferred with a high degree of accuracy, will provide a better understanding about the anatomy of our Universe. A lot of research has been conducted in an attempt to remove the bias in the measurements accredited to noise. Noise produces random pixel intensities that further distort the appearance of galaxies making the lensing signal very faint. Current galaxy shape measurement methods necessitate correction and calibration techniques to reach the required degree of accuracy. Ensemble Learning was applied for the first time to shed light onto the problem of bias currently reported in lensing. Chapter 2 provides a thorough explanation of the Bayesian method together with other standard techniques, mainly; Maximum Likelihood, Maximum A Posteriori and sampling methods. Previous research and results are provided in Chapter 3 whilst galaxy profile simulations are depicted in the beginning of Chapter 4. There onwards, different applications of Ensemble Learning were utilised on the simulated images, each providing insight on the bias problem and current methods' limitations. The research conducted in this thesis demonstrated that Bayesian methods arc sensitive to noisy pixels present in the data. Ensemble Learning demonstrated a slight improvement in all tests. This shows that whilst the approximate posterior distributions were still skewed, these recover some symmetry in comparison to the skewed likelihood distributions produced when noisy pixels propagate non-linearly into the observable galaxy shape parameters. Correction and calibration methods will, however, still be required for Ensemble Learning to reach the desired degree of accuracy. In conclusion, future shape measurement techniques should focus on deriving a convolution model-fitting algorithm with a linear function that converts pixels into galaxy shape measurements.