Bayesian Computation in Astronomy: Novel methods for parallel and gradient-free inference

The goal of this thesis is twofold; introduce the fundamentals of Bayesian inference and computation focusing on astronomical and cosmological applications, and present recent advances in probabilistic computational methods developed by the author that aim to facilitate Bayesian data analysis for the next generation of astronomical observations and theoretical models. The first part of this thesis familiarises the reader with the notion of probability and its relevance for science through the prism of Bayesian reasoning, by introducing the key constituents of the theory and discussing its best practices. The second part includes a pedagogical introduction to the principles of Bayesian computation motivated by the geometric characteristics of probability distributions and followed by a detailed exposition of various methods including Markov chain Monte Carlo (MCMC), Sequential Monte Carlo (SMC), and Nested Sampling (NS). Finally, the third part presents two novel computational methods (Ensemble Slice Sampling and Preconditioned Monte Carlo) and their respective software implementations (zeus and pocoMC). [abridged]