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

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