Latent slice sampling

The thesis develops a new and generic Markov chain Monte Carlo sampling methodology, naming latent slice sampling, that originates from slice sampling and is capable of efficient sampling. More specifically, three angles are studied to cover different types of random variables: (i). We develop a latent slice sampler for discrete variables by designing a transition probability function that can perform direct sampling without knowing the exact form of target distributions. (ii). We manage to derive a latent slice sampler for continuous variables which has the potential to be a more efficient alternative to the Metropolis-Hasting algorithm, obviates the need for a proposal distribution, and has no accept/reject component. (iii). We further propose a novel algorithm based on latent slice sampling methodology which copes well with multi-modal problem, which can approach well-studied problems from a different angle and provide new perspectives. All the methods bring clear gains, which demonstrate the benefits of applying latent slice sampling to improve Markov chain simulation.