This dissertation introduces an adaptive Markov chain Monte Carlo technique called Bayesian Adaptive Independence Sampling with Latent variables (BAIS+L). BAIS+L, which extends an earlier technique known as Bayesian Adaptive Independence Sampling, has been designed with multimodal target distributions in mind. The dissertation discusses the development of BAIS+L, including an approximation that makes it possible, before assessing its performance through a comparison to the Equi-Energy Sampler and an application to spin glass simulation. It finishes with a discussion of a modification of BAIS+L, which avoids the use of the approximation, at the expense of greater computational complexity.