Markov Chain Monte Carlo (MCMC) algorithms have seen tremendous development and have been applied for a variety of problems leading to excellent inference. Notwithstanding, there still is a collection of difficult problems such as sampling from a multimodal distribution that require the development of new techniques. In case of multimodal distribution, the MCMC sampler may get stuck in a local mode, essentially never escaping to visit other modes of the distribution. Many MCMC-based methods have been proposed in the literature. The multiset sampler (MSS) is another MCMC algorithm designed to improve mixing by avoiding getting stuck in a local mode. The MSS algorithm is generalized by redefining the same with an explicit link between target distribution and sampling distribution. After giving a brief review of the MSS, the formulation of the generalized MSS (GMSS) and its properties are described. A simple implementation of the GMSS is then illustrated through two simulation examples. The role of parameters used in the GMSS is further investigated and an illustration is also given on how to find a good tuning parameter in a high-dimensional setting. Application of the GMSS algorithm is presented using an example of a breast cancer microarray study.
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