Generalized species sampling priors with latent Beta reinforcements

Area of Science:

• Bayesian statistics
• Nonparametric modeling
• Species sampling sequences

Background:

• Popular Bayesian nonparametric priors rely on exchangeable species sampling sequences.
• Exchangeability is not always suitable for certain applications.
• Existing methods lack complete characterization of the joint process.

Purpose of the Study:

• Introduce a novel, probabilistically coherent family of non-exchangeable species sampling sequences.
• Provide a tractable predictive probability function with Beta-distributed weights.
• Characterize the theoretical clustering properties and compare them with existing processes.

Main Methods:

• Developed a novel family of non-exchangeable species sampling sequences.
• Utilized a sequence of independent Beta random variables for weighting.
• Proposed the use of this process as a prior in hierarchical Bayes modeling.
• Implemented a Markov Chain Monte Carlo (MCMC) sampler for posterior inference.

Main Results:

• The proposed non-exchangeable sequences offer a complete characterization of the joint process.
• Theoretical clustering properties were compared against Dirichlet Process and Poisson-Dirichlet processes.
• Simulation studies demonstrated the performance and robustness of the novel prior.
• Application to array CGH data successfully detected chromosomal aberrations in breast cancer.

Conclusions:

• The novel non-exchangeable species sampling sequences provide a flexible and coherent alternative to exchangeable priors.
• The proposed framework is suitable for hierarchical modeling and offers robust inference.
• The method shows promise for applications in genomics, such as detecting chromosomal aberrations.