Bayesian Circle Segmentation with Application to DNA Copy Number Alteration Detection

Several statistical approaches have been proposed to consider circumstances under which one universal distribution is not capable of fit- ting into the whole domain. This paper studies Bayesian detection of mul- tiple interior epidemic/square waves in the interval domain, featured by two identical statistical distributions at both ends. We introduce a simple dimension-matching parameter proposal to implement the sampling-based posterior inference for special cases where each segmented distribution on a circle has the same set of regulating parameters. Molecular biology research reveals that, cancer progression may involve DNA copy number alteration at genome regions and connection of two biologically inactive chromosome ends results in a circle holding multiple epidemic/square waves. A slight modification of a simple novel Bayesian change point identification algo- rithm, random grafting-pruning Markov chain Monte Carlo (RGPMCMC), is proposed by adjusting the original change point birth/death symmetric transition probability with a differ-by-one change point number ratio. The algorithm performance is studied through simulations with connection to DNA copy number alteration detection, which promises potential applica- tion to cancer diagnosis at the genome level.