Bayesian Analysis of Pulse Trains With Hidden Missingness

In this paper we present a Bayesian approach for analysis of a pulse train that is corrupted by noise and missing pulses at unknown locations. The existence of missing pulses at unknown locations complicates the analysis and model selection process. This type of hidden missingness in the pulse data is different than the usual missing observations problem that arise in time-series analysis where standard methodology is available. We develop Bayesian methodology for dealing with the hidden missingness. Our development is based on Markov chain Monte Carlo methods and involves both inference and model selection.