ABSTRACT
ABSTRACT In this chapter, a Bayesian framework is presented for analysis of pulse trains that are 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 from the usual missing observations problem that arises in time-series analysis where standard methodology is available. We develop a Bayesian methodology for dealing with the hidden missingness. Bayesian analysis of pulse trains with hidden missingness presents a structure
Control and
similar to the hidden Markov models considered in the literature. Our development is based on Markov Chain Monte Carlo (MCMC) methods and involves both inference and model selection. Analysis of the pulse trains also requires formal treatment of correlated noise terms. The presented framework deals with this issue via the use of MCMC methods and it allows for sequential processing of data by using a Bayesian dynamic linear model (DLM) setup.
