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Bayesian analysis of LISA data sets based on Markov chain Monte Carlo methodshas been shown to be a challenging problem, in part due to the complicatedstructure of the likelihood function consisting of several isolated localmaxima that dramatically reduces the efficiency of the sampling techniques.Here we introduce a new fully Markovian algorithm, a Delayed RejectionMetropolis-Hastings Markov chain Monte Carlo method, to efficiently explorethese kind of structures and we demonstrate its performance on selected LISAdata sets containing a known number of stellar-mass binary signals embedded inGaussian stationary noise.

Studying stellar binary systems with the Laser Interferometer Space Antenna using Delayed Rejection Markov chain Monte Carlo methods