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This is a summary of the methods we used to analyse the first IPTA Mock DataChallenge (MDC), and the obtained results. We have used a Bayesian analysis inthe time domain, accelerated using the recently developed ABC-method whichconsists of a form of lossy linear data compression. The TOAs were firstprocessed with Tempo2, where the design matrix was extracted for use in asubsequent Bayesian analysis. We used different noise models to analyse thedatasets: no red noise, red noise the same for all pulsars, and individual rednoise per pulsar. We sampled from the likelihood with four different samplers:"emcee", "t-walk", "Metropolis-Hastings", and "pyMultiNest". All but emceeagreed on the final result, with emcee failing due to artefacts of thehigh-dimensionality of the problem. An interesting issue we ran into was thatthe prior of all the 36 (red) noise amplitudes strongly affects the results. Aflat prior in the noise amplitude biases the inferred GWB amplitude, whereas aflat prior in log-amplitude seems to work well. This issue is only apparentwhen using a noise model with individually modelled red noise for all pulsars.Our results for the blind challenges are in good agreement with the injectedvalues. For the GWB amplitudes we found h_c = 1.03 +/- 0.11 [10^{-14}], h_c =5.70 +/- 0.35 [10^{-14}], and h_c = 6.91 +/- 1.72 [10^{-15}], and for the GWBspectral index we found gamma = 4.28 +/- 0.20, gamma = 4.35 +/- 0.09, and gamma= 3.75 +/- 0.40. We note that for closed challenge 3 there was quite somecovariance between the signal and the red noise: if we constrain the GWBspectral index to the usual choice of gamma = 13/3, we obtain the estimates:h_c = 10.0 +/- 0.64 [10^{-15}], h_c = 56.3 +/- 2.42 [10^{-15}], and h_c = 4.83+/- 0.50 [10^{-15}], with one-sided 2 sigma upper-limits of: h_c <= 10.98[10^{-15}], h_c <= 60.29 [10^{-15}], and h_c <= 5.65 [10^{-15}].

Analysis of the first IPTA Mock Data Challenge by the EPTA timing data analysis working group