  This is a summary of the methods we used to analyse the first IPTA Mock Data
Challenge (MDC), and the obtained results. We have used a Bayesian analysis in
the time domain, accelerated using the recently developed ABC-method which
consists of a form of lossy linear data compression. The TOAs were first
processed with Tempo2, where the design matrix was extracted for use in a
subsequent Bayesian analysis. We used different noise models to analyse the
datasets: no red noise, red noise the same for all pulsars, and individual red
noise per pulsar. We sampled from the likelihood with four different samplers:
"emcee", "t-walk", "Metropolis-Hastings", and "pyMultiNest". All but emcee
agreed on the final result, with emcee failing due to artefacts of the
high-dimensionality of the problem. An interesting issue we ran into was that
the prior of all the 36 (red) noise amplitudes strongly affects the results. A
flat prior in the noise amplitude biases the inferred GWB amplitude, whereas a
flat prior in log-amplitude seems to work well. This issue is only apparent
when using a noise model with individually modelled red noise for all pulsars.
Our results for the blind challenges are in good agreement with the injected
values. 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 GWB
spectral 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 some
covariance between the signal and the red noise: if we constrain the GWB
spectral 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}].
