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 \pm 0.11 [ \times 10 ^ { -14 } ] , h _ { c } = 5.70 \pm 0.35 [ \times 10 ^ { -14 } ] , and h _ { c } = 6.91 \pm 1.72 [ \times 10 ^ { -15 } ] , and for the GWB spectral index we found \gamma = 4.28 \pm 0.20 , \gamma = 4.35 \pm 0.09 , and \gamma = 3.75 \pm 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 \pm 0.64 [ 10 ^ { -15 } ] , h _ { c } = 56.3 \pm 2.42 [ 10 ^ { -15 } ] , and h _ { c } = 4.83 \pm 0.50 [ 10 ^ { -15 } ] , with one-sided 2 \sigma upper-limits of : h _ { c } \leq 10.98 [ 10 ^ { -15 } ] , h _ { c } \leq 60.29 [ 10 ^ { -15 } ] , and h _ { c } \leq 5.65 [ 10 ^ { -15 } ] .