  We search for a stochastic gravitational wave background (SGWB) generated by
a network of cosmic strings using six millisecond pulsars from Data Release 2
(DR2) of the European Pulsar Timing Array (EPTA). We perform a Bayesian
analysis considering two models for the network of cosmic string loops, and
compare it to a simple power-law model which is expected from the population of
supermassive black hole binaries. Our main strong assumption is that the
previously reported common red noise process is a SGWB. We find that the
one-parameter cosmic string model is slightly favored over a power-law model
thanks to its simplicity. If we assume a two-component stochastic signal in the
data (supermassive black hole binary population and the signal from cosmic
strings), we get a $95\%$ upper limit on the string tension of $\log_{10}(G\mu)
< -9.9$ ($-10.5$) for the two cosmic string models we consider. In extended
two-parameter string models, we were unable to constrain the number of kinks.
We test two approximate and fast Bayesian data analysis methods against the
most rigorous analysis and find consistent results. These two fast and
efficient methods are applicable to all SGWBs, independent of their source, and
will be crucial for analysis of extended data sets.
