In this thesis we create a program which samples subsea resistivity modelsfrom the a posteriori probability distribution based on marine controlled source electromagnetic (CSEM) data. In the ﬁrst part we create a draft version of the code which assumes that any subsea resistivity model can be described by only three parameters. We use this code to identify the challenges we face when higher dimensional model spaces are allowed. The necessary improvements to the code is made and the ﬁnal program developed. The ﬁnal program is then used to study the resolution power of marine CSEM data. The results conﬁrm several resolution properties which have previously been identiﬁed using other approaches. In addition we ﬁnd a probability measure describing the probability that certain resistivity properties are present in the model that produced a given dataset. Throughout these studies both synthetic cases and the Troll West Oil Province are under investigation.