It's a radome to cover the AN/APS-15 search radar, first fitted to an experimental model designated XPBM-3E then rolled out to production models starting with the PBM-3C (from Squadron/Signal's PBM Mariner in Action).

The most common installation of APS-15, also known as H2X (and "Mickey" due to some early installations resembling Mickey Mouse), was on B-17s, B-24s and B-29s as ground mapping radar for blind bombing; on naval patrol aircraft like the PBM it was used for general search operations, capable of detecting a 5000 ton ship at a range of around 40 miles. See [Radar Bulletin No. 2A: The Tactical Use of Radar in Aircraft] (https://www.ibiblio.org/hyperwar/USN/ref/RADTWOA/RADTWOA-2.html#an/aps-15) for further details, including some example images from the APS-15 scope.

It's a radome - aerodynamic fairing for a radar. The PBM-3C (and presumably the pictured -3D) was fitted with radar on some airframes. Such equipment would vary depending on mission requirements and the operator. For example, the Royal Australian Air Force operated the Mariner without a radome in transport and air-sea rescue duties.