There may not be any “parallel” because we have no priesthood or ecclesiastical hierarchy in the sense of the Catholic church…however we have an order nonetheless.
The Writings of Baha’u’llah, the Bab and the interpretations of Abdul-Baha and Shoghi Effendi are the scripture (the Writings) and authoritative interpretations…
The Universal House of Justice does “speak” for the Baha’i Faith… It is the Center of the Faith today and it defers to the Writings of Baha’u’llah, the Bab and Abdul-Baha along with the interpretations of Shoghi Effendi…
**The provenance, the authority, the duties, the sphere of action of the Universal House of Justice all derive from the revealed Word of Bahá’u’lláh which, together with the interpretations and expositions of the Centre of the Covenant and the Guardian of the Cause - who, after `Abdu’l-Bahá, is the sole authority in the interpretation of Bahá’í Scripture - constitute the binding terms of reference of the Universal House of Justice and are its bedrock foundation. The authority of these Texts is absolute and immutable until such time as Almighty God shall reveal His new Manifestation to Whom will belong all authority and power.
bahai-library.com/uhj_constitution**
The Universal House of Justice has conferred infallibility and anything not specifically mentioned in the Writings concerning the Baha’i community are within it’s purview.
Authority in our institutions today is centered in the House of Justice… The House is elected internationally every five years … It has powers to appoint counselors that have authority over certain areas such as protection and propagation of the Faith carried out by appointed Auxiliary Board Members.
The elective institutions start at the local level as Spiritual Assemblies in each jurisdiction…Unit Conventions then elect delegates that meet in a National Convention and elect a National Spiritual Assembly …Delegates from the National Assemblies meet every five years to elected the House of Justice that administers the Faith from Mount Carmel.