AN SMA FLYING INTO UUU; RI; SWITCHES OVER TO CTAF; ONLY TO HAVE A NEAR MISS WITH ANOTHER SMA THAT DOESN'T ANNOUNCE POS OR INTENTIONS ON THE CTAF FREQ.

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I WAS PIC OF A C172RG ON AN INST FLT PLAN FROM MMU TO UUU. THE ASOS 40 MI OUT WAS 300 FT OVCST AND 2.5 MI VISIBILITY. THE ASOS 20 MI OUT WAS 500 FT OVCST AND 2.5 MI VISIBILITY. I WAS VECTORED FOR THE LOC 22 APCH. THE MINIMUMS FOR THE APCH ARE 760 FT FOR CIRCLING AND 640 FT FOR STRAIGHT-IN. 5 MI FROM THE IAF; I WAS CLRED FOR THE APCH AND I SWITCHED TO THE CTAF. I ANNOUNCED MY POS ON THE LOC 22 APCH OUTSIDE SMARI. I THEN ANNOUNCED MYSELF OVER SMARI (IAF). AFTER I ANNOUNCED MYSELF OVER DAAME; I HEARD A BONANZA (36) ANNOUNCE HIS POS ON A R BASE FOR RWY 16. THIS WAS HIS FIRST ANNOUNCEMENT. I WAS CONFUSED AS I WAS IMC AND KNEW THE ARPT TO BE IMC SO I ESSENTIALLY IGNORED THE CALL. HE ANNOUNCED HE WAS ON FINAL FOR RWY 16 AND AT THAT TIME I SPOTTED RWY 22 AND ANNOUNCED I WAS ON SHORT FINAL. I THEN SAW THE OTHER PLANE ON FINAL FOR RWY 16. HE THEN ANNOUNCED HE WAS GOING AROUND AND I TRIED TO LAND. HE PASSED OVER AND BEHIND ME AS I WAS 20 FT ABOVE THE RWY (RWY 22). THE SEPARATION WAS 100 FT VERT AND 100 FT HORIZ ALTHOUGH IT IS VERY APPROX. I WAS HIGH AND FAST SO I WENT AROUND TWICE MAKING L TFC FOR RWY 22. HE CIRCLED L AND LANDED ON RWY 22. ALL RWYS AT UUU ARE L TFC. VIOLATIONS FOR THE BONANZA PLT: 1) NO INST FLT PLAN WHEN IMC EXISTED AT THE ARPT. 2) MAKING R TFC WHEN L TFC IS USED FOR ALL RWYS AT THE ARPT. 3) NOT ANNOUNCING BEFORE HE WAS AT A R BASE FOR RWY 16.