This poem clearly describes the death of somebody that the speaker had a very strong bond with, perhaps a mother or father or family member. The details that the speaker gives about this person's life are very intimate, and it is clear that the speaker knew this person very intimately. The repetition of the phrase "I believe" which begins every line except the last line perhaps points towards the speaker trying to convince him or herself about their suspicions of the person who has died. The way that every line begins with this phrase suggests that the speaker is trying to work out what happened in this person's life, and what was the reason for the tremendous bitterness that blighted this person's existence. Note how it is referred to in the poem:
I believe no trinket, no precious metal, shone so bright as your bitterness.
The bitterness of the person being addressed is compared to the shining of a piece of metal, with the bitterness being much brighter and stronger than the metal. The prhase "I believe" perhaps indicates therefore a conclusion that the speaker has arrived at after long hours of thought and consideration about this person's life. This is the conclusion they have reached and this is what they think happened in that person's life and why they died as they did.