To guess.
Example:
They could conjecture that he had met his end in the Andes at the hands of the guerrillas.
Formed with the prefix con-, conjecture means literally "to throw together" -- that is, to produce a theory by putting together a number of facts. From his calculations, Columbus conjectured that he would reach Asia if he sailed westward. His later conjecture of a Northwest Passage from the Atlantic to the Pacific over the North American continent was eventually proved correct, but only after hundreds of years had passed.