A formal term for an idea or explanation based on incomplete evidence; often used in academic or intellectual contexts. Similar to 仮説 but with a stronger nuance of personal guesswork.
推測 is a general term for 'guess' or 'inference' and can be used as a verb (推測する). 臆説 is a noun and sounds more formal and abstract.
Etymology
Compound of 臆 (conjecture, guess) and 説 (theory, explanation). The exact historical derivation is uncertain, but the word follows a common Sino-Japanese pattern for abstract concepts.