臆测

Carries a negative tone — 臆 ('chest, breast') hints at a guess pulled from one's own gut rather than from evidence. Use 臆测 when criticizing a guess as unfounded; for neutral hypothesizing, prefer 推测 (tuīcè, 'to infer/conjecture'), which assumes some reasoning behind the guess.

memory

Same 臆 appears in 臆想 (yìxiǎng, fanciful imagining) and 臆断 (yìduàn, judgement made on a hunch) — all sharing the 'wishful, evidence-light' flavor.