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.