The _____ theory of perception states that detection of sensory stimuli depends on a variety of factors besides the physical intensity of the stimulus and the sensory abilities of the observer.

According to the Signal Detection Theory, the sensation and perception of any sensory stimulus does not depend only upon the intensity of the stimulus received or the capability of the observer to detect the stimulus.
It depends on other factors as well:

Multiple stimuli is perceived by an observer at the same time but the observer responds to only those stimuli which he thinks to be essential for him. He ignores the remaining stimuli.
When the observer is engaged into some work with complete concentration, his sense organs usually stops responding to any other stimuli, irrespective of whether the stimuli is important or not important to the person (except stimulus indicating emergency).
The observer becomes receptive to a particular stimulus if his immediate response is the urgent need of the situation.
An observer fails to respond to a stimulus when he is physically weak and his body is not permitting him to respond, even though he perceives the stimulus.
An observer gives immediate response to a stimulus when he perceives danger.
The emotional state of mind, psychology and mentality of the observer also influence his decision about whether to respond to a particular stimulus or not.